Optimal free-form shapes for holes in flat plates under uniaxial and biaxial loading

Abstract

This paper presents new and transferable design data defining precise optimal free-form shapes for holes in large and finite width plates under biaxial and uniaxial loading conditions respectively. An iterative two-dimensional finite element gradientless shape optimization procedure was used to obtain the optimal shapes, which offer the lowest possible stress concentration, subject to geometric constraints. Precise non-dimensional coordinates are given for a range of hole aspect ratios and are presented in tabular form that allows them to be easily used by designers. The optimal shapes were determined both with and without minimum radius of curvature constraints. Optimal shapes in large plates were found to provide up to a 28 per cent reduction in peak local stress over elliptical shapes of the same aspect ratio. For finite width plates the reduction in peak local stress was as high as 44 per cent. The results obtained are applicable to both the initial design of components with cut-outs and the shape reworking of existing components to remove damage.

Inverse Problem of Elasticity for a Plate Weakened by Hole and Cracks

“…providing uniqueness of displacements when tracing the contours of the inner crack. Under additional conditions (16), the singular integral equation 15is reduced [29][30][31] to the system of algebraic equations with respect to approximate values 0 1 ( ) ( = 1, 2, . .…”

“…If the crack with one end arrives at the hole surface, then equality (16) and (24) in each approximation is replaced by an additional condition expressing the finiteness of stresses at the edge crack on the hole's contour.…”

Investigation on the Material Failure in a Small Scale Automotive Camera Module via Root Cause Analysis and Experimental Validation

“…Topology optimization can be incorporated in the early phase of the product development process to propose an optimized design [31]- [33]. Several methods have been introduced for topology optimization of complex continuum structures, such as the level set method, the evolutionary structural optimization method, the solid isotropic microstructure with penalization (SIMP) method and so on [34], [35].…”