2001 Vol. 18 No. 5
2001, 18(5): 1-7.
Abstract：
A new step-by-step integral procedure of dynamics equations is presented. The general expression of solution of dynamics equations is obtained on the basis of the homogenous analytical solutions of dynamics equations. The explicit analytical integration algorithm, which is characterized by fourth-order accuracy, self-starting and self-correcting, is employed to discretize the equivalent load terms at the right-hand terms of the equations. The transfer matrix is not limited by time step size. If the group solution method is used, the size of stiffness matrix and mass matrix will be reduced and the method will be more cost-effective. Numerical examples show that the results are highly accurate in comparison with those of Newmark, Wilson-θ Houbolt and central difference method. Moreover, the present results are closer to the exact solution, than those of other methods. In addition, the method is also suitable for treatment of nonlinear dynamics problems since no iterative procedure is needed in the present algorithm.
A new step-by-step integral procedure of dynamics equations is presented. The general expression of solution of dynamics equations is obtained on the basis of the homogenous analytical solutions of dynamics equations. The explicit analytical integration algorithm, which is characterized by fourth-order accuracy, self-starting and self-correcting, is employed to discretize the equivalent load terms at the right-hand terms of the equations. The transfer matrix is not limited by time step size. If the group solution method is used, the size of stiffness matrix and mass matrix will be reduced and the method will be more cost-effective. Numerical examples show that the results are highly accurate in comparison with those of Newmark, Wilson-θ Houbolt and central difference method. Moreover, the present results are closer to the exact solution, than those of other methods. In addition, the method is also suitable for treatment of nonlinear dynamics problems since no iterative procedure is needed in the present algorithm.
2001, 18(5): 8-17,3.
Abstract：
In accordance with the self-excited ice force theory, which was proposed by Maattanen, the influences of various parameters of ice and structure on the self-excited structural vibration were investigated. For simplified structure models of different dynamic properties, response simulations of ice-induced vibration were performed, and from the simulations some features of self-excited ice forces and structural vibrations were found. The results in this paper are useful for both promoting understanding of self-excited vibration and avoidance or control of this kind of vibration.
In accordance with the self-excited ice force theory, which was proposed by Maattanen, the influences of various parameters of ice and structure on the self-excited structural vibration were investigated. For simplified structure models of different dynamic properties, response simulations of ice-induced vibration were performed, and from the simulations some features of self-excited ice forces and structural vibrations were found. The results in this paper are useful for both promoting understanding of self-excited vibration and avoidance or control of this kind of vibration.
2001, 18(5): 18-28.
Abstract：
To search direction of each solution branch at pitch-fork bifurcation point, a numerical method is proposed in this paper. Because this method does not require information of derivatives of tangential stiffness matrix, it is suitable for general nonlinear finite element program. Stability of equilibrium corresponding to each solution curve is judged by Lagrange-Dirichlet theorem. The solution path in post-buckling of a square plate is traced globally and equilibrium stability of the plate was judged. The stable equilibrium can simulate the whole process of snap-through of square plate during loading and unloading. The result in this paper agrees with available experimental data. In part I, numerical methods and algorithm are proposed. In part II, numerical results of snap-through of square plate are compared with experimental data.
To search direction of each solution branch at pitch-fork bifurcation point, a numerical method is proposed in this paper. Because this method does not require information of derivatives of tangential stiffness matrix, it is suitable for general nonlinear finite element program. Stability of equilibrium corresponding to each solution curve is judged by Lagrange-Dirichlet theorem. The solution path in post-buckling of a square plate is traced globally and equilibrium stability of the plate was judged. The stable equilibrium can simulate the whole process of snap-through of square plate during loading and unloading. The result in this paper agrees with available experimental data. In part I, numerical methods and algorithm are proposed. In part II, numerical results of snap-through of square plate are compared with experimental data.
2001, 18(5): 29-35.
