Explicit topology optimization of nearly incompressible materials using polytopal composite elements. (November 2020) - Hoang, Van-Nam; Nguyen, Hoang B.; Nguyen-Xuan, H.
Highlights: Displacement-based PCEs for accurately modeling incompressible materials. Mitigating volumetric locking issue by a polynomial projection of compatible strains. A robust topology optimization approach with PCEs for incompressible material designs. Discarding load-transferring gray-elements. No requiring filtering techniques or perimeter constraints as in the SIMP. Abstract: In this paper, an efficient explicit topology optimization approach to nearly incompressible materials was proposed. The crucial idea is based on a smooth projection of discrete moving morphable bars (MMBs) onto an analytical grid of polytopal composite finite elements (PCEs). The PCEs, which are built with piecewise linear shape functions and assumed strain fields, aim to mitigate the inherent volumetric locking issue and accurately model nearly incompressible materials. Unlike most existing techniques that use the mixed displacement-pressure formulation and conventional topology optimization, the current method is based on the pure displacement formulation and explicit topology optimization with only hundreds of design variables. Numerical results demonstrated that the proposed approach works stably and produces proper optimal designs of nearly incompressible structures without the mesh-dependence while filtering techniques or perimeter constraints are not required. The investigation promises the potential for solving a wide range of incompressible problems.