力-变位关系全过程模拟的有限元位移控制新方法

材料、构件及结构的力-变位关系非线性全过程曲线有限元数值模拟中,极限强度和其后的软化下降段模拟一直是未得到较好解决的难题。位移增量控制法可以方便跨越力-变位关系中的极值点,因此它常被用于求解材料、构件及结构包含极限强度后软化下降段的力-变位关系非线性全过程曲线。但是,传统的位移增量控制法需要重新排列有限元方程的刚度矩阵,并存在求解非对称和非带状系数方程的问题,因而限制了其推广应用。该文提出了求解材料、构件及结构的力-变位关系非线性全过程曲线的一种新的位移增量控制方法,该方法通过修改刚度矩阵中相关对角系数的方式,将边界和力作用点的控制位移条件隐含到有限元方程中,从而可以采用有限元荷载控制方法同样的方式进行求解,保证了有限元方程系数矩阵在求解过程中的对称性和带状性,并可方便地在现有通用商业有限元软件中实现。算例分析表明了该文方法的有效性。

A NEW FINITE ELEMENT DISPLACEMENT CONTROL METHOD OF THE WHOLE PROCESS SIMULATION OF FORCE-DISPLACEMENT RELATION

In the finite element numerical simulation of the non-linear whole process curve of the force-displacement relation of materials,components and structures,the simulation of ultimate strength and the subsequent softening and declining curve segment are always a difficult problem not well solved.The incremental displacement control method can conveniently step over the extreme point of the force-displacement relation curve,thusly it is usually applied in solving the non-linear whole process curve of the force-displacement relation of materials,components and structures containing the softening and declining curve segment behind the ultimate strength point.But the traditional incremental displacement control method needs to rearrange the stiffness matrix of the finite element equations,and there is also a problem of solving asymmetric or non-zonal coefficient equations,consequently its popularization and application are restricted.In this paper,a new incremental displacement control method is proposed.By modifying the related diagonal coefficients in the stiffness matrix,this method conceals the displacement control conditions of the boundary and the force functional points in the finite equations,and thereby it can be solved in the same way with the finite element load control method,ensuring the symmetry and zonality of the coefficient matrix of the finite element equations in the solving processes,and it can be conveniently implemented in current commercial finite element software.The example analysis shows the effectiveness of this method.