摘要
为求解桁架大位移问题,提出了一种基于节点坐标变量的非线性有限元法——以杆端节点坐标向量为显函变量写出单元杆端力向量表达式,由单元杆端力向量装配结构非线性平衡方程。求解时,首先根据矩阵微分理论求出单元杆端力向量关于杆端节点坐标向量的导数矩阵,由该导数矩阵装配结构非线性微分平衡方程;然后按照Newton切线法原理建立等效线性逼近方程,引入边界约束条件得到结构节点坐标的迭代公式。研究结果表明:该方法稳定性好、精度高、收敛速度快且简单易用,为求解桁架大位移问题提供了一种有效方法。
In order to solve the large displacement problems of trusses, a nonlinear finite element method was proposed, which used the node coordinate variables as unknowns. An expression ofthe member end force vector was written in terms of member＇s end coordinates, by which the global nonlinear equilibrium equation was fabricated. In solution, firstly, based on matrixdifferential theory, element derivative matrix was obtained with respect to the member end force vector, by which the global differential nonlinear equilibrium equation was fabricated. Secondly,based on Newton tangent method theory, the global equivalent linear matrix equation was established, then the structure＇s boundary restraints was introduced, the iterative formulae forstructure node coordinates were obtained. The research results show that the present method has good stability, high precision, quick convergence and easiness in use, and is very efficient forsolving the large displacement problems of trusses.
出处
《建筑科学与工程学报》
CAS
北大核心
2014年第2期138-142,共5页
Journal of Architecture and Civil Engineering
关键词
非线性分析
Newton切线法
大位移
有限元法
平面扁桁架
节点
nonlinear analysis
Newton tangent method
large displacement
finite element method
planar flat truss
node
作者简介
刘树堂（1959-），男，辽宁锦州人，教授，工学硕士，E—mail：lquuth@163．com。
