在动载荷作用下框架结构大变形分析的微分代数方法

Differential-Algebraic Approach to Large Deformation Analysis of Frame Structures Subjected to Dynamic Loads

采用弧坐标首先建立了在动载荷作用下,具有不连续性条件和初始位移的框架结构大变形分析的非线性数学模型.其次,在空间区域内,采用微分求积单元法(DQEM)来离散非线性数学模型,并提出了在使用DQEM来求解结构大变形分析中,多个变量具有间断性条件的有效方法,得到了一组非线性DQEM的离散化方程,它是时间域内的一组具有奇异性的非线性微分-代数方程.同时也给出了求解非线性微分-代数方程组的一个解法.作为应用,求解了受集中力和分布力作用的框架和组合框架的大变形静动力学问题,并与现有结果进行了比较.数值算例表明,处理多个变量具有间断性条件的方法和求解代数-微分系统的方法是一个有效的和一般的方法,它具有较少的节点、较小的计算工作量、较高的精度、良好的收敛性、操作简单以及应用广泛等优点.

A nonlinear mathematical model for the lathe deformation analysis of frame structures with discontinuity conditions as well as initial displacements subjected to the dynamic loads was first formulized by the arc-coordinate. Secondly, the differential quadrature element method （DQEM） was applied to discretize the nonlinear mathematical model in the spatial domain, and an effective method was presented to deal with discontinuity conditions of multi-variables in application of DQEM. A set of DQEM discretization equations were obtained, which are a set of nonlinear differential-algebraic equations with singularity in the temporal domain. A method to solve the nonlinear differential-algebraic equations was presented also. As application, the static and dynamical analyses of large deformation of frames and combined frame stmcl^res, subjected to the concentrated and distributed were presented. The obtained results were compared with the results in existing Literatures. The numerical results show that the methods of dealing with the discontinuity conditions of multi-variables and solving the differential-algebraic equations presented are effective and general, which have the advantages of little amount of nodes and cmputation, high precision and good convergence and so on.