薄壁箱梁约束扭转相关插值单元列式及与Timoshenko梁单元的相似性

INTERDEPENDENT INTERPOLATION ELEMENT FORMULATION OF RESTRAINED TORSION FOR THIN-WALLED BOX GIRDER AND ITS SIMILARITY TO TIMOSHENKO BEAM ELEMENT

  • 摘要: 利用薄壁箱梁约束扭转角与广义翘曲位移之间的约束关系,采用多项式对约束扭转位移场进行相关插值,构造了约束扭转单元列式。发现约束扭转相关插值单元与Timoshenko梁单元在两广义位移间的约束关系、形函数、刚度矩阵系数、非节点荷载的等效公式等方面存在高度相似性。基于有限元后处理结果,提出了二次力矩和自由扭矩的分离算法,完善了有限元的计算功能。算例结果表明:约束扭转的相关插值单元的计算精度依赖于网格划分密度,但具有良好的收敛性。在算例的单元网格密度条件下,扭转角、广义翘曲位移、总扭矩和二次力矩的极值误差小于0.12%,双力矩极值误差为4.55%,加密网格则误差降至1.17%,相比已有单元,性能有所改善。

     

    Abstract: Based on the interdependent relation between the torsion angle and the generalized warp displacement, cubic polynomials are used to interpolate the displacement fields of the restrained torsion and to formulate the restrained torsion element. High similarities are found between the interdependent interpolation element of restrained torsion and the Timoshenko beam element, such as the interdependent relation between the generalized displacements, shape functions, stiffness matrix coefficients, and equivalence of non-nodal loads. Based on the post-processing results, a separation algorithm for the secondary moment and free torque is proposed for the finite element, which improves the computing functions and facilitates the stress calculation of cross-section. Results of example demonstrate that the interdependent interpolation element depends on the mesh density to improve the calculating accuracy, but obtains an excellent convergence. Under the mesh density condition of the example, there are errors of less than 0.12% for torsion angle, generalized warp displacement, free torsion moment and secondary moment, and error of 4.55% for bimoment. If the mesh density is refined, the error of bimoment is reduced to 1.17%. Compared with those existing elements, the properties of the present element have been improved.

     

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