考虑剪切影响的Mindlin板单元质量阵

Element mass matrix of Mindlin plate with shear effect

Mindlin板的弹性势能中含有剪切应变能项,而与动能相对应的质量阵中却不包含与剪切变形相对应的质量项,因此求得结构的固有频率偏高,在高阶频率时偏差更大。为了提高板壳结构频率的计算精度,本文提出在形成Mindlin板单元质量阵时将剪应变看作等效的转角项计入系统的动能中,从而使Mindlin板的质量阵中包含剪切变形的影响。算例表明:在同样的网格条件下,采用该质量阵计算得到的频率比采用原先的Mindlin板的质量阵计算得到的频率精度更高。本文还给出了四结点任意四边形考虑剪切影响的Mindlin板单元质量阵的构造方法。

The elastic potential energy of Mindlin plate includes shear strain energy item,but the mass matrix corresponding to kinetic energy does not contain the items related to the shearing deformation.Thus the obtained natural frequency is higher, especially in high orders.In order to improve the computational accuracy of natural frequencies of plate/shell structures,a method is given in when forming the mass matrix of Mindlin plate:taking the shear strain as the effective rotation into the kinetic energy of the system,making the mass matrix of Mindlin plate include the effect of shearing deformation.The computational example indicates that the accuracy of the frequencies calculated by the revised mass matrix is higher than that of the frequency calculated by the mass matrix of Mindlin plate. Also a conformation method of the mass matrix of 4-node arbitrary quadrilateral Mindlin plate element with the consideration of shear effect is presented.