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基于一种修正的余能原理 ,建立了具有一个无外力圆柱面的新型三维层合杂交应力元 ,它可高效地分析具有圆柱形槽孔的厚、中厚、及薄层合材料的自由孔边三维应力分布 .根据建立的应力分量的应力函数表达式导出的单元应力场 ,严格满足层内以柱坐标表示的平衡方程、层间界面上应力连续条件、及圆柱面上无外力边界条件 .元间反力连续条件通过Lagrange乘子进行松弛 .层间位移保持连续 ,同时计入了横向剪切变形影响 .数值算例表明 ,该元不仅可以提供远较一般假定位移元及一般假定应力元准确的孔边应力分布 ,而且计算效率高、收敛快 ,同时 ,亦可用于多种圆弧形槽孔的应力分析 .
Based on a modified principle of residual energy, a new three-dimensional laminated hybrid stressor with a cylindrical surface without external force is established, which can efficiently analyze the free holes of thick, medium and thin laminated materials with cylindrical slots Edge three-dimensional stress distribution.According to the stress function expression of the established stress component, the stress field of the unit is strictly satisfied with the equilibrium equation expressed by the cylindrical coordinates in the layer, the continuous stress condition at the interface between layers and the no external boundary conditions on the cylindrical surface. The continuous reaction conditions of the metamaterials are relaxed by Lagrange multipliers, the displacement between layers remains continuous, and the influence of transverse shear deformation is taken into account. The numerical example shows that the element can not only provide far more displacement than the general assumed stressors Accurate hole edge stress distribution, and the calculation of high efficiency, fast convergence, but also can be used for a variety of arc-shaped slot stress analysis.