复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论，用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值，推导了复合材料层合板刚度阵，质量阵列式，阻尼阵列式，并由Lagrange方程导出了层合板的动力学方程，通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性，在Kirchhoff假设的基础上，对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计，数值算列验证了算法的有效性。

Analysis of Mechanics Properties of Composite Laminated Plates and Optimization of Angle Arrangement of plies

The geometric parameters of composite laminated plates are usually random due to various uncertainties in engineering structure. Thus, study of stochastic parameters of the mechanics properties of laminated plates and optimization analysis of these parameters is of important significance for reliability estimation of the structural design. Based on Kirchhoff classical theory of plates,the laminated plate with anti-symmetric multi-angle plies is studied. The spline finite element method is adopted, and the cubic B spline function is employed as the interpolation functions for three independent displacements. The stillness matrix, mass matrix, and the damping matrix of the laminated plate are derived. The dynamic equations are formulated by means of the Lagrange equation and then translated to an eigen-equation by using Rayleigh- Ritz method. The inherent frequencies and the dynamic response of the laminated plate arc obtained and analyzed. The nonlinear behavior of the laminated plate is discussed. The design optimization of the angle arrangement of plies is carried out. The numerical example shows the validity of this algorithm.