Optimality Conditions for Shape and Topology Optimization Subject to a Cone Constraint

• Published in: SIAM journal on control and optimization Vol. 48; no. 6; pp. 4056 - 4077
• Main Authors: Amstutz, Samuel, Ciligot–Travain, Marc
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2010
• Subjects: Calculus of variations and optimal control; Derivatives; Exact sciences and technology; Functionals; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematics; Optimization; Physics; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Studies; Topology; Topology optimization; Geometrical shape; topological derivative; Sensitivity analysis; Cone; shape optimization; Necessary and sufficient condition; Constraint; shape derivative; Multiobjective programming; 35J05; Topology; Partial differential equation; Optimization; Lagrange multiplier; 49K20; Variational calculus; Optimality condition; Optimality criterion; topology optimization; 49Q10

This paper provides first order necessary optimality conditions for simultaneous shape and topology optimization subject to a cone constraint. These conditions are expressed with the help of the shape and topological derivatives of the objective and constraint functionals. Several examples of applic...