具有任意截面形状的各向异性平面杆系结构静力分析的回传波射矩阵法  

Static Analysis of 2D Anisotropic Bar-Structures with Arbitrary Cross Sections by MRRM

作　　者：胡立新[1] 聂国华[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2016年第1期56-64,共9页Chinese Quarterly of Mechanics

摘　　要：基于Timoshenko梁静力理论和各向异性材料的本构关系,对于一般截面形状的杆系结构,推导了杆端内力与杆端位移之间的关系,并给出了作用于杆件上的荷载转化为等效节点荷载的方法.以混合节点为例,根据结构节点的力平衡和位移协调条件,推导了常见形式节点的传递分配矩阵和载荷源向量,进而得到结构的回传波射矩阵列式,求解以杆端位移为基本未知量的矩阵方程,给出了杆端位移和内力的计算公式.文中给出了算例分析.与有限元法数值结果的比较表明,回传波射矩阵法用于分析各向异性材料平面杆系结构的静力问题是有效和精确的.The relation between the internal forces and displacements at ends of the beam members with arbitrary cross section had been developed using Timoshenko beam equations and constitutive equations for anisotropic materials. In addition, the procedure for transforming applied loads on the member to equivalent loads at ends was illustrated. According to the equilibrium and compatibility equations at a structural node, distribution matrix and load source vector of that node were obtained, and the reverberation-ray matrix was given. The formulae for the internal forces and displacements at ends of the beam members were presented by the resulting equations in the form of matrix for the displacements at ends. Numerical examples were given, and the results of MRRM were compared with those from FEM. The results indicate the MRRM can be applied effectively and accurately to the static analysis of 2D bar-structures of anisotropic materials with arbitrary cross sections.

关 键 词：回传波射矩阵法 各向异性平面杆系结构 TIMOSHENKO梁 静力分析 位移和内力 

分 类 号：O342[理学—固体力学]