工程结构几何非线性有限元研究述评

Comments on Research of Geometric Nonlinear Finite Element Method in Engineering Structure

在结构线弹性计算中,一般都假定在加载过程中用结构变形前的形状来代替变形后的形状。然而在实际工程结构中,往往存在着大位移、大转角或大应变等问题。这时平衡条件就应如实的建立在变形后的位形上,以考虑变形对平衡的影响;同时应变表达式也应包括位移的二次项,这就需要采用几何非线性来研究。以此为出发点与当前流行的有限元方法相结合,分析了几何非线性有限元法分析的一般过程。综合比较了几何非线性有限元法在杆、梁、板、壳等方面的国内外研究成果,指出目前仍存在的问题,提出今后的发展方向,为几何非线性有限元的理论研究与程序设计提供参考。

In the calculation of linear and elastic problems, the original shape is generally assumed to be substituted for the real shape in the process of applying load. However, in the real engineering stnlctures,some problems such as large displacement, large angle of rotation and large strain are shown on. In this case, in order to consider the influence of deformation on balance, the equilibrium condition must be built according to the current real shape. At the same time, the quadratic term of displacement should also be included in the expression of strain. As a result, geometric nonlinear finite element method is strongly needed. Based on the above theories and combined with popular fi- nite element method, the general analytic process of geometric nonlinear finite element method is presented. Compared with the research of the geometric nonlinear finite element method home and a- board in the components such as bar, plate, beam and shell element, the present problems is analyzed and the future research direction is described for the theoretical research and program design of geo- metric nonlinear finite element method.