Finite variation sensitivity analysis for discrete topology optimization of continuum structures

Autor(es)

Cunha, Daniel Candeloro ^[1] ; de Almeida, Breno Vincenzo ^[1] ; Lopes, Heitor Nigro ^[1] ; Pavanello, Renato ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Computat Mech, Sch Mech Engn, R Mendeleyev 200, Cidade Univ, BR-13083860 Campinas - Brazil

• Tipo de documento: Artigo Científico
• Fonte: STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION; v. 64, n. 6 OCT 2021.
• Citações Web of Science: 0

Resumo

This paper proposes two novel approaches to perform more suitable sensitivity analyses for discrete topology optimization methods. To properly support them, we introduce a more formal description of the Bi-directional Evolutionary Structural Optimization (BESO) method, in which the sensitivity analysis is based on finite variations of the objective function. The proposed approaches are compared to a naive strategy; to the conventional strategy, referred to as First-Order Continuous Interpolation (FOCI) approach; and to a strategy previously developed by other researchers, referred to as High-Order Continuous Interpolation (HOCI) approach. The novel Woodbury Sensitivity (WS) approach provides exact sensitivity values and is a better alternative to HOCI. Although HOCI and WS approaches may be computationally prohibitive, they provide useful expressions for a better understanding of the problem. The novel Conjugate Gradient Sensitivity (CGS) approach provides sensitivity values with arbitrary precision and is computationally viable for a small number of steps. The CGS approach is a better alternative to FOCI since, for appropriate initial conditions, it is always more accurate than the conventional strategy. The standard compliance minimization problem with volume constraint is considered to illustrate the methodology. Numerical examples are presented together with a broad discussion about BESO-type methods. (AU)

• Processo FAPESP: 13/08293-7 - CECC - Centro de Engenharia e Ciências Computacionais
• Beneficiário: Munir Salomao Skaf
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 19/05393-7 - Maximização de frequências naturais e da separação de frequências de estruturas contínuas por um método de otimização topológica evolucionária
• Beneficiário: Heitor Nigro Lopes
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto
• Processo FAPESP: 19/19237-7 - Explorando as potencialidades de redes neurais artificiais na concepção topológica de metamateriais
• Beneficiário: Daniel Candeloro Cunha
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 20/07391-9 - Otimização topológica de dispositivos piezoelétricos utilizando metamateriais piezocompósitos
• Beneficiário: Breno Vincenzo de Almeida
• Modalidade de apoio: Bolsas no Brasil - Doutorado