Abstract：
In recent years, network parallel environment is an important direction of parallel environment, PVM is one of the best popular software platforms which support heterogeneous or isogeneous network parallel computing. In this paper, a network parallel finite element method based on PVM is studied with substructure conjugate gradient method. In the method, the finite element grid is divided into n substructures, the information of n substructures is distributed to n microcomputers. The generation and formation of stiffness matrixes and loading arrays of n substructures are done by n microcomputers simultaneously. Preconditioned conjugate gradient method is employed to compute the nodal displacements, then each microcomputer determines the strains and stresses for its associated substructure. The method does not require the formation of global stiffness and loading array, the nodal displacements can be simultaneously obtained. The speed of convergency is faster than general superposition method. Examples show that the proposed parallel substructure conjugate gradient method can achieve better parallel speedup ratio for network.
In recent years, network parallel environment is an important direction of parallel environment, PVM is one of the best popular software platforms which support heterogeneous or isogeneous network parallel computing. In this paper, a network parallel finite element method based on PVM is studied with substructure conjugate gradient method. In the method, the finite element grid is divided into n substructures, the information of n substructures is distributed to n microcomputers. The generation and formation of stiffness matrixes and loading arrays of n substructures are done by n microcomputers simultaneously. Preconditioned conjugate gradient method is employed to compute the nodal displacements, then each microcomputer determines the strains and stresses for its associated substructure. The method does not require the formation of global stiffness and loading array, the nodal displacements can be simultaneously obtained. The speed of convergency is faster than general superposition method. Examples show that the proposed parallel substructure conjugate gradient method can achieve better parallel speedup ratio for network.
2001, 18(5): 36-42,4.
Abstract：
Experimental study of complete tensile stress-strain curves of high strength concrete and compact reinforced concrete was conducted. Two sets of test devices, were designed. The deviations of the measured complete curves are small, indicating that the devices are effective. In addition, the theoretical equations of complete curves are proposed and compared with measured ones. Good agreement is reached.
Experimental study of complete tensile stress-strain curves of high strength concrete and compact reinforced concrete was conducted. Two sets of test devices, were designed. The deviations of the measured complete curves are small, indicating that the devices are effective. In addition, the theoretical equations of complete curves are proposed and compared with measured ones. Good agreement is reached.
2001, 18(5): 43-49.
Abstract：
In this study, the interface failure under the joint action of constant compression and periodical anti-plane shear were investigated. This paper is the second part of this study. With the so-called “shear beam model”, analytical solutions were presented for the evolution law and distributions of shear stress and displacement along the entire length of the shear beam during reloading processes. Results indicate that, owing to the existing of the damage process zone ahead of the crack tip, reloading is inelastic from the beginning. Furthermore, “stress locking” always occurs if a loading process cannot cover the damage zone left by its neighboring loading process. Analysis of synthesis of response presented at the end of the paper reveal two modes of structural responses: 1) contact plastic shakedown and 2) progressive failure.
In this study, the interface failure under the joint action of constant compression and periodical anti-plane shear were investigated. This paper is the second part of this study. With the so-called “shear beam model”, analytical solutions were presented for the evolution law and distributions of shear stress and displacement along the entire length of the shear beam during reloading processes. Results indicate that, owing to the existing of the damage process zone ahead of the crack tip, reloading is inelastic from the beginning. Furthermore, “stress locking” always occurs if a loading process cannot cover the damage zone left by its neighboring loading process. Analysis of synthesis of response presented at the end of the paper reveal two modes of structural responses: 1) contact plastic shakedown and 2) progressive failure.
2001, 18(5): 50-63.
Abstract：
The additional incompatible displacement terms on internal parameters for plane elasticity problems were given in a previous publication[12]. With reference to the general formulas in[12], new incompatible displacement elements can be constructed directly, avoiding the previous tedious trial and error process. This paper aims to extend the previous work [12] to three-dimensional cases. Formulations of the additional incompatible displacement terms are established in terms of isoparametric coordinates and Cartesian coordinates, respectively. Taking H8 and H20 solid elements as examples, two new incompatible elements are developed. To illustrate the feasibility of the present approach, numerical examples are provided. It is shown that the two new elements produce convergent and highly accurate results.
