Multimaterial topology design for optimal elastic and thermal response with material‐specific temperature constraints

Abstract

Summary We present an original method for multimaterial topology optimization with elastic and thermal response considerations. The material distribution is represented parametrically using a formulation in which finite element–style shape functions are used to determine the local material properties within each finite element. We optimize a multifunctional structure that is designed for a combination of structural stiffness and thermal insulation. We conduct parallel uncoupled finite element analyses to simulate the elastic and thermal response of the structure by solving the two‐dimensional Poisson problem. We explore multiple optimization problem formulations, including structural design for minimum compliance subject to local temperature constraints so that the optimized design serves as both a support structure and a thermal insulator. We also derive and implement an original multimaterial aggregation function that allows the designer to simultaneously enforce separate maximum temperature thresholds based upon the melting point of the various design materials. The nonlinear programming problem is solved using gradient‐based optimization with adjoint sensitivity analysis. We present results for a series of two‐dimensional example problems. The results demonstrate that the proposed algorithm consistently converges to feasible multimaterial designs with the desired elastic and thermal performance.

Multiphysics design of programmable shape-memory alloy-based smart structures via topology optimization

“…In terms of the multi-material case, the material distribution is represented parametrically using the Shape Functions with Penalization (SFP) method [45,46]. In the case of four material candidates for example, the relative volume fraction of a given candidate material, µ (j) , j = 1, 2, 3, 4, can be expressed as 24.…”

An Artificial Neural Network Approach for Generating High-Resolution Designs From Low-Resolution Input in Topology Optimization

“…The domain is discretized into a uniform grid containing 6144 square elements. The thermal structures are optimized for maximum average temperature throughout the material domain, based on a linear, steady-state, thermal conductivity analysis [33], and subject to a constraint on the material volume. We test the neural network using two different structures, both optimized using the same boundary conditions, but containing different materials with different thermal conductivity values, and constrained to different volume fractions.…”

Topology optimization of thermo‐elastic structures considering stiffness, strength, and temperature constraints over a wide range of temperatures

“…Moreover, two conflicting design criteria, that is, the overall stiffness and heat conduction, are combined into objective function to investigate the effect of heat conduction on structure and material 17 . Recently, multi‐material TO with elastic and thermal response was presented by Kang and James 18 . The uncoupled finite element analyses were carried out in parallel to compute the structural and thermal responses.…”

“…17 Recently, multi-material TO with elastic and thermal response was presented by Kang and James. 18 The uncoupled finite element analyses were carried out in parallel to compute the structural and thermal responses. For the TO of coupled thermo-elastic problems, minimum structural compliance with volume and temperature constraints was proposed to achieve the design meeting stiffness and temperature requirements.…”