2007 Vol. 24 No. 7
Abstract：
The vibration transmissibility of the conical shell with composite material honeycomb structure is investigated by modal experiment and vibration table experiment. Theoretical analysis and experimental results show that the experimental structure has a higher modal damping ratio, and can effectively control the vibration transmissibility in a broad bandwidth, which is the characteristic of vibration isolation system with high damping. The application of composite material reduces the weight of the whole system without sacrificing the dependability of structure.
The vibration transmissibility of the conical shell with composite material honeycomb structure is investigated by modal experiment and vibration table experiment. Theoretical analysis and experimental results show that the experimental structure has a higher modal damping ratio, and can effectively control the vibration transmissibility in a broad bandwidth, which is the characteristic of vibration isolation system with high damping. The application of composite material reduces the weight of the whole system without sacrificing the dependability of structure.
2007, 24(7): 6-010.
Abstract：
A virtual node method for coupling the eXtended Finite Element Method (XFEM) with commercial finite element software ABAQUS is presented. The relationship between the subdomain integration and the Heaviside function is formulated, and a subtriangle integration algorithm is improved. The brittle fracture process of a 3-point bending beam was simulated. The computational results demonstrate the capacity of the presented method to simulate the moving discontinuities. Crack path is not necessary to coincide with element boundaries in XFEM and re-meshing can be avoided. The coupling with commercial finite element software proposes an efficient way for solving practical complex problem using XFEM.
A virtual node method for coupling the eXtended Finite Element Method (XFEM) with commercial finite element software ABAQUS is presented. The relationship between the subdomain integration and the Heaviside function is formulated, and a subtriangle integration algorithm is improved. The brittle fracture process of a 3-point bending beam was simulated. The computational results demonstrate the capacity of the presented method to simulate the moving discontinuities. Crack path is not necessary to coincide with element boundaries in XFEM and re-meshing can be avoided. The coupling with commercial finite element software proposes an efficient way for solving practical complex problem using XFEM.
Abstract：
To improve some deficiency of calculation of reliability index in response surface method (RSM), point estimation of probability moment deduced by Resonbluth was introduced into response surface method. Improved response surface method (IRSM) can take into account the departure degree for probability density curve of basic random variables when sampling. Calculation formula for the sample values of random variables was changed and the reliability degree index was calculated through probability moment in improved RSM. Some special points of real limit state curve surface was adopted when calculating reliability degree index in the IRSM. There are no need for linearization and fitting of approximate limit state function while calculating reliability degree index. Iterative and cumulate error of reliability degree index does not arise. Principle and calculation process of IRSM is much simpler than RSM. Stability reliability degree for surrounding rock of a large underground engineering was analyzed by ISRM and RSM and Monte-Carlo method respectively. Result calculated by Monte-Carlo was taken as a standard solution to show the accuracy of solution of IRSM. Comparison between the solutions of IRSM and RSM shows that result calculated by IRSM is more accurate than that of RSM. Accuracy of IRSM can meet engineering requirement. IRSM has both theoretical and practical value.
To improve some deficiency of calculation of reliability index in response surface method (RSM), point estimation of probability moment deduced by Resonbluth was introduced into response surface method. Improved response surface method (IRSM) can take into account the departure degree for probability density curve of basic random variables when sampling. Calculation formula for the sample values of random variables was changed and the reliability degree index was calculated through probability moment in improved RSM. Some special points of real limit state curve surface was adopted when calculating reliability degree index in the IRSM. There are no need for linearization and fitting of approximate limit state function while calculating reliability degree index. Iterative and cumulate error of reliability degree index does not arise. Principle and calculation process of IRSM is much simpler than RSM. Stability reliability degree for surrounding rock of a large underground engineering was analyzed by ISRM and RSM and Monte-Carlo method respectively. Result calculated by Monte-Carlo was taken as a standard solution to show the accuracy of solution of IRSM. Comparison between the solutions of IRSM and RSM shows that result calculated by IRSM is more accurate than that of RSM. Accuracy of IRSM can meet engineering requirement. IRSM has both theoretical and practical value.
2007, 24(7): 16-022.
Abstract：
A 1D finite element method in time domain is developed, which is used to calculate the in-plane wave motion of free field in elastic layered semispace by oblique seismic incidence. First, the layered semispace is discretized virtually according to the propagation characteristic of elastic wave. Then, the finite element method with lumped mass and the central difference method are combined together to establish the 2D wave motion equations. On the basis of the discretization principle and by the advantage of the explicit finite element method, the 2D wave motion equations can be transformed into 1D equations. By solving the 1D equations, the displacement of nodes in one vertical line can be obtained. Finally, the wave motions of the whole free field are determined on the basis of the characteristic of traveling wave. As an example, P-wave is assumed as the incident wave. Theoretical analysis and numerical results demonstrate that the proposed method possesses high accuracy and good stability.
A 1D finite element method in time domain is developed, which is used to calculate the in-plane wave motion of free field in elastic layered semispace by oblique seismic incidence. First, the layered semispace is discretized virtually according to the propagation characteristic of elastic wave. Then, the finite element method with lumped mass and the central difference method are combined together to establish the 2D wave motion equations. On the basis of the discretization principle and by the advantage of the explicit finite element method, the 2D wave motion equations can be transformed into 1D equations. By solving the 1D equations, the displacement of nodes in one vertical line can be obtained. Finally, the wave motions of the whole free field are determined on the basis of the characteristic of traveling wave. As an example, P-wave is assumed as the incident wave. Theoretical analysis and numerical results demonstrate that the proposed method possesses high accuracy and good stability.
2007, 24(7): 23-027.
