基于局部移动Kriging无网格方法的层合板自由振动分析

利用基于局部移动Kriging插值无网格法对层合板自由振动进行了数值分析，基于一阶剪切层合理论导出了层合板振动的控制方程和边界条件，进一步得到了自由振动的离散化特征方程。由于Kriging插值函数具有Kronecker delta函数性质，可以直接施加本质边界条件。通过本文给出的方法，对不同边界条件、不同跨厚比、不同材料参数和铺设角度的层合板的振动频率进行了计算，均得到满意结果。最后用该方法对层合板的铺设角度进行优化设计，得到了与已有文献完全一致的优化结果。数值结果充分表明了无网格Kriging方法分析层合板自由振动问题的有效性和高精确度。

Free vibration analysis of laminated composite plates by local moving Kriging meshless method

The local moving Kriging interpolation meshless method is used to numerically analysis the natural frequencies of laminated composite plates in this paper.The governing equations and boundary conditions of the laminated plates are derived based on the first order shear theory.Then the discrete characteristic equations are obtained by the collocation method.As the Kriging interpolation function has the Kronecker delta function properties,the essential boundary conditions can be applied directly.Natural frequencies of the laminated composite plates with various boundary conditions,side-to-thickness ratios,material parameters and laying angle are computed by present method,and the numerical results are all well.Finally,the optimal angle design of laminated composite plates is studied by present method,and the optimization results are agreed well with the existing solutions in the literature.Numerical experiments demonstrate that the present method for free vibration analysis of laminated plates is efficient and highly accurate.