Stress distribution analysis and optimization for composite laminate containing hole of different shapes

Abstract

This paper proposes a flexible analytical method to obtain the circumferential stress of hole's edge in composite laminate, which can provide convenience for the optimization of hole's shape meanwhile. Firstly, different shapes of hole are expressed in one map function based on the conformal transformation. Secondly, stress function method is applied to the anisotropic elastic theory, which derives the stress expressions to calculate arbitrary point's stress in equivalent anisotropic plate. Thirdly, the circumferential stress of hole's edge in composite laminate can be calculated by combining the map function with the stress expressions. This method is verified by finite element simulation for the hole of circle, triangle and square, which draw a conclusion that circle hole is not always the best choice for aeronautical structure design. Meanwhile, an optimal shape of hole is obtained by the mentioned method with help of gradient descent algorithm and mesh deformation technique. The optimization result is validated by simulation and it meets the conclusion identically, which also means the method's accuracy is reliable.