Abstract：
The following points are proved in this paper: (1) Non-probabilistic reliability index of an arbitrary structure merely exists at one of the crossing points at which standard failure surface of the structure intersects the straight lines passing through both origin of a standard infinite space and vertices of holohedric convex polyhedron centered at the origin, and (2) The non-probabilistic reliability index equals to the absolute value of the coordinate of one of the crossing points. Based on the reduction of feasible region from the standard infinite space to finite crossing points within the standard infinite space, a one-dimensional optimization algorithm for non-probabilistic reliability index is developed to replace the interval algorithm and multi-variable optimization approach. The algorithm is reliable and efficient in arithmetic operations.
The following points are proved in this paper: (1) Non-probabilistic reliability index of an arbitrary structure merely exists at one of the crossing points at which standard failure surface of the structure intersects the straight lines passing through both origin of a standard infinite space and vertices of holohedric convex polyhedron centered at the origin, and (2) The non-probabilistic reliability index equals to the absolute value of the coordinate of one of the crossing points. Based on the reduction of feasible region from the standard infinite space to finite crossing points within the standard infinite space, a one-dimensional optimization algorithm for non-probabilistic reliability index is developed to replace the interval algorithm and multi-variable optimization approach. The algorithm is reliable and efficient in arithmetic operations.
Abstract：
Incremental FEM is developed for incompressible and nearly incompressible viscoelastic problems and the three-dimensional analysis of SRM grain is presented. Firstly the constitutive relation of incompressible and nearly incompressible viscoelastic material is derived based on the Herrmann functional and correspondence principle. Afterwards three-dimensional finite element formulations are obtained using the principle of virtual work. Finally incompressible and nearly incompressible analysis of a hollow cylindrical grain with elastic restraint is presented. The results illustrate that the proposed method is valid for viscoelastic problems whose Poisson’s ratio is close or equal to 0.5, especially suitable for the structural analysis of solid propellant grain.
Incremental FEM is developed for incompressible and nearly incompressible viscoelastic problems and the three-dimensional analysis of SRM grain is presented. Firstly the constitutive relation of incompressible and nearly incompressible viscoelastic material is derived based on the Herrmann functional and correspondence principle. Afterwards three-dimensional finite element formulations are obtained using the principle of virtual work. Finally incompressible and nearly incompressible analysis of a hollow cylindrical grain with elastic restraint is presented. The results illustrate that the proposed method is valid for viscoelastic problems whose Poisson’s ratio is close or equal to 0.5, especially suitable for the structural analysis of solid propellant grain.
2007, 24(7): 33-038.
Abstract：
A three-degree-of-freedom vibro-impact system is considered in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six-dimensional Poincaré maps of periodic motion are established. The two-parameter unfoldings of local dynamical behavior in resonance are investigated. By numerical simulation, as two controlling parameters varying on the two-parameter plane, the topology regions of parameter plane are divided. An invariant torus via Hopf bifurcation and period motions via subharmonic bifurcation are analyzed, which are characterized by “four-square” and “four-leaf ” different lodge orbits and exist near the critical point, and the route from order 4 subharmonic bifurcation to chaos is further analyzed.
A three-degree-of-freedom vibro-impact system is considered in this paper. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six-dimensional Poincaré maps of periodic motion are established. The two-parameter unfoldings of local dynamical behavior in resonance are investigated. By numerical simulation, as two controlling parameters varying on the two-parameter plane, the topology regions of parameter plane are divided. An invariant torus via Hopf bifurcation and period motions via subharmonic bifurcation are analyzed, which are characterized by “four-square” and “four-leaf ” different lodge orbits and exist near the critical point, and the route from order 4 subharmonic bifurcation to chaos is further analyzed.
2007, 24(7): 39-043.
Abstract：
A new two-node beam element considering the second-order effect of beams is developed. Based on the interpolation theory, the displacement fields of the three-node Euler-Bernoulli beam element are constructed at first: the quintic Hermite interpolation polynomial is used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then the linear and geometric stiffness matrices of the three-node beam element are derived according to the nonlinear finite element theory. Finally the degrees of freedom of the middle node of the element are eliminated using the static condensation method, and a new two-node beam element including axial-force effect is obtained. The results of several examples show that the second-order displacements and internal forces with high precision can be obtained with this new beam element.
A new two-node beam element considering the second-order effect of beams is developed. Based on the interpolation theory, the displacement fields of the three-node Euler-Bernoulli beam element are constructed at first: the quintic Hermite interpolation polynomial is used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then the linear and geometric stiffness matrices of the three-node beam element are derived according to the nonlinear finite element theory. Finally the degrees of freedom of the middle node of the element are eliminated using the static condensation method, and a new two-node beam element including axial-force effect is obtained. The results of several examples show that the second-order displacements and internal forces with high precision can be obtained with this new beam element.
Abstract：
Two harmonically excited systems with symmetrical rigid constraints are considered. Repeated impacts usually occur in such systems due to the rigid constraints. The impact formats that occur in two systems are different, i.e., the components of one system collide with each other, and one of components of the other system collides with rigid obstacles. Dynamics of these systems are studied with special attention to pitchfork and Neimark-Sacker bifurcations associated with several periodic-impact motions. Two important parameters, the clearance and the excitation frequency, are considered, and the influence of these parameters on the symmetrical double-impact periodic motion and bifurcations is analyzed with emphases. With a decrease in the excitation frequency, symmetrical double-impact periodic motion usually undergoes Neimark-Sacker bifurcation for large values of clearances and pitchfork bifurcation for small values of clearances. Neimark-Sacker bifurcations, associated with symmetrical double-impact periodic motion, asymmetrical double-impact periodic motion, single-period four-impact symmetrical motion, double-period four-impact motion and double-period six-impact motion, etc., are analyzed in detail. The studies show that the vibratory systems with symmetrical rigid amplitude constraints may exhibit complex and rich quasi-periodic impact motions associated with several periodic-impact ones.
