对偶性与特大增量步算法在复杂平面框架中的应用

发布时间：2018-01-31 12:05

本文关键词： 特大增量步法对偶性支座约束组合结点广义逆　出处：《重庆大学学报》2017年02期 　论文类型：期刊论文

【摘要】：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。
[Abstract]:The extraordinarily incremental step algorithm (limm) is an iterative algorithm based on force method and generalized inverse matrix theory, which is applied in the elementary application of simple truss and rigid frame nonlinearity. The computational efficiency of finite element method is equal or even higher than that of displacement finite element method under the same calculation precision. The dual property of balance and coordination is used for the complex bar structure in engineering. The application of LIM in complex plane frame structure is discussed, and the basic LIM equation of plane frame structure is established. A method for dealing with typical support constraints and combined nodes is proposed. The example of linear elasticity problem of this method shows that the proposed method can be used to solve the problem of linear elasticity. Compared with the displacement finite element method, the method has at least the same accuracy and equivalent computational efficiency. This method is also suitable for the elastoplastic problem without considering the plasticity of the bearing itself. It lays a foundation for the elastoplastic analysis of complex bar structures by LIM.
【作者单位】：重庆大学土木工程学院;重庆大学山地城镇建设与新技术教育部重点实验室;
【基金】：国家自然科学基金面上项目(11272362)~~
【分类号】：O342;O302
【正文快照】： 结构内力分析需满足平衡、协调和本构三大基本方程以及边界条件。传统的矩阵位移法和矩阵力法[1]通常是将这3个方程和边界条件统一在一套结构刚度方程或柔度方程中,通过求解节点位移或多余未知力达到求解结构内力的目的。这种思路,对于求解材料非线性问题的位移法而言,存在“

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