Level-set topology optimization considering nonlinear thermoelasticity

Abstract

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.

A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method

“…Hybrid-TO where ∆C reg | n represents the stabilising part of the regularised elasticity tensor (34) and C| 0 denotes the elasticity tensor in the origin (i.e. F = I).…”

“…In addition, Figure 7 shows the spherical parametrisation of the non-stabilised elasticity tensor C| n in a region where the stabilisation indicator s reaches its maximum value. Furthermore, its regularised counterpart C solid reg n and the purely stabilisation component of the latter ∆C solid reg n (see equations ( 33) and (34)) are also displayed. For a spherically parametrised vector U , spherically parametrised elasticity tensor C(C) is defined as…”

“…For instance, the additive hyperelasticity technique presented in [33]; the combination of a polyconvex strain energy density in conjunction with an ad-hoc relaxation introduced in [27] to stabilise those excessively distorted elements of an underlying Finite Element mesh, or an original interpolation scheme for the strain energy density as proposed in [15]. We also mention the very recent work [34] on the optimal design of hyperelastic structures in the context of thermoelasticity.…”

Concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties

“…Later, researchers also developed various topology optimization methods for thermo-mechanical design problems considering transient response, heat conduction properties, manufacturability, nonlinearity, and so forth. [15][16][17][18][19] These achievements are mostly based on solid materials, which limit the capability and functionality of the optimal structural designs. The concurrent designs in both macro structural and micro material levels provide promising means to acquire new lightweight and high-performance structures.…”

A density‐based boundary evolving method for buckling‐induced design under large deformation

“…Luo et al 44 presented an effective TO methodology for the compliance design of hyperelastic material with frictionless contact supports. Chung et al 45 proposed a level‐set‐based TO method for designing structures undergoing large deformation due to thermal and mechanical loads, where the thermo‐mechanical response can be controlled via TO. Xue et al 46 performed structural TO under finite deformation using explicit geometry description, where a MMV‐based approach is developed for designing large deformation mechanism.…”