Two harmonically excited systems with symmetrical rigid constraints are considered. Repeated impacts usually occur in such systems due to the rigid constraints. The impact formats that occur in two systems are different, i.e., the components of one system collide with each other, and one of components of the other system collides with rigid obstacles. Dynamics of these systems are studied with special attention to pitchfork and Neimark-Sacker bifurcations associated with several periodic-impact motions. Two important parameters, the clearance and the excitation frequency, are considered, and the influence of these parameters on the symmetrical double-impact periodic motion and bifurcations is analyzed with emphases. With a decrease in the excitation frequency, symmetrical double-impact periodic motion usually undergoes Neimark-Sacker bifurcation for large values of clearances and pitchfork bifurcation for small values of clearances. Neimark-Sacker bifurcations, associated with symmetrical double-impact periodic motion, asymmetrical double-impact periodic motion, single-period four-impact symmetrical motion, double-period four-impact motion and double-period six-impact motion, etc., are analyzed in detail. The studies show that the vibratory systems with symmetrical rigid amplitude constraints may exhibit complex and rich quasi-periodic impact motions associated with several periodic-impact ones.
2007, 24(7): 53-058.
Abstract：
Simplifying the floatation ring which is one of very important components of the deep-water anti-storm wave cages into a flexible ring, we obtain the nonlinear governing equations of the out-of-plane motion and deformation of a circular ring based on the fluid-structure interaction theory. The mode superposition approach is utilized to solve the equations, and the motion and deformation of the ring are numerically computed under the actual action of water waves. The computational results have shown that the deformation of the ring can not be neglected in the first three modes, and that the effect of the fluid-structure interaction is significant.
Simplifying the floatation ring which is one of very important components of the deep-water anti-storm wave cages into a flexible ring, we obtain the nonlinear governing equations of the out-of-plane motion and deformation of a circular ring based on the fluid-structure interaction theory. The mode superposition approach is utilized to solve the equations, and the motion and deformation of the ring are numerically computed under the actual action of water waves. The computational results have shown that the deformation of the ring can not be neglected in the first three modes, and that the effect of the fluid-structure interaction is significant.
Abstract：
It is one of the important requisites in the engine mounting system design to accurately determine the inertia properties of a powertrain rigid body. Observing that trifilar torsional pendulum can precisely measure mass moment of inertia of complex rigid body, an experimental methodology for inertia parameter identification is proposed, in which the rigid body is positioned at 6~9 different orientations represented with three-points on the rigid body. The key points include: (1) the orientation of the rigid body is indirectly determined with three points on the rigid body, and a movable coordinate system is defined with the normal vector of plane formed by the three on-body points; (2) distances between the three on-body points and reference points on the pendulum plate (defining a global coordinate system) are measured for each test, and global coordinates of the three on-body points and the coordinate transformation between the two coordinate frames are determined；(3) the rotation axis orientation of the rigid body and the moment of inertia for each test under the movable coordinates are calculated; and (4) utilizing least square principle, the optimal intersection “point” of the rotation axis of each test is determined to be the center of gravity, and then a set of linear equations derived from the transformation formula of rigid-body moment of inertia about different axis rotation is solved to identify inertia tensor of the rigid body. Some factors that may produce errors still exist in the proposed identification procedure, but they can be estimated and effectively reduced at every step with least square method. The practicability and reliability of the procedure is illustrated by error analysis, validation of cuboid mass block and many tests of real powertrains.
It is one of the important requisites in the engine mounting system design to accurately determine the inertia properties of a powertrain rigid body. Observing that trifilar torsional pendulum can precisely measure mass moment of inertia of complex rigid body, an experimental methodology for inertia parameter identification is proposed, in which the rigid body is positioned at 6~9 different orientations represented with three-points on the rigid body. The key points include: (1) the orientation of the rigid body is indirectly determined with three points on the rigid body, and a movable coordinate system is defined with the normal vector of plane formed by the three on-body points; (2) distances between the three on-body points and reference points on the pendulum plate (defining a global coordinate system) are measured for each test, and global coordinates of the three on-body points and the coordinate transformation between the two coordinate frames are determined；(3) the rotation axis orientation of the rigid body and the moment of inertia for each test under the movable coordinates are calculated; and (4) utilizing least square principle, the optimal intersection “point” of the rotation axis of each test is determined to be the center of gravity, and then a set of linear equations derived from the transformation formula of rigid-body moment of inertia about different axis rotation is solved to identify inertia tensor of the rigid body. Some factors that may produce errors still exist in the proposed identification procedure, but they can be estimated and effectively reduced at every step with least square method. The practicability and reliability of the procedure is illustrated by error analysis, validation of cuboid mass block and many tests of real powertrains.
2007, 24(7): 66-071.
Abstract：
For the springback problem of sheet metal stretch-bending, a mathematical model was proposed based on Hill’s yielding criterion, exponential hardening and plane strain assumption. The model was validated by a stretch-bending example. The effects of stretching force per unit width, die profile radius, friction and anisotropy on the springback were studied. The results from the proposed model indicate that only if the shift distance of neutral surface exceeds one-fourth of sheet thickness, the increase of stretching force can control the springback effectively. Furthermore, the larger the bending radius, the more effective the increase of binder force in controling the sheet springback. However, the stretching force cannot increase without limit. Its calculation criterion is that the effective strain at the outer sheet layer is not greater than the material limit strain. It also shows that with the increase of stretching force, the friction has much larger influence on the sheet springback. Besides, the anisotropy also has effect on the sheet springback of stretch-bending. Comparison with FE simulation results shows that the predicted results by the mathematical model consist well with those by FEM.
