任意四边形薄板大挠度弯曲问题研究

本文用pb-2 Ritz能量法求解任意四边形薄板的几何非线性弯曲问题.首先通过坐标变换将任意四边形区域转换到一个2×2单位正方形求解区域,并建立求解域内的能量泛函,然后取一个完备的二元多项式级数(p-2)与描述边界形状的一个基本函数(b)的乘积作为Ritz函数,由能量最小原理建立结构的刚度方程,非线性代数方程采用拟牛顿法求解.文中给出了详细的数学公式,并对四边简支方板和四边固定菱形板进行了数值分析,算例表明,本方法具有公式简单、精度较高的优点,用以分析大挠度问题是非常有效的.

Bending Analysis of Arbitrary Quadrilateral Plates with Large Deflection

In this paper, a numerical solution technique, which is based on the pb-2 Ritz method is presented for the investigation of the geometric nonlinear bending of quadrangular thin plates. First, the arbitrary quadrilateral physical domain is mapped onto the 2x2 unit square computational domain by using the parametric mapping concept, and the energy functional is established. Then the the Ritz functions are composed of a set of complete two dimensional polynomials and a basic function which describes the geometric shape of the computational domain. By minimizing the energy functional, a set of algebraic nonlinear equations is derived. A quasi-Newton' s iterative approach is used for searching the solutions of the algebraic nonlinear equations, and the detailed formulations are described. A simply supported square plate and a clamped edges rhombus plate are calculated. The numerical examples show that the accuracy is ascertained by comparing the deflection solutions with existing literatures.