新的一个求解带孔薄板弹性问题的二维杂交应力单元

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，得到了消除了该应力的能量方程，基于这个能量方程建立了杂交应力单元列式。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 2-DIMENSIONAL HYBRID STRESS ELEMENT FOR STRESS ANALYSES OF ORIFICE PLATE

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. Firstly, a stress in polar coordinates is obtained by physical equations and geometric equations. Secondly, the obtained 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 introduced into the hybrid stress finite element formation. Numerical results show that, the new method gives a good accuracy of the stress near the holes.