For the springback problem of sheet metal stretch-bending, a mathematical model was proposed based on Hill’s yielding criterion, exponential hardening and plane strain assumption. The model was validated by a stretch-bending example. The effects of stretching force per unit width, die profile radius, friction and anisotropy on the springback were studied. The results from the proposed model indicate that only if the shift distance of neutral surface exceeds one-fourth of sheet thickness, the increase of stretching force can control the springback effectively. Furthermore, the larger the bending radius, the more effective the increase of binder force in controling the sheet springback. However, the stretching force cannot increase without limit. Its calculation criterion is that the effective strain at the outer sheet layer is not greater than the material limit strain. It also shows that with the increase of stretching force, the friction has much larger influence on the sheet springback. Besides, the anisotropy also has effect on the sheet springback of stretch-bending. Comparison with FE simulation results shows that the predicted results by the mathematical model consist well with those by FEM.
2007, 24(7): 72-076.
Abstract：
Under pitching excitation, the Lagrange equation for nonlinear sloshing of liquid in circle cylindrical tank by variational principle in the form of volume integration of pressure is developed. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematical and dynamic free surface boundary conditions are derived. At last, these equations are solved by the fourth order Runge-Kutta method. Through numerical simulation, synchronous Hopf bifurcation of the primary and the secondary nonplanar sloshing modes is observed, and the region of frequency is given.
Under pitching excitation, the Lagrange equation for nonlinear sloshing of liquid in circle cylindrical tank by variational principle in the form of volume integration of pressure is developed. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematical and dynamic free surface boundary conditions are derived. At last, these equations are solved by the fourth order Runge-Kutta method. Through numerical simulation, synchronous Hopf bifurcation of the primary and the secondary nonplanar sloshing modes is observed, and the region of frequency is given.
Abstract：
Based on Computational Fluid Dynamics (CFD), the numerical wind tunnel technique (NWTT) is studied, which is effectively applied to the investigation of the wind pressure distribution of complicated structural shapes. The wind fields around and close to structural surface and the wind-load shape coefficients were calculated. Some comparisons between numerical results and wind tunnel model test data were carried out. The changes of the wind-load shape coefficients and wind fields around the structures caused by other structural system were analyzed, and the possible errors and their reasons of the wind tunnel model test were discussed by means of the NWTT. Based on the wind pressure contours or constant value line of wind-load shape coefficients, the sub-areas subjected to different wind actions were plotted and the local wind-load shape coefficients corresponding to these sub-areas were obtained in terms of area weighted average strategy. Additionally, the wind-load shape coefficients under different wind angles were analyzed.
Based on Computational Fluid Dynamics (CFD), the numerical wind tunnel technique (NWTT) is studied, which is effectively applied to the investigation of the wind pressure distribution of complicated structural shapes. The wind fields around and close to structural surface and the wind-load shape coefficients were calculated. Some comparisons between numerical results and wind tunnel model test data were carried out. The changes of the wind-load shape coefficients and wind fields around the structures caused by other structural system were analyzed, and the possible errors and their reasons of the wind tunnel model test were discussed by means of the NWTT. Based on the wind pressure contours or constant value line of wind-load shape coefficients, the sub-areas subjected to different wind actions were plotted and the local wind-load shape coefficients corresponding to these sub-areas were obtained in terms of area weighted average strategy. Additionally, the wind-load shape coefficients under different wind angles were analyzed.
Abstract：
Based on the results of other researchers on the corrosion rate of tensile reinforcement steel, moment resistance deterioration models of reinforced concrete girder bridges due to steel corrosion induced by chloride attack or concrete carbonation are developed with pitting corrosion being considered for chloride attack and average corrosion being considered for concrete carbonation. A computer program for time- dependent reliability assessment of highway concrete bridges based on Monte Carlo method and statistic regression is also developed. A concrete girder bridge in Beijing area is taken as an example. The results show that the ultimate limit state reliability of the bridge due to chloride attack reduces to the design target reliability at the 30th year or so and the reliability due to concrete carbonation to the value at the 50th year or so. Therefore, the bridge can not work through the presumed working life of 100 years without major repair. The results also show that cracking time of concrete cover induced by corrosion of tensile reinforcement is much earlier than the time when the ultimate limit state reliability reduces to the target value. This is important for bridge inspection/repair schedule.
Based on the results of other researchers on the corrosion rate of tensile reinforcement steel, moment resistance deterioration models of reinforced concrete girder bridges due to steel corrosion induced by chloride attack or concrete carbonation are developed with pitting corrosion being considered for chloride attack and average corrosion being considered for concrete carbonation. A computer program for time- dependent reliability assessment of highway concrete bridges based on Monte Carlo method and statistic regression is also developed. A concrete girder bridge in Beijing area is taken as an example. The results show that the ultimate limit state reliability of the bridge due to chloride attack reduces to the design target reliability at the 30th year or so and the reliability due to concrete carbonation to the value at the 50th year or so. Therefore, the bridge can not work through the presumed working life of 100 years without major repair. The results also show that cracking time of concrete cover induced by corrosion of tensile reinforcement is much earlier than the time when the ultimate limit state reliability reduces to the target value. This is important for bridge inspection/repair schedule.
2007, 24(7): 94-098,.