The additional incompatible displacement terms on internal parameters for plane elasticity problems were given in a previous publication[12]. With reference to the general formulas in[12], new incompatible displacement elements can be constructed directly, avoiding the previous tedious trial and error process. This paper aims to extend the previous work [12] to three-dimensional cases. Formulations of the additional incompatible displacement terms are established in terms of isoparametric coordinates and Cartesian coordinates, respectively. Taking H8 and H20 solid elements as examples, two new incompatible elements are developed. To illustrate the feasibility of the present approach, numerical examples are provided. It is shown that the two new elements produce convergent and highly accurate results.
2001, 18(5): 64-70.
Abstract：
A new algorithm for dynamic elastoplastic analysis is put forward on the basis of parametric quadratic programming and exact integration. The equations of dynamic elastoplastic problems are derived from the parametric variational principle and parametric quadratic programming, being valid for both associated and non-associated plastic constitutive models in finite element analysis. Exact integration method, which has been widely used in linear problems, is adopted for the solution of dynamic nonlinear equations. A numerical example is provided to demonstrate the correctness and the advantage of the proposed theory and algorithm.
A new algorithm for dynamic elastoplastic analysis is put forward on the basis of parametric quadratic programming and exact integration. The equations of dynamic elastoplastic problems are derived from the parametric variational principle and parametric quadratic programming, being valid for both associated and non-associated plastic constitutive models in finite element analysis. Exact integration method, which has been widely used in linear problems, is adopted for the solution of dynamic nonlinear equations. A numerical example is provided to demonstrate the correctness and the advantage of the proposed theory and algorithm.
2001, 18(5): 71-76,1.
Abstract：
This paper deals with the random response of elastic-viscoelastic combined systems. A method is proposed on the basis of the complex analysis in the time domain, in which the differential and integral dynamic equation of an elastic-viscoelastic combined system is transformed into an ordinary state equation. The covariance matrices of random responses of elastic-viscoelastic systems under stationary random excitations are obtained. The characteristics of the systems under typical stationary random excitations are investigated and complex algebraic expressions of covariance matrices are given. It is shown that the present method is simple and widely applicable.
This paper deals with the random response of elastic-viscoelastic combined systems. A method is proposed on the basis of the complex analysis in the time domain, in which the differential and integral dynamic equation of an elastic-viscoelastic combined system is transformed into an ordinary state equation. The covariance matrices of random responses of elastic-viscoelastic systems under stationary random excitations are obtained. The characteristics of the systems under typical stationary random excitations are investigated and complex algebraic expressions of covariance matrices are given. It is shown that the present method is simple and widely applicable.
Abstract：
In this paper, a model of self-excited aerodynamic forces acting on a section of bridge deck with additional airfoil attached below the trailing edge is established. A suspension bridge project is taken as an example, in which the evolution of critical wind speed of flutter during bridge erection is studied by a multi-mode flutter analysis approach. With the most dangerous construction stage as an example, the effectiveness of the airfoil in the flutter stability of the system is investigated. The analysis shows that the additional airfoil attached below the trailing edge of bridge deck is an effective aerodynamic means for suppressing the flutter of the suspension bridge during erection.
In this paper, a model of self-excited aerodynamic forces acting on a section of bridge deck with additional airfoil attached below the trailing edge is established. A suspension bridge project is taken as an example, in which the evolution of critical wind speed of flutter during bridge erection is studied by a multi-mode flutter analysis approach. With the most dangerous construction stage as an example, the effectiveness of the airfoil in the flutter stability of the system is investigated. The analysis shows that the additional airfoil attached below the trailing edge of bridge deck is an effective aerodynamic means for suppressing the flutter of the suspension bridge during erection.
2001, 18(5): 84-94.
Abstract：
The vertical resonance phenomenon which may take place for many kinds of different simply supported girder bridges on high-speed railway is studied with a vehicle-bridge interaction system model. The train's critical velocities are obtained when the vertical resonant vibration occurs. The influence of different spans upon the peak value of the vertical resonant vibration of the bridges is investigated. The precautions against the vertical resonance phenomenon of the bridges are addressed.
