梁弯曲、扭转、稳定分析的三维退化层合梁单元有限元法

The Finite Element Analysis on Bending and Torsion and Stability of Beam by the Degenerated 3D Laminated Beam Element

首先在20结点三维块体等参元及16结点相对位移板壳元的基础上,引入梁的基本假定,采用等效数值积分法,构造出12—20结点三维退化层合梁单元,然后考虑几何非线性,给出用于梁线弹性稳定分析的有限元列式,文中单元直接由三维块体等参元退化而得,只有线位移自由度,可以方便地与相对位移板单元和三维块体单元协调连结.又用三维退化梁单元分析了实心杆的弯曲、自由扭转及分支屈曲的临界荷载,其数值结果和理论解符合很好.

Based on 3D iso - parameter and the plate shell element of relative displacement (Xu Xing 1993),and combining with beam assume and layer integration,we proposed the degenerated 3 dimensional laminated beam element concerming geometrical nonlinear, which canbe used for analysis on bending and torsion and critical load of linearelastic buckling of beam. Being degenerated from 3D iso - parameter element , the new element, whose nodes have no rotation freedom, can be connected coordinately with many of other types elements. On the other hand, the geometric shape, boundary contritions, material composition and load locations in the element can be simulated easily and naturally. All the applicatitions and results of them elucidate that the method and the elements presented in the paper are more effectively than much of the others.