求解不连续中厚板自由振动的微分容积单元法

基于区域叠加原理和微分容积法，发展了一种新型的数值方法——微分容积单元法，用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元，在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程．在相邻的单元连接处应用位移连续条件和平衡条件，引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程，由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程，并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。

Differential cubature element method for free vibration analysis of moderately thick plates with discontinuities

A new numerical method, the differential cubature element method has been developed based on the domain superposition method and the differential cubature method for free vibration analysis of moderately thick plates with geometric discontinuities. The basic idea of the differential cubature element method is to divide the entire variable domain into several sub-domains(elements) and to apply the differential cubature method for each element. Compatibility conditions are developed for the conjunction nodes on the interface boundaries of elements in order to connect the elements. As the plate boundary conditions are introduced, a set of linear algebraic homogeneous equations about the displacements of grid points can be derived, from which the natural frequencies of the plate can be calculated numerically. The convergent characteristics and accuracy of the differential cubature element method are carefully investigated for the solution of discontinuous thick plate vibration problems. The applicability of the present method has been demonstrated by comparing the differential cubature element method solutions with other existing numerical solutions or analytical solutions.