含圆孔有限厚度板的三维弹性应力场分析

通过三维有限元计算来研究含圆孔有限厚度板的圆孔边缘应力场,找出了应力集中系数与板的厚度、圆孔半径之间的关系,同时还分析了圆孔边缘的三维应力约束程度和三维应力约束区域的大小.研究结果表明:离面应力约束系数在板的中面最大,而在表面为0,三维应力约束影响区域的长度约为板厚的一半;应力集中系数沿厚度的分布是不均匀的,其最大值及位置与厚度有关;有限厚度板中面的应力集中系数及其最大值均大于平面应力或平面应变的应力集中系数;对含圆孔任意厚度板的应力集中问题,按平面应力或平面应变来考虑是不安全的;Sternberg等人对含圆孔任意厚度板的应力分布及应力集中系数的近似三维求解,仅适用于厚度较小的板,当板超过一定厚度时同样也是不安全的.

Three-Dimensional Elastic Stress Fields in Finite Thickness Plate with a Hole

The problems considered here are the finite width plates in different thickness with through-thickness hole subjected to a uniaxial tension. Detailed three-dimensional finite element computations were performed to investigate the stress fields in finite thickness plate with a hole, and the relations of the stress concentration factors with the plate thickness and the diameter of hole were revealed. The size of the constraint area and the constraint degree were also analyzed. The out-of-plane stress constraint factor tends to the maximum on the mid-plane and approaches to zero on the free plane, and the size of the three-dimensional effect region is about the half of the plate thickness. Stress concentration factors (SCF) distribute ununiformly through the plate thickness, the value and location of maximum SCF depend on the plate thickness. Both the SCF in the middle plane and the maximum SCF are greater than the one under plane stress or plane strain states, so it is unsafe to suppose a tensioned plate with finite thickness as one under-gone plane stress or plane strain. The Sternberg's approximate solution for 3D stress distributions and SCF in an infinite plate of arbitrary thickness with a circular hole is only suitable for thinner plate.