Abstract：
The key problem for displacement method in creep and shrinkage effect analysis of statically indeterminate structures is to determinate inelastic fixed-end forces caused by creep and shrinkage of the element. Based on the concepts of force method and virtual-work principle, calculation formulae of the inelastic fixed-end forces in structure elements are deduced. The methods for considering the effects of construction process, creep and shrinkage in the analysis of high-rise frame structures are then introduced. The corresponding computational procedure was programmed using FORTRAN language. Creep and shrinkage analysis of a frame structure was conducted by using this program. The results show that creep, shrinkage and construction process have great effects on the mechanical and deformational performances of high-rise frame structures. These effects should be taken into accounts in the design of high-rise frame structures.
The key problem for displacement method in creep and shrinkage effect analysis of statically indeterminate structures is to determinate inelastic fixed-end forces caused by creep and shrinkage of the element. Based on the concepts of force method and virtual-work principle, calculation formulae of the inelastic fixed-end forces in structure elements are deduced. The methods for considering the effects of construction process, creep and shrinkage in the analysis of high-rise frame structures are then introduced. The corresponding computational procedure was programmed using FORTRAN language. Creep and shrinkage analysis of a frame structure was conducted by using this program. The results show that creep, shrinkage and construction process have great effects on the mechanical and deformational performances of high-rise frame structures. These effects should be taken into accounts in the design of high-rise frame structures.
2007, 24(7): 99-103,.
Abstract：
The multi-scale damage analysis method for steel box girder is presented with respect to Runyang Cable-stayed Bridge. The full-scale dynamic responses and fine-scale local damage of steel box girder are connected by the substructure method to realize structural multi-scale damage analysis. The modal curvature index, modal strain energy index, modal flexibility index and cable tension index for damage localization of steel box girder are further comparatively investigated. The analysis results show that (i) in the absence of noise, all damage indices can properly identify structural damage cases of steel box girder except the damage case of ventral plate using the modal flexibility index; (ii) for most damage cases, flexibility index is the best of the four indices in anti-noise and the cable tension index is the worst; (iii) modal strain energy index and modal flexibility index are complementary to each other in damage location identification for steel box girder.
The multi-scale damage analysis method for steel box girder is presented with respect to Runyang Cable-stayed Bridge. The full-scale dynamic responses and fine-scale local damage of steel box girder are connected by the substructure method to realize structural multi-scale damage analysis. The modal curvature index, modal strain energy index, modal flexibility index and cable tension index for damage localization of steel box girder are further comparatively investigated. The analysis results show that (i) in the absence of noise, all damage indices can properly identify structural damage cases of steel box girder except the damage case of ventral plate using the modal flexibility index; (ii) for most damage cases, flexibility index is the best of the four indices in anti-noise and the cable tension index is the worst; (iii) modal strain energy index and modal flexibility index are complementary to each other in damage location identification for steel box girder.
2007, 24(7): 104-109,.
Abstract：
The equivalent static wind loads (ESWL) provide an effective approach to deal with the spatiotemporally varying wind loads for structures with long span roofs. Two schemes for calculating the ESWL have been proposed in this paper. In the first scheme ESWL are formulated in terms of a weighted combination of modal ESWL components. In the second scheme ESWL are expressed in a separated form as the resonant component of modal ESWL and the background component in which the proper orthogonal decomposition (POD) technique can be introduced to simplify the computation of load-response-correlation. The modal coupling effects are considered with the weighting factor in both schemes. Wind tunnel tests of a single-layer latticed cylinder were carried out with the synchronous multi-pressure scanning technique. With the wind-induced responses of the cylinder calculated using approaches of the Complete Quadratic Combination (CQC) and the Square Root Sum of Square (SRSS), it is found that the modal coupling effects may be neglected in this case, and the responses can be obtained with only a few modes. The obtained responses by ESWL are checked by CQC. By comparing the two schemes for calculating ESWL, it can be concluded that the first scheme is an effective and practical method for analysis of the equivalent static wind loads, and the second scheme is useful to investigate background and resonant static loads component respectively.
The equivalent static wind loads (ESWL) provide an effective approach to deal with the spatiotemporally varying wind loads for structures with long span roofs. Two schemes for calculating the ESWL have been proposed in this paper. In the first scheme ESWL are formulated in terms of a weighted combination of modal ESWL components. In the second scheme ESWL are expressed in a separated form as the resonant component of modal ESWL and the background component in which the proper orthogonal decomposition (POD) technique can be introduced to simplify the computation of load-response-correlation. The modal coupling effects are considered with the weighting factor in both schemes. Wind tunnel tests of a single-layer latticed cylinder were carried out with the synchronous multi-pressure scanning technique. With the wind-induced responses of the cylinder calculated using approaches of the Complete Quadratic Combination (CQC) and the Square Root Sum of Square (SRSS), it is found that the modal coupling effects may be neglected in this case, and the responses can be obtained with only a few modes. The obtained responses by ESWL are checked by CQC. By comparing the two schemes for calculating ESWL, it can be concluded that the first scheme is an effective and practical method for analysis of the equivalent static wind loads, and the second scheme is useful to investigate background and resonant static loads component respectively.
Abstract：
The calculation method for the influence quantity is discussed for single-layer multi-span frames under moving load, which are wildly used in bridges, industrial and public buildings. Based on the concept of moment distribution method for continuous beam, the concept of anti-rotation stiffness of bar end and the transfer of node rotational angle is established, and the corresponding calculation formula is proposed. An exact calculation method is put forward to determine the influence quantity of single-layer multi-span frames under moving load. Examples show that the proposed method is simple and feasible.
The calculation method for the influence quantity is discussed for single-layer multi-span frames under moving load, which are wildly used in bridges, industrial and public buildings. Based on the concept of moment distribution method for continuous beam, the concept of anti-rotation stiffness of bar end and the transfer of node rotational angle is established, and the corresponding calculation formula is proposed. An exact calculation method is put forward to determine the influence quantity of single-layer multi-span frames under moving load. Examples show that the proposed method is simple and feasible.
