Topological derivative-based topology optimization of structures subject to design-dependent hydrostatic pressure loading

• Published in: Structural and multidisciplinary optimization Vol. 56; no. 1; pp. 47 - 57
• Main Authors: Xavier, M., Novotny, A. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2017; Springer Nature B.V
• Subjects: Algorithms; Asymptotic series; Computational Mathematics and Numerical Analysis; Cracks; Design optimization; Engineering; Engineering Design; Hydrostatic pressure; Inclusions; Modulus of elasticity; Nucleation; Perturbation; Perturbation methods; Plane strain; Plane stress; Potential energy; Pressure dependence; Research Paper; Theoretical and Applied Mechanics; Topology optimization; Design-dependent loading; Structural topology optimization; Hydrostatic pressure; Topological derivatives
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-016-1646-4

In this paper the topological derivative concept is applied in the context of compliance topology optimization of structures subject to design-dependent hydrostatic pressure loading under volume constraint. The topological derivative represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes, inclusions, source-terms and cracks. In particular, the topological asymptotic expansion of the total potential energy associated with plane stress or plane strain linear elasticity, taking into account the nucleation of a circular inclusion with non-homogeneous transmission condition on its boundary, is rigorously developed. Physically, there is a hydrostatic pressure acting on the interface of the topological perturbation, allowing to naturally deal with loading-dependent structural topology optimization. The obtained result is used in a topology optimization algorithm based on the associated topological derivative together with a level-set domain representation method. Finally, some numerical examples are presented, showing the influence of the hydrostatic pressure on the topology of the structure.