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On the topological derivative in shape optimization. (English) Zbl 0940.49026
Author’s abstract: “The topological derivative for an arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can be used for solving shape optimization problems in structural mechanics”.

MSC:
49Q10Optimization of shapes other than minimal surfaces
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35J50Systems of elliptic equations, variational methods
35B37PDE in connection with control problems (MSC2000)
74P15Topological methods in solid mechanics
74K99Thin bodies, structures (solid mechanics)