对偶性与特大增量步算法在复杂平面框架中的应用

特大增量步算法(LIM)是一种基于力法和广义逆矩阵理论的迭代算法,在简单桁架和刚架非线性初步应用中,达到相同计算精度下有同等甚至超过位移有限元的计算效率。针对工程中的复杂杆系结构,利用平衡与协调的对偶性,探讨LIM在复杂平面框架结构中的应用,建立了平面框架结构的LIM基本方程,提出了针对典型支座约束以及组合结点的处理方法。该处理方法的线弹性问题算例表明,与位移有限元相比具有至少同等的精度和相当的计算效率。在支座本身不考虑塑性的情况下,该处理方法同样适用于弹塑性问题,为LIM在复杂杆系结构的弹塑性分析中奠定了基础。

Application of contragradient law and large increment method to the analysis of complex frame structure

The large increment method(LIM) is an iterative method based on the force method and the generalized inverse matrix theory. In the nonlinear initial application of trusses and rigid frames, LIM reaches the same solution as the displacement-based finite element method with the same number of iterations or even less. Aiming at the complex bar structure, we discussed the application of LIM and contragradient law to the complex frame structure, established the LIM basic formula in frame structure and proposed the analysis approaches for complex boundary condition and composite joints. The illustrative example of linear elastic problem clearly reveals that the accuracy and the efficiency of LIM are the same as those of displacement-based finite element method. The method is also applicable to elasto-plastic problems without considering the plasticity of the support itself, which lays the foundation for LIM in the elasto-plastic analysis of complex bar structures.