新的一个求解带孔薄板弹性问题的二维杂交应力单元  

A NOVEL2-DIMENSIONAL HYBRID STRESS ELEMENT FOR STRESS ANALYSES OF PLATE WITH HOLES

作　　者：曹子龙[1] 关玉璞[1] 陈伟[1] 

机构地区：[1]南京航空航天大学能源与动力学院江苏省航空动力系统重点实验室,南京210016

出　　处：《固体力学学报》2015年第4期329-336,共8页Chinese Journal of Solid Mechanics

摘　　要：建立了一个新的求解带圆孔薄板弹性问题的二维杂交应力单元,该单元为四节点四边形平面单元,名为P-HS4-8β.由极坐标系下的物理方程和几何方程求解出了一个极坐标方向的应力,通过将这个应力带入由Hellinger-Reissner原理推导的极坐标系下平面应力问题的能量方程中,得到消除了该应力的能量方程,基于这个能量方程建立杂交应力单元列式.根据圆孔边无外力条件和相容方程,推导了适用于求解带圆孔薄板问题的极坐标系下的二应力插值矩阵,并将此矩阵应用于新的有限单元列式中.数值算例表明新单元在求解孔边附近的应力时具有较高的精度.A novel 2-dimensional hybrid stress finite element is proposed for stress analyses of plate with holes. The new element,which is a 4-node quadrilateral plane element,is denoted as P-HS4-8β. First- ly, a stress in polar coordinates is obtained by physical equations and geometric .equations. Secondly, the ob- tained stress is introduced into energy functional of the Hellinger-Reissner variational principle for plane stress problem in polar coordinates. In the new energy functional, the number of the stress variables is 2. According to this,the hybrid stress finite element formation is established. A matrix for stress interpolation is obtained by the traction-free condition along the edge of hole and the compatibility equation, and is intro- duced into the hybrid stress finite element formation. Numerical results show that, the new method gives a good accuracy of the stress near the holes.

关 键 词：圆孔板 杂交应力元 二维应力分析 极坐标 有限元法 

分 类 号：O344.1[理学—固体力学]