2007, 24(7): 116-121.
Abstract：
The provisions in Technical Specification for Concrete Structures of Tall Building on torsional irregularity are problematic and the specified measures for torsional vibration control need to be revisited. The ratio of torsion-controlled first period to translation-controlled first period (i.e. the coupled period ratio), combined with the drift ratio, is incorporated in the specification to exclude tall structures with severe torsional irregularity, and its limits should be satisfied in seismic design. By changing the magnitudes of the parameters (i.e. eccentricity, torsional stiffness, and lateral stiffness), the analysis of the difference between the coupled period ratio and uncoupled period ratio shows that the provisions cannot guarantee torsional vibration control in certain situations. In this respect, the coupled-period-ratio index is not well-founded and the ratio of lateral energy to torsional energy is proposed as an alternative.
The provisions in Technical Specification for Concrete Structures of Tall Building on torsional irregularity are problematic and the specified measures for torsional vibration control need to be revisited. The ratio of torsion-controlled first period to translation-controlled first period (i.e. the coupled period ratio), combined with the drift ratio, is incorporated in the specification to exclude tall structures with severe torsional irregularity, and its limits should be satisfied in seismic design. By changing the magnitudes of the parameters (i.e. eccentricity, torsional stiffness, and lateral stiffness), the analysis of the difference between the coupled period ratio and uncoupled period ratio shows that the provisions cannot guarantee torsional vibration control in certain situations. In this respect, the coupled-period-ratio index is not well-founded and the ratio of lateral energy to torsional energy is proposed as an alternative.
2007, 24(7): 122-127.
Abstract：
The nonlinear coupled vibration model of cables and bridge decks is established. The decks are simplified as continuous beams with uniform cross section. The sag of cable, aerodynamics and geometric non-linearity caused by large displacement are considered. The numerical results of different cables are obtained. Serious internal resonance with beat rhythm can occur when the ratio of cable frequency and deck frequency is close to 1:1 and 2:1. The results show that the vibration characteristic of the coupled system is related with the sag of cable, vibration frequency, wind velocity, yaw angle of wind velocity, inclined angle and damping. It can provide theoretical basis for bridge design and calculation.
The nonlinear coupled vibration model of cables and bridge decks is established. The decks are simplified as continuous beams with uniform cross section. The sag of cable, aerodynamics and geometric non-linearity caused by large displacement are considered. The numerical results of different cables are obtained. Serious internal resonance with beat rhythm can occur when the ratio of cable frequency and deck frequency is close to 1:1 and 2:1. The results show that the vibration characteristic of the coupled system is related with the sag of cable, vibration frequency, wind velocity, yaw angle of wind velocity, inclined angle and damping. It can provide theoretical basis for bridge design and calculation.
2007, 24(7): 128-133,.
Abstract：
Using the method of the nonlinear finite element and numerical integration, the short steel reinforced concrete (SRC) columns reinforced by inner circular steel tubes are analyzed and calculated. With the program, the whole curve of ultimate bearing capacity in axial force is simulated. Effects of the ratios of longitudinal steel bars, different stirrup characteristic values, concrete grades from C40~C70, and ratio of inner steel tubes are discussed. The outlook of applied range of these parameters is also given. Results show that these ranges are reasonable and efficient, which can be used in engineering directly. A simplified formula to estimate the appropriate thickness of inner steel tube is put forward for optimizing the column. Application of this column in two actual engineering indicates the correction of this formula.
Using the method of the nonlinear finite element and numerical integration, the short steel reinforced concrete (SRC) columns reinforced by inner circular steel tubes are analyzed and calculated. With the program, the whole curve of ultimate bearing capacity in axial force is simulated. Effects of the ratios of longitudinal steel bars, different stirrup characteristic values, concrete grades from C40~C70, and ratio of inner steel tubes are discussed. The outlook of applied range of these parameters is also given. Results show that these ranges are reasonable and efficient, which can be used in engineering directly. A simplified formula to estimate the appropriate thickness of inner steel tube is put forward for optimizing the column. Application of this column in two actual engineering indicates the correction of this formula.
Abstract：
The purpose of this paper is to investigate an analysis model to evaluate the ultimate strength of RC shear wall with edge-frame columns or concealed columns based on the shear resistant mechanism and failure modes. According to its mechanical behavior, failure process and modes, shear resistant mechanism of RC shear wall can be simplified as a composition of concrete inclined strut with an inclination of θ，horizontal and longitudinal bars. The calculating equations for ultimate strength are provided from shear resistant mechanism, and a program is developed to evaluate the strengths of RC shear walls. Simultaneously, the ultimate strengths of 14 RC shear walls are analyzed with this program. The analysis results agree well with those of test. It can be concluded that the analysis model verified in this paper can evaluate the ultimate strengths of RC shear walls, and the model can be used to check the ultimate strength of RC shear wall subjected to different loads.
The purpose of this paper is to investigate an analysis model to evaluate the ultimate strength of RC shear wall with edge-frame columns or concealed columns based on the shear resistant mechanism and failure modes. According to its mechanical behavior, failure process and modes, shear resistant mechanism of RC shear wall can be simplified as a composition of concrete inclined strut with an inclination of θ，horizontal and longitudinal bars. The calculating equations for ultimate strength are provided from shear resistant mechanism, and a program is developed to evaluate the strengths of RC shear walls. Simultaneously, the ultimate strengths of 14 RC shear walls are analyzed with this program. The analysis results agree well with those of test. It can be concluded that the analysis model verified in this paper can evaluate the ultimate strengths of RC shear walls, and the model can be used to check the ultimate strength of RC shear wall subjected to different loads.
