无单元法求解正交各向异性板自由振动问题

Element Free Method in Vibration Problem of Anisotropic Plates

无单元法是一种新出现的数值方法。本文对无单元法的数学基础—滑动最小二乘法进行了详细的研究,推导了无单元法的形函数,并对一些关键问题,如权函数的选取,正交基函数,边界条件,数值实现方法等得出了研究结论。用无单元法研究了正交各向异性板的自由振动问题,由动力学变分原理和滑动最小二乘法导出了正交各向异性板的无单元法质量矩阵和刚度矩阵,编制了相应的计算程序,通过计算实例验证了该方法的有效性。

Element free method（EFM） is a new numerical method. The fundamental theory of Moving Least Squares Method which is the mathematical basis of EFM was studied thoroughly, and the shape function of EFM was also devised by this paper. Detailed research was conducted on some key problems, such as selection of weight function, selection of influence radius of nodes, orthogonal basis function, boundary condition and method of numerical realization, the results of these problems were obtained. The vibration problem of orthogonal anisotropic plates was studied by use of Element free Method. The corresponding mass matrices and stiffness matrices of orthogonal anisotropic plates were derived by using dynamic variational principle and moving least squares method, and the computer program was also developed. Numerical examples show that the method is reasonable and feasible on vibration problem of orthogonal anisotropic plates.