Search

The problem refers to an elastic infinite plate bounded by two oval holes, which is subjected to uniform surface tractions on the boundary of the holes and uniform tension and shear stress at infinity. By looking for a new mapping function, the considered region is conformally mapped onto an annulus, and a complex variable method is used to obtain the stress solution. The problem that an elastic infinite plate contains two circular holes or a circular hole and an oval hole is the special case of this article. The present solution has been validated by both published solutions for special cases and ANSYS software. Some computational examples are given to investigate the effects of the separation distance of the two holes, relative ratio of applied stresses, surface tractions on the boundaries, the size of a hole, shear stress at infinity and the loading orientation angle on the stress distribution of the hole boundaries. Practical significance of the solution is placed in the fact that it could be used as a quick-solver with high accuracy. [ABSTRACT FROM AUTHOR]

This paper presents an effective optimization approach based on the equi-stress criterion and conformal transformation to determine two equi-stress holes with different areas in an infinite plate subjected to biaxial loads at infinity and internal uniform pressure on hole boundaries. Conformal transformation in the complex variable method is used to map the outer domain of two holes in the physical plane onto an annulus in the image plane. Mathematically, the hole shapes are parameterized and expressed in one mapping function, therefore, the shape of two holes can be determined by obtaining the coefficients of the mapping function. In the process of optimization, the coefficients are used as design variables in the differential evolution (DE) algorithm to determine the hole shapes. As examples, the results has high accuracy, the optimal hole shapes under different conditions are given and the effect of each parameter are analyzed. What's more, the contour plots of principal stresses are presented to clearly show the stress distribution in the domain for the optimal hole shape. • Obtaining the shape of two equi-stress holes with different areas. • The equi-stress criterion and conformal transformation were used. • The process is simple and the scope of application is wide. • Presenting the hole shapes for different parameters. • Presenting the stress filed of the domain. [ABSTRACT FROM AUTHOR]