On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Optimality Conditions for Simultaneous Topology and Shape Optimization
SIAM Journal on Control and Optimization
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Optimization of layout and shape of stiffeners in 2D structures
Computers and Structures
Optimization of the fatigue life of threaded connections by the positioning method
Structural and Multidisciplinary Optimization
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The topological sensitivity derivative of a functional expressed in terms of displacement, strain or stress fields and boundary tractions is derived for the case of an elliptical hole introduced in the plate. The derivative is specified with respect to the hole area, the length of ellipse axes and their orientation in terms of primary and adjoint state fields. The shape sensitivity derivative for a finite hole can be applied and the topological derivative with respect to the hole area is obtained in the limiting case. The transition to a plane crack occurs for vanishing length of minor axis and the topological derivative with respect to crack length is then derived from the general formulae. The results can be useful in optimal design procedures by selecting positions, shape and orientation of elliptical cutouts.