非协调实体壳元及其在振动分析中的应用

Incompatible Solid Shell Element and Its Application to Vibration Analysis

在八节点三维实体等参单元的基础上,为局部坐标系下的挠度位移分量附加单元内非协调位移项,构造了能很好反映横向剪切变形影响的八节点非协调实体壳单元,并将该单元用于板壳结构的振动分析。修正的应力—应变关系可有效地克服实体壳元的厚度自锁,高阶非协调位移项的附加可免除剪切和厚度锁闭。通过修正单元常应变矩阵和非协调形函数,保证单元在不规则网格时能通过常应力分片检验。数值算例表明:单元计算精度高,且对于厚板和薄板结构的动力分析都能适用。

A non-conforming solid shell element is developed for the vibration analysis of shell structures by introducing the assumption of Mindlin＇s plate into stress-strain relation of three-dimensional elastic problem. The local coordinate systems are used to conveniently introduce the incompatible displacement modes. Hierarchical incompatible modes selectively added to the ordinary 8-node solid element displacement assumptions are effective to obtain locking-free element. The present element has only four internal parameters. And the satisfaction of the patch test is ensured by using revision techniques of the incompatible strain matrix and shape function. To verify the validation and improvement of the proposed element, several numerical tests are carried out. Numerical results show that the element has the advantage of convergence, stability and higher precision and is suitable for simulating shell structures with a wide range of thickness.