Topological Derivatives in Shape Optimization

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Shape optimization of a layer by layer mechanical constraint for additive manufacturing (2017, background): “[2, 23]), the (tedious) proof of these formulae is not so easily found in the literature in the context of the linearized elasticity system.”
Distributed shape derivative via averaged adjoint method and applications (2015, background): “1) is the Eshelby energy momentum tensor in continuum mechanics introduced in [14]; see also [33].”
Topological derivatives applied to fluid flow channel design optimization problems (2016, methodology): “Then, we assume that a given shape functional j(χε(x̂)), associated to the topologically perturbed domain, admits the following topological asymptotic expansion [31] j(χε(x̂)) = j(χ) + f(ε)DT j(x̂) + o(f(ε)) , (2.”