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具有不同边界条件厚、分层矩形板的三维线性小变形解己经用有限层法建立,这种方法是众所熟知的有限元法的发展。在这种方法中,将板分成许多层,并假没位移函数u、v和w采用X(x)Y(y)Z(z)的形式并由此求得一层元素的刚度矩阵,其中X(x)和Y(y)是满足板的适当边界条件的梁函数级数,而Z(z)取简单的线性多项式。相容质量矩阵也是按每层表示的。集合板所有分层的刚度矩阵和质量矩阵可组成一特征值矩阵,用中等容量的计算机即可求出频率和振型。
The three-dimensional linear small deformation solutions of thick, layered rectangular plates with different boundary conditions have been established using the finite layer method. This method is known as the development of the finite element method. In this method, the plate is divided into a number of layers, and the displacement function u, v, and w are assumed to be in the form of X(x)Y(y)Z(z) and the stiffness matrix of one layer of the element is thus obtained, wherein X(x) and Y(y) are the series of beam functions satisfying the proper boundary conditions of the plate, and Z(z) is a simple linear polynomial. The consistent quality matrix is also expressed on a per-layer basis. All hierarchical stiffness matrices and mass matrices of the assembly plate can form an eigenvalue matrix, and the frequency and mode shape can be found using a medium-capacity computer.