广义增量法在三维扁平桁架结构的弹塑性屈曲分析中的应用

本文利用广义逆矩阵,提出了解决非线性屈曲问题的广义增量法。并用该法分析了非线性荷载-位移关系曲线(其中包括极值点)。最后,给出一数值算例—三维扁平桁架结构的弹塑性屈曲分析,证明了本文方法的正确性和实用性。

Elastic-Plastic Buckling Analysis of Shallow Truss Structures by the Generalized Incremental Method

The generalized incremental method to analyze the nonlinear load-displacement relations including the limit point in the elasticplastic regions is presented and illustrative examples for shallow truss structures are shown.The load-incremental method is one of the basic analytical methods for the numerical analysis of nonlinear problems of structures. However. when there exist critical points on the equilibrium path, the determinat of the tangent stiffness matrix becomes zero at these points , and a numerically unstable situation develops in the vicinity of critical point. Therefore, it is impossible to pursue the equilibrium path beyond the critical point by type load-incremental method. To avoid such a situation, the displacement-incremental method, the perturbation method, the arc-length method, etc. have been developed. But these methods have also disadvantages for the selection of an incremental parameter and the addition a nonlinear constraint.Based on the above consideration, a new incremental method, which will be called " Generalized Incremental Method" , is presented by using the generalized inverse.