广义协调COONS曲面厚薄板通用单元振动分析

Vibration analysis of generalized conforming and COONS' surface thick/thin plate element

厚薄板通用单元一直是板壳有限元研究中的重点和难点。根据单向厚板的基本方程推导得到内含剪切变形因子的插值基函数,基于Mindlin-Reissner厚板理论并结合广义协调思想,通过第2类有限元COONS曲面构造法及挠度和转角导数相关法构造出一个新的有效的厚薄板通用矩形单元,采用集中质量矩阵法得到单元的质量矩阵。通过编制MATLAB程序,采用子空间迭代法计算结构在不同板厚时的自振频率。将计算结果与理论解和大型通用有限元软件ABAQUS解进行比较,该单元具有良好的数值计算结果,能够实现动力学范围内薄板、中厚板以及厚板完全通用,具有工程应用价值。

Thick/thin plate element has been the focus and difficulty in the study of shell finite element.According to the basic equation of one-way thick plate,the base function of interpolation containing the shear deformation factor is derived.Based on the Mindlin-Reissner thick plate theory and the idea of generalized coordination,the second kind of finite element COONS＇surface construction method and the derivative correlation method of deflection displacement and angular rotation displacement are used to derive a new effective thick/thin general rectangular plate element,then the lumped mass matrix method is used to get the mass matrix of the element.By using MATLAB programming,the natural frequencies of the plates with different thickness are acquired by a sub-space iteration method.Compared with the theoretical solution and the numerical value of ABAQUS,it is concluded that this element has good numerical calculation results,which can realize entirely common use for thin plate,cut deal and thick plate in dynamic range,and it has engineering application value.