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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。
Materials, components and structure of the force - displacement relationship Non-linear curve of the whole process of finite element numerical simulation, the ultimate strength and subsequent softening descending section simulation has been a problem not been solved. The displacement incremental control method can easily cross the extremum point in the force-displacement relationship. Therefore, it is often used to solve the non-linear curve of force-displacement relationship during the softening descent of materials, components and structures. However, the traditional displacement incremental control method needs to rearrange the stiffness matrix of the finite element equation, and has the problem of solving the asymmetric and non-band coefficient equations, thus limiting its generalization and application. In this paper, a new incremental control method of displacement for solving the nonlinear process of force-displacement relationship is proposed for the solution of materials, components and structures. By modifying the relevant diagonal coefficients in the stiffness matrix, The controlling displacement condition of the point of action is implicit in the finite element equation so that the finite element load control method can be used to solve the problem in the same way, which ensures the symmetry and banding of the finite element equation coefficient matrix in the solution process and is convenient In the existing general commercial finite element software to achieve. The example analysis shows the validity of the method.