复合材料层合板的动态非线性分析及优化设计

Nonlinear Dynamic Analysis and Optimization of Composite Laminates

分别采用经典薄板理论、一阶剪切变形理论及高阶剪切变形理论对复合材料层合板进行动态非线性分析。根据位移场导出层合板的虚应变能、虚动能及虚功,由虚位移原理得出层合板的控制方程。结合Navier三角函数解求出四边简支层合板的固有频率;将纤维铺设角、跨厚比、弹性模量比对固有频率的影响进行比较分析;基于高阶剪切变形理论,用改进的适应度函数遗传算法对复合材料层合板的固有频率进行优化设计。结果表明:同经典薄板理论和一阶剪切变形理论相比,高阶剪切变形理论更能精确地预报结构的固有频率,优化后的层合板固有频率明显提高。

Dynamic nonlinear analysis has been made for composite laminated plates by using the classical plate theory, first-order shear deformation theory and higher-order shear deformation theory. According to the displacement field derived of laminates virtual strain energy, kinetic energy, and virtual work, governing equations of laminates are obtained by the principle of virtual displacement. Using Navier series, the natural frequency of a simply supported laminated plates is compared and analyzed for effect of fiber laying angle, length to thickness ratio, elastic modulus ratio on the natural frequencies. The optimal design is made for the natural frequency of laminated composite plates based on the higher-order shear deformation theory. The numerical results show that it is available to use genetic algorithm for optimal design of the composite laminates, and the natural frequency using higher-order shear deformation theory is more accurate than that of the classical plate theory and the first order shear deformation theory. The natural frequency of laminated structures is obviously increasing after optimal design.