From Shape Variation to Topology Changes in Constrained Minimization: a Velocity Method Based Concept
نویسندگان
چکیده
The ability of velocity methods to describe changes of topology by creating defects like holes is investigated. For the shape optimization energy-type objective functions are considered, which depend on the geometry by means of state variables. The state system is represented by abstract, quadratic, constrained minimization problems stated over domains with defects. The velocity method provides the shape derivative of the objective function due to finite variations of a defect. Sufficient conditions are derived which allow us to pass the shape derivative to the limit with respect to diminishing defect, thus, to obtain the “topological derivative” of the objective function due to a topology change. An illustrative example is presented for a circular hole bored at the tip of a crack.
منابع مشابه
From shape variation to topological changes in constrained minimization: a velocity method-based concept
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