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This paper proposes two novel approaches to perform more suitable sensitivityanalyses for discrete topology optimization methods. To properly support them,we introduce a more formal description of the Bi-directional EvolutionaryStructural Optimization (BESO) method, in which the sensitivity analysis isbased on finite variations of the objective function. The proposed approachesare compared to a naive strategy; to the conventional strategy, referred to asFirst-Order Continuous Interpolation (FOCI) approach; and to a strategypreviously developed by other researchers, referred to as High-Order ContinuousInterpolation (HOCI) approach. The novel Woodbury approach provides exactsensitivity values and is a better alternative to HOCI. Although HOCI andWoodbury approaches may be computationally prohibitive, they provide usefulexpressions for a better understanding of the problem. The novel ConjugateGradient Method (CGM) approach provides sensitivity values with arbitraryprecision and is computationally viable for a small number of steps. The CGMapproach is a better alternative to FOCI since, for appropriate initialconditions, it is always more accurate than the conventional strategy. Thestandard compliance minimization problem with volume constraint is consideredto illustrate the methodology. Numerical examples are presented together with abroad discussion about BESO-type methods.

Finite Variation Sensitivity Analysis for Discrete Topology Optimization of Continuum Structures