2007, 24(7): 140-145.
Abstract：
A new type electricrheological (ER) smart isolator is developed with ER smart damper and rubber isolator. The new type ER smart isolator is firstly designed. Controlled force formulas of rotation ER damper are proposed. The functions between electric field intensity and shear transform of ER damper are presented. Two kinds of hysteretic models are proposed as pseudo-displacement limited model and pseudo-friction model. Based on the controlled characteristic of ER smart isolator, friction control rule and formulas are then put forward and coded into a program for application. Finally, a SDOF structure with ER smart isolator is analysed. The results show that: two kinds of ER isolators are both efficiency for displacement decrease in the isolation layer, and the acceleration does not increase at the same time.
A new type electricrheological (ER) smart isolator is developed with ER smart damper and rubber isolator. The new type ER smart isolator is firstly designed. Controlled force formulas of rotation ER damper are proposed. The functions between electric field intensity and shear transform of ER damper are presented. Two kinds of hysteretic models are proposed as pseudo-displacement limited model and pseudo-friction model. Based on the controlled characteristic of ER smart isolator, friction control rule and formulas are then put forward and coded into a program for application. Finally, a SDOF structure with ER smart isolator is analysed. The results show that: two kinds of ER isolators are both efficiency for displacement decrease in the isolation layer, and the acceleration does not increase at the same time.
Abstract：
To perform a wind-induced response analysis for large span electricity transmission tower-line systems in time domain, considering various influences such as tower-line distribution, variation of mean velocity profile, power spectral energy and cross-spectral coherence in relation with structural style and power spectral characteristics of stochastic fluctuating wind field, a simplified scheme which can transform a multivariable 3D fluctuating wind field ( ) acting on large span transmission tower-line systems into a multivariable 1D stochastic wind field ( ) has been presented. Based on harmonic wave superimposing method and appropriate modified spectral decomposition, time marching generating method of fluctuating wind has been developed, which is suitable to analyze the wind-induced response of transmission tower-line system in combination with the finite element method. Finally, taking a real case as example, the time-marching curves were simulated. The results from statistical analysis of simulated data and comparison with target spectrum demonstrated the validity of the presented method and the applicability of simulated wind time-marching for wind-induced response analysis.
To perform a wind-induced response analysis for large span electricity transmission tower-line systems in time domain, considering various influences such as tower-line distribution, variation of mean velocity profile, power spectral energy and cross-spectral coherence in relation with structural style and power spectral characteristics of stochastic fluctuating wind field, a simplified scheme which can transform a multivariable 3D fluctuating wind field ( ) acting on large span transmission tower-line systems into a multivariable 1D stochastic wind field ( ) has been presented. Based on harmonic wave superimposing method and appropriate modified spectral decomposition, time marching generating method of fluctuating wind has been developed, which is suitable to analyze the wind-induced response of transmission tower-line system in combination with the finite element method. Finally, taking a real case as example, the time-marching curves were simulated. The results from statistical analysis of simulated data and comparison with target spectrum demonstrated the validity of the presented method and the applicability of simulated wind time-marching for wind-induced response analysis.
2007, 24(7): 152-155.
Abstract：
By Complex Mapping theory, doing mutual numerical calculation to finite odd and even interpolation points on the non-circle cross-section profile of special-shaped products, the conformal mapping function which can mutually transform cross-section region into unit dish region is set up. Translating the extrusion forming of special-shaped products into two-dimension problem, plastic stream function is determined, and the mathematical models of die cavity surface with various vertical curves are built up. Using the upper bound method, three types of vertical curves and their optimized parameters of die cavity are compared. Taking ellipse-shaped products as examples, their analysis and optimization are carried out.
By Complex Mapping theory, doing mutual numerical calculation to finite odd and even interpolation points on the non-circle cross-section profile of special-shaped products, the conformal mapping function which can mutually transform cross-section region into unit dish region is set up. Translating the extrusion forming of special-shaped products into two-dimension problem, plastic stream function is determined, and the mathematical models of die cavity surface with various vertical curves are built up. Using the upper bound method, three types of vertical curves and their optimized parameters of die cavity are compared. Taking ellipse-shaped products as examples, their analysis and optimization are carried out.
2007, 24(7): 156-160.
Abstract：
A review is made for HJC concrete model which includes strain rate effects and material damage. Sensitivity of damage parameters in HJC model are discussed through a collision of a rigid ball with a concrete plate, and the parameters used in HJC concrete model are determined. A scenario of a 12000 DWT bulk cargo collision with a bridge pier is simulated by the software of LS-DYNA, and the time history of ship collision force and the damage of the bridge pier are presented. The results show that the peak value of ship collision force decreases remarkably due to the failure of concrete. Damage characteristic of concrete should be taken into account to achieve objective result in the simulation of ship collision with thin-wall bridge pier.
A review is made for HJC concrete model which includes strain rate effects and material damage. Sensitivity of damage parameters in HJC model are discussed through a collision of a rigid ball with a concrete plate, and the parameters used in HJC concrete model are determined. A scenario of a 12000 DWT bulk cargo collision with a bridge pier is simulated by the software of LS-DYNA, and the time history of ship collision force and the damage of the bridge pier are presented. The results show that the peak value of ship collision force decreases remarkably due to the failure of concrete. Damage characteristic of concrete should be taken into account to achieve objective result in the simulation of ship collision with thin-wall bridge pier.
2007, 24(7): 161-166,.
