小波加权残值法在固支矩形板后屈曲上的应用

根据Von Karman板大挠度方程,以小波函数作为试函数,采用小波加权残值法将四边固支矩形板的平衡控制方程和变形协调方程化解为两个非线性方程组,将后屈曲路径的求解转化为两个非线性方程组的求解问题.将载荷分为多个水平,利用Newton-Raphson迭代算法求得非线性方程组的解,从而得到四边固支矩形板的后屈曲平衡路径和四级渐进解.通过算例表明小波可以用于解决矩形板的后屈曲问题.

Application of the Method of Wavelet Weighted Residuals to Post-buckling Behavior of Clamped Rectangular Plates

Based on Von Karman's large deflection equations,the method of wavelet weighted residuals is employed to derive two systems of nonlinear equations. The non-dimensional load is divided into many levels. At every level of the non-dimensional load Newton-Raphson iteration algorithm is employed based on a least squares method to solve the system of nonlinear equations.The post-buckling equilibrium path of the rectangular plates with clamped boundaries can be obtained by solving these two systems of nonlinear equations.The post-buckling equilibrium equations are also obtained by regressing the numerical data.The numerical examples demonstrate that the method of wavelet weighted residuals is a useful tool to solve the post-buckling behavior of rectangular plates.