带有加强筋的Mindlin板动态刚度阵法

以加筋中厚矩形板为研究对象，推导了加筋板的动态刚度阵，为动态刚度阵法提供一种新单元。板的运动微分方程由Mindlin厚板理论给出，同时还考虑了板平面内的振动。对于板上加强筋的处理，则通过Hamilton原理对板的运动方程作相应的修正，最终得到加筋板的运动微分方程。而方程的解析解直接用于单元刚度阵的推导，所得加筋板单元的动态刚度阵结合传统有限元方法的单元组装和求解方法即可用于计算整个结构的动力响应。此外，还给出了加筋板单元的均方响应计算公式，可用来计算结构的平均振动能量。最后通过数值算例验证本文方法，计算结果与传统有限元方法进行分析比较。

Dynamic Stiffness Matrix of Mindlin Plate with Intermediate Stiffeners

A dynamic stiffness matrix is presented for the analysis of stiffened moderate thick plate.The plate differential equations are based on Mindlin thick plate theory and include the in-plane vibrations.The stiffeners are taken to be smeared over the surface of the element,and Hamilton's principle is used to derive the appropriate modifications which must be made to the plate differential equations.The resulting differential equations are solved exactly to yield the dynamic stiffness matrix of the element.Any number of elements may be assembled to model the cross-section of a building-up structure by using classical finite element techniques.The equation governing the complete structure can also be solved by employing classical techniques to obtain the dynamic responses of structure.In addition,a formula for mean squared displacement of the stiffened plate is derived,and it can be used to calculate the averaged kinetic energy of the complete structure.The method is applied to a simply supported rectangular stiffened plate,and the calculated results are compared with those obtained by finite element method.