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

Abstract

A concurrent topology optimization for thermoelastic structures with random and interval hybrid uncertainties is discussed in this work. A robust topology optimization method is proposed for structures composed of periodic microstructures under thermal and mechanical coupled loads. The robust objective function is defined as a linear combination of the mean and standard variance under the worst case for the robust optimization model. An efficient hybrid orthogonal polynomial expansion (HOPE) method is developed to evaluate the robust objective function. The sensitivities for the robust topology optimization are then calculated based on the uncertainty analysis. Three numerical examples are provided to verify the effectiveness of the proposed method, and the Monte Carlo scanning test is used to validate the numerical accuracy of our proposed method. For comparison purpose, the topology optimizations under deterministic assumptions are also provided for these examples to show the importance of considering hybrid uncertainties.

Topology optimization of thermo‐elastic structures with temperature‐dependent material properties under large temperature gradient

“…20 The elastic matrix is interpolated as a whole in more recent papers. 10,28,33,35,52,53 Here, the temperature-dependent elastic matrix D(T) is fitted as:…”

“…In fact, variations of Poisson's ratio can lead to significant changes in thermal stress 20 . The elastic matrix is interpolated as a whole in more recent papers 10,28,33,35,52,53 . Here, the temperature‐dependent elastic matrix D ( T ) is fitted as: $$$$ \mathbf{D}(T)=\sum \limits_{k=0}^{N^{(D)}-1}\kern.15em {\mathbf{C}}_k{T}^k, $$$$ where C k is the coefficient matrix and N ( D ) is the defined number of coefficient matrices.…”

“…24,25 Similar works were focused on the stress design for thermo-elastic problems. [26][27][28][29][30] Recently, complicated problems including geometrical nonlinearity, 31 uncertainty, 32,33 buckling, 34,35 and transient problems 36 have been addressed. The level-set method was also extended to deal with thermo-elastic problems and has become popular in the past five years.…”

On concurrent multiscale topology optimization for porous structures under hygro‐thermo‐elastic multiphysics with considering evaporation

“…76 Furthermore, multiscale thermo-elastic optimization was investigated. 77,78 Despite the fact that, numerical homogenization was also utilized to calculate the moisture diffusivity and hygral expansion coefficient, 79,80 yet hygro-elastic multiscale topology optimization is not yet investigated.…”

“…Moreover, some work was performed to extend the design problem to include heat conductivity extremum of the microscale structure as well as minimizing the microstructure's compliance 76 . Furthermore, multiscale thermo‐elastic optimization was investigated 77,78 . Despite the fact that, numerical homogenization was also utilized to calculate the moisture diffusivity and hygral expansion coefficient, 79,80 yet hygro‐elastic multiscale topology optimization is not yet investigated.…”