用样条配点法求解反对称角铺设层合板响应的统计特性

Statistical properties response analysis of antisymmetric angle-ply laminated plates by using spline collocation method

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板响应 的统计特性,这对正确估计结构设计的可靠性有着非常重要的意义.用样条配点法,将复合材料层 合板结构离散后,应用Lagrange方程,建立了复合材料层合板的力学模型,研究了随机参数反对称 层合板响应的统计特性,推导出层合板位移、速度和加速度的标准差.在数值算例中,对于各种边界 条件,选择样条函数作为振型函数,用样条配点法求出了结构的位移响应量及统计特征值,并与 Newmark法进行了比较,验证了该方法的有效性.

The geometrie parameters of composite laminated plates are usually random due to the effect of vari-ous underministric factors in engineering structure.The study of statistical properties response of random parameter laminated plates plays an important role in the right estimation of the reliability of constructiondesign.This article uses spline collocation method to disperse the structure of composite laminated plates,then establishes the mechanics model of composite laminated plates and studies the statistical characteristics of random parameter of antisymmetric laminated plates,derives out the displacement of laminated plates and the standard deviation between speed and accelerated speed by using lagrange equation.Dynamic respones problems are solved by spline collocation method,through choosing and the functions as mode shape function for various boundary conditions in several numerical examples and the results are compared with those in Newmark's method.And good result was got.