The vertical resonance phenomenon which may take place for many kinds of different simply supported girder bridges on high-speed railway is studied with a vehicle-bridge interaction system model. The train's critical velocities are obtained when the vertical resonant vibration occurs. The influence of different spans upon the peak value of the vertical resonant vibration of the bridges is investigated. The precautions against the vertical resonance phenomenon of the bridges are addressed.
2001, 18(5): 95-99.
Abstract：
Techniques of automatic modeling for dynamic analysis of flexible multibody system of guns are introduced in this paper. With these techniques, identification of systems configuration, determination of coordinate frames and degrees of freedom, application of load, generation and solution of motion equations can be processed automatically. Thus, the dynamic simulation for launching of any guns can be carried out easily, offering useful guidelines on design of guns.
Techniques of automatic modeling for dynamic analysis of flexible multibody system of guns are introduced in this paper. With these techniques, identification of systems configuration, determination of coordinate frames and degrees of freedom, application of load, generation and solution of motion equations can be processed automatically. Thus, the dynamic simulation for launching of any guns can be carried out easily, offering useful guidelines on design of guns.
2001, 18(5): 100-107.
Abstract：
Based on the Euler-Beam theory, the moving vehicle loads on bridges were identified from the response of bridges using the Time Domain Method (TDM) and Frequency-Time Domain Method (FTDM). This paper aims to investigate the effect of various parameters on the two methods. These parameters include mode number, sampling frequency, vehicle speed, locations and numbers of measured stations. Assessment results show that the vehicle-bridge model in laboratory is successful. Both methods are effective and acceptable with higher accuracy, and the TDM is the preferred in-situ method with good feasibility and robustness.
Based on the Euler-Beam theory, the moving vehicle loads on bridges were identified from the response of bridges using the Time Domain Method (TDM) and Frequency-Time Domain Method (FTDM). This paper aims to investigate the effect of various parameters on the two methods. These parameters include mode number, sampling frequency, vehicle speed, locations and numbers of measured stations. Assessment results show that the vehicle-bridge model in laboratory is successful. Both methods are effective and acceptable with higher accuracy, and the TDM is the preferred in-situ method with good feasibility and robustness.
2001, 18(5): 108-114.
Abstract：
The cylindrical and boxlike reinforced concrete rockshaft is one of the important and widely used structures in colliery. Due to its complexity, it is rather difficult to acquire its natural frequencies using analytical methods. Although the finite element method is capable of coping with the problem, a large number of degrees of freedom is often needed and the convergence speed is slow. In this paper, a generalized conforming triangular plate element is employed to study the free vibration of cylindrical and boxlike reinforced concrete rockshaft. The present approach is validated by a numerical example. It is shown that the numerical results are in good agreement with those of commercial computer code SAP93 and the experimental data.
The cylindrical and boxlike reinforced concrete rockshaft is one of the important and widely used structures in colliery. Due to its complexity, it is rather difficult to acquire its natural frequencies using analytical methods. Although the finite element method is capable of coping with the problem, a large number of degrees of freedom is often needed and the convergence speed is slow. In this paper, a generalized conforming triangular plate element is employed to study the free vibration of cylindrical and boxlike reinforced concrete rockshaft. The present approach is validated by a numerical example. It is shown that the numerical results are in good agreement with those of commercial computer code SAP93 and the experimental data.
2001, 18(5): 115-118,.
Abstract：
In the paper, impact compression test on concrete is performed with a modified right cone variable cross-section SHPB. A prearranged-gap method is used to avoid the influence of dispersion of loading wave. The experimental results show that the concrete manifests itself in two aspects: strain rate stiffening and damage softening.
In the paper, impact compression test on concrete is performed with a modified right cone variable cross-section SHPB. A prearranged-gap method is used to avoid the influence of dispersion of loading wave. The experimental results show that the concrete manifests itself in two aspects: strain rate stiffening and damage softening.
2001, 18(5): 119-126.
Abstract：
Continuously reinforced concrete pavement is treated as orthotropic plate on viscoelastic foundation. Dynamic responses of the pavement under transient load are studied using triangular series and integral transformation. Analytic solutions for displacements, internal forces and stresses are obtained. Numerical results are given and compared with the responses of pavement under static and transient load on non-viscosity foundation. The effects of transient load period and foundation viscosity on the responses are discussed.
