Thermoelastic Structures Research Articles

Comprehensive stress-driven multi-material problem for heat-sinking heterogeneous structures

In the realm of designing thermoelastic structures, particularly within aerospace and broader engineering fields, complex challenges arise from the diverse behaviors of heterogeneous materials and the intricate requirements of stress-based systems in coupled thermomechanical considerations. This study addresses these challenges by proposing a comprehensive methodology with two main contributions: (i) the development of an effective unified solution for stress-driven designs that tackle heat-sinking problems by accommodating a wide range of materials, from homogeneous to heterogeneous and (ii) the introduction of a robust stress-based optimization approach for multi-material problems within coupled thermomechanical systems. The methodology employs the well-established P-norm approach to consolidate heterogeneous stresses into a unified global metric. Additionally, it integrates effective material interpolation with the generalized Solid Isotropic Material with Penalization (SIMP) framework, resulting in comprehensive multi-material models that include the constitutive matrix, thermal conductivity, thermal stress coefficient, and thermoelastic stress distributions. To further enhance adaptability and flexibility, the methodology incorporates a polygonal discretization technique. Detailed sensitivity analyses, using the adjoint variable technique, are conducted to improve computational efficiency in gradient-based mathematical programming algorithms. The efficiency, robustness, and practicality of the proposed methodology are validated through numerical examples, demonstrating its effectiveness and reliability in real-world applications.

Additive manufacturing-driven simultaneous optimization of topology and print direction for thermoelastic structures considering strength failure

Abstract This paper presents a strength-based simultaneous optimization method for optimizing thermoelastic structural topology and print direction in the presence of anisotropy induced by additive manufacturing. The approach utilizes the bi-directional evolutionary structural optimization framework and defines design variables including element density and print-off angle. Firstly, an anisotropic thermoelastic