基于有限等参单元的等效平面桁架模型

Equivalent Plane Truss Model Based on Finite Isoparametric Element

针对有限元分析的复杂性,从弹性力学平面应力单元出发,结合无限小单元法和有限单元法,提出了等效平面桁架模型。基于平面应力单元和等效桁架单元在同样节点荷载下的位移等效,分析了等效后桁架杆件的初始刚度、截面面积及等效弹性模量等特征值;建立了等效平面桁架模型的单元刚度矩阵、应变矩阵和单元的轴力矩阵;给出了等效平面桁架模型的分离式模型,分析了非规则带钢筋的四边形等参单元,建立了等参单元等效平面桁架模型的单元刚度矩阵。以某混凝土简支梁和混凝土重力坝作为研究对象,将等效桁架模型与有限元分析软件ANSYS 9.0的计算结果做比较。结果表明,等效桁架模型对平面问题的处理可以满足工程精度的要求,同时使计算模型简单化,体现了等效平面桁架模型的科学性。

In order to solve the complexity of finit element method （FEM）, embarking from the plane stress element in the elastic mechanics, infinite element method and finite element method were unioned, an equivalent plane truss model was proposed. Based on the equivalent of displacement between the plane stress element and the equivalent plane truss element, the equivalent element rigidity, equivalent section area of the truss bar and characteristic values of equivalent elastic module were analyzed. The element stiffness matrix, strain matrix and axis matrix of the equivalent truss model were built. Authors put forward the separate model of equivalent plane truss model, analyzed the common non-normal quadrilateral isoparametric element with the rebar, set up the isoparametric element stiffness matrix. A cantilever and a dam were researched, comparing the results which got from the equivalent plane truss model with that of finite element analysis software ANSYS 9.0. The results show that this model is feasible to analyze plane stress problem, it can satisfy the requirements of engineering precision. Meanwhile, the calculation model of the structure can be simplified, these adequately prove the scientificity of the equivalent plane truss model.