薄壁弯曲结构有限元计算精度研究

Finite element calculating precision study of thin-wall bending structure

基于h-p型有限元精度计算法,以薄壁弯曲结构为研究对象,系统地介绍了实体单元常见的分类方法及优缺点;通过理论公式推导了薄壁弯曲结构发生弹性和弹塑性变形时的位移和应力理论解;采用有限元法计算数值解,研究了影响有限元计算精度的因素和规律,并用算例证实了研究结果的合理性。研究结果表明:当单元类型、积分方式、阶次、长高比相同时,只有1层实体单元情况下得到的计算误差总是大于多层单元;只要严格控制单元长高比为1左右,单元层数不小于4层,采用一阶全积分六面体单元就可以控制位移及应力误差在5%以内;当采用一阶减缩积分六面体单元,只需2层单元就可以控制弹性位移误差在1%左右,但此时应力误差达30%以上,对于塑性变形,单元层数达6层时其位移误差仍达8%以上;对于二阶六面体及二阶四面体单元,只需2层单元,且不需严格控制单元长高比为1左右就可以使位移及应力计算误差在5%以内。

Base on h-p type finite element accuracy calculating method, the paper takes a thin-walled bending structure as research objective. The common classification method, the advantages and disadvantages of solid element are introduced. The displacement and stress of thin-walled bending structure under elastic and plastic deformation are calculated by theoretical formula and FEM respectively. After comparing the theoretical and FEM results, the laws and factors influencing the FEM precision are investigated. The results are validated by an example. The results show that： when element shape, integral type, length-to-height ratio, orders and layers are the same, the calculating precision of only one layer element is poor than the one of more layer; as long as the element length-to-height ratio is about one, and the element layer is more than three, the displacement and stress errors can be controlled within 5% for the one-order exact integral hexahedron element; for one order reduced integration hexahedron element, the elastic displacement and stress calculating errors are about 1% and 30% respectively under two element layers, and the plastic displacement calculating error is more than 8% even the element layer is six; for two order hexahedral and two order tetrahedral element, it only needs two element layers, and do not need to strictly control the element length-high ratio about 1 to control the displacement and stress calculation errors within 5%.