几何刚度矩阵的推导和应用

以虚功原理为基础有限元进行梁柱的分析,应用很少,主要是于在计算中,荷载很小时,计算结果就不收敛了。因而也就很难应用于工程分析中。以虚功原理为基础推导得出了几何刚度矩阵,分析了计算不收敛的原因,得出结论：不考虑节点力因位移产生的不平衡力对几何刚度矩阵的影响,是计算结果不收敛的主要原因。算例说明了当考虑了这个影响以后,计算结果和文献给出的计算结果符合良好。

Derivation And Application Of Stiffness Matrix For Geometric Nonlinear Analysis

It is used poorly to apply the finite elements method for calculation of the beam-columns based on the virtual work principle .It is the main cause that no convergent results can be got when the loads are still small,so it is diffcult to apply it for analyse in engineering. In this paper a stiffness is derived for geometric nonlinear analysis based on virtual work principle ,and the reason of divergence is also analysed ,a conclusion is drawn that it is the main cause that it is no consideration of displacements and rotations acting on the balanced forces and moments .Two examples considered this effects demonstrate the correctness of the analysis and the efficiency of the method in engineering analysis .