Abstract：
The stress concentration factor distribution along the weld toe for tubular X-joints subjected to axial loads have been analyzed using finite element method. Through numerical analysis, it has been found that the peak stress concentration factor for the analyzed model is located at the saddle position. The effect of the geometric parameters of a tubular X-joint on the stress concentration factor has been investigated. Based on the numerical results, a parametric equation used to calculate the stress concentration factor of tubular X-joints has been proposed. The accuracy of this equation has been verified against the requirement of the Fatigue Guidance Review Panel, and it has been found that the proposed equation can produce reasonably accurate stress concentration factor values for tubular X-joints subjected to axial loads.
The stress concentration factor distribution along the weld toe for tubular X-joints subjected to axial loads have been analyzed using finite element method. Through numerical analysis, it has been found that the peak stress concentration factor for the analyzed model is located at the saddle position. The effect of the geometric parameters of a tubular X-joint on the stress concentration factor has been investigated. Based on the numerical results, a parametric equation used to calculate the stress concentration factor of tubular X-joints has been proposed. The accuracy of this equation has been verified against the requirement of the Fatigue Guidance Review Panel, and it has been found that the proposed equation can produce reasonably accurate stress concentration factor values for tubular X-joints subjected to axial loads.
Abstract：
Using the Euler elastic stability theory for reference, the stability equation of piles in frozen soil is established and solved to obtain a general formula for calculating the buckling loads of piles under the action of frost heave forces and resistance to deformation of frozen soil. A discrete spring element model is established using the commercially available finite element analysis program ANSYS to calculate the forces generated by frozen soil. The results obtained from the two methods are compared with the experimental data of piles in Kunlunshan permafrost test field, and they are shown to be in good agreement. Through parameter analysis, the major factors affecting the stability of piles in frozen soil region are obtained.
Using the Euler elastic stability theory for reference, the stability equation of piles in frozen soil is established and solved to obtain a general formula for calculating the buckling loads of piles under the action of frost heave forces and resistance to deformation of frozen soil. A discrete spring element model is established using the commercially available finite element analysis program ANSYS to calculate the forces generated by frozen soil. The results obtained from the two methods are compared with the experimental data of piles in Kunlunshan permafrost test field, and they are shown to be in good agreement. Through parameter analysis, the major factors affecting the stability of piles in frozen soil region are obtained.
2007, 24(7): 174-183.
Abstract：
The mechanical model of SMA fiber pull-out is discussed and simplified in the paper. On the basis of one-dimensional Liang-Rogers constitutive model and Tanaka exponent model for Martensite volume fraction, with limited numerical value of interfacial friction effect considered, the functional relationships between the displacement of fiber in the pull-out zone and the external load and friction upon loading and unloading are deduced under isothermal condition. In addition, a series of relative curves are given, and the influences of interfacial friction to the mechanical properties of SMA fiber are obtained. The good agreement of the results from cosine and exponent models indicates that the varying axial force model is reasonable to some extent.
The mechanical model of SMA fiber pull-out is discussed and simplified in the paper. On the basis of one-dimensional Liang-Rogers constitutive model and Tanaka exponent model for Martensite volume fraction, with limited numerical value of interfacial friction effect considered, the functional relationships between the displacement of fiber in the pull-out zone and the external load and friction upon loading and unloading are deduced under isothermal condition. In addition, a series of relative curves are given, and the influences of interfacial friction to the mechanical properties of SMA fiber are obtained. The good agreement of the results from cosine and exponent models indicates that the varying axial force model is reasonable to some extent.
2007, 24(7): 184-188.
Abstract：
Magnetoelastic forced vibration of a thin round plate subjected to mechanical loading in magnetic field is studied. Based on axisymmetric vibration equations, electromagnetic field equations and electromagnetic forces derived form Maxwell’s equations, the vibration problem of a round plate with clamped and simple support boundary is analyzed in the uniform magnetic field. With the aid of displacement mode hypothesis, the differential forced vibration equation is obtained by using of Galerkin method. By numerical method, the amplitude-frequency resonance and phase-frequency are gained, and the influences of magnetic induction as well as plate thickness on vibration characteristics are discussed.
Magnetoelastic forced vibration of a thin round plate subjected to mechanical loading in magnetic field is studied. Based on axisymmetric vibration equations, electromagnetic field equations and electromagnetic forces derived form Maxwell’s equations, the vibration problem of a round plate with clamped and simple support boundary is analyzed in the uniform magnetic field. With the aid of displacement mode hypothesis, the differential forced vibration equation is obtained by using of Galerkin method. By numerical method, the amplitude-frequency resonance and phase-frequency are gained, and the influences of magnetic induction as well as plate thickness on vibration characteristics are discussed.
2007, 24(7): 189-192.
Abstract：
The three-parameters rheology equation of viscoelasticity of rubber waterstop material is formulated by use of constitutive model of differential coefficient. Combining with the test of viscoelasticity of waterstop material, the influence of the waterstop effect of the viscoelasticity of waterstop material is analyzed when the flood peak is high. By means of principle of stress relaxation function of material, effectual waterstop time of three kinds of waterstop material is obtained theoretically. The equation is significant for viscoelasticity research of rubber waterstop material, and it can offer useful reference for pertinent practical engineering.
The three-parameters rheology equation of viscoelasticity of rubber waterstop material is formulated by use of constitutive model of differential coefficient. Combining with the test of viscoelasticity of waterstop material, the influence of the waterstop effect of the viscoelasticity of waterstop material is analyzed when the flood peak is high. By means of principle of stress relaxation function of material, effectual waterstop time of three kinds of waterstop material is obtained theoretically. The equation is significant for viscoelasticity research of rubber waterstop material, and it can offer useful reference for pertinent practical engineering.
