框架结构P-△效应分析的微分求积单元法

采用一种新的数值方法——微分求积单元法分析框架结构的P-△效应。微分求积单元法采用微分求积法直接求解微分方程的技术，并结合有限分割技术而形成。首先建立考虑剪切变形和轴力二阶效应的框架结构单元平衡微分方程，通过微分求积离散而得到梁单元的一般弹性刚度方程；同时考虑变形后节点的平衡条件和变形协调条件，导出框架结构整体二阶分析的微分求积单元法力学模型。由于该分析模型中包括了单元及结构的所有离散形式的控制方程，因此采用该模型进行结构分析可得出较为精确的解。数值算例的分析比较，表明了该法用于框架结构P-△效应分析的正确性和有效性。本文导出的框架结构二阶分析的微分求积单元法力学模型可用于框架结构剪切变形与几何非线性的耦合效应分析。

Second Order Analysis of Frames by Differential Quadrature Element Method

A new numerical approach entitled ' differential quadrature element method' was used for the second order analysis of frames. The approach is based on the differential quadrature method (DQM) and finite-cut technique. The equilibrium differential equations of second order analysis of frames were established and the shearing deformation of members was taken into consideration. The differential quadrature method was used to discretize the equilibrium equations and then the general elastic stiffness equation can be obtained. The transition conditions of inter-nodes of frames and the boundary conditions of structures were considered and the model of the second order anlaysis of frames was dervied. Because all of the control equations of elements and structures can be involved in this new model, the accurate conclusion can be obtained by using this new model. The results of numerical examples demonstrate the validity of differential quadrature element method (DQEM) using in the second order analysis of frames. The new model can be used in the second-order coupling analysis of shearing deformation and P-A effect of frames.