Continuously reinforced concrete pavement is treated as orthotropic plate on viscoelastic foundation. Dynamic responses of the pavement under transient load are studied using triangular series and integral transformation. Analytic solutions for displacements, internal forces and stresses are obtained. Numerical results are given and compared with the responses of pavement under static and transient load on non-viscosity foundation. The effects of transient load period and foundation viscosity on the responses are discussed.
2001, 18(5): 127-132,.
Abstract：
Due to the existence of various micro-defects in brittle or quasi-brittle materials, the mechanical behavior, such as the nominal failure stress, stiffness and fracture toughness etc., varies with the dimension of specimens. This is defined as the size effect of such materials. In general, the Bazant size effect law is established experimentally using a series of similar specimens. In this paper, a new experimental procedure by which the fracture toughness and effective fracture process zone length are measured using the specimens with fixed crack length is proposed, and the associated formulas are also presented. Under the condition that identical brittleness numbers must be ensured for both the proposed and commonly-used similar specimen method, relatively small specimens can be used under laboratory conditions. It is shown that and good agreement is reached in comparison with the results of the commonly-used similar specimen method.
Due to the existence of various micro-defects in brittle or quasi-brittle materials, the mechanical behavior, such as the nominal failure stress, stiffness and fracture toughness etc., varies with the dimension of specimens. This is defined as the size effect of such materials. In general, the Bazant size effect law is established experimentally using a series of similar specimens. In this paper, a new experimental procedure by which the fracture toughness and effective fracture process zone length are measured using the specimens with fixed crack length is proposed, and the associated formulas are also presented. Under the condition that identical brittleness numbers must be ensured for both the proposed and commonly-used similar specimen method, relatively small specimens can be used under laboratory conditions. It is shown that and good agreement is reached in comparison with the results of the commonly-used similar specimen method.
2001, 18(5): 133-139,.
Abstract：
Cancellous bone is modelled as a transversely isotropic, liquid saturated porous solid based on experimental observation. The finite element formulation for dynamic response of cancellous bone is set up on the basis of Galerkin weighted residual method. Introducing the ratio of pressure p to penalty parameter β in the continuity equation, a penalty finite element formulation is established which can eliminate the pressure term in governing equations. Thus, the coupling effect between the solid phase and the fluid phase in cancellous bone is studied when the tissue is subjected to impact loading. Computational results show that the reciprocity between the solid osseous and the marrow in the cavity results from the coupling effects between the solid and the fluid. It is found that the cancellous bone is characterized by its viscoelasticity and energy dissipation.
Cancellous bone is modelled as a transversely isotropic, liquid saturated porous solid based on experimental observation. The finite element formulation for dynamic response of cancellous bone is set up on the basis of Galerkin weighted residual method. Introducing the ratio of pressure p to penalty parameter β in the continuity equation, a penalty finite element formulation is established which can eliminate the pressure term in governing equations. Thus, the coupling effect between the solid phase and the fluid phase in cancellous bone is studied when the tissue is subjected to impact loading. Computational results show that the reciprocity between the solid osseous and the marrow in the cavity results from the coupling effects between the solid and the fluid. It is found that the cancellous bone is characterized by its viscoelasticity and energy dissipation.
2001, 18(5): 140-144.
Abstract：
A model is proposed for predicting the effective longitudinal shear modulus of fiber reinforced composite materials. The cross section aspect ratio of fiber and the distribution of matrix surrounding are taken into consideration in the model. It is applicable to a full range of aspect ratios. Numerical examples are provided to verify the model. It is found that the longitudinal shear modulus is sensitive to aspect ratios. A comparison is made between the numerical and experimental result to demonstrate the reliability of the present model.
A model is proposed for predicting the effective longitudinal shear modulus of fiber reinforced composite materials. The cross section aspect ratio of fiber and the distribution of matrix surrounding are taken into consideration in the model. It is applicable to a full range of aspect ratios. Numerical examples are provided to verify the model. It is found that the longitudinal shear modulus is sensitive to aspect ratios. A comparison is made between the numerical and experimental result to demonstrate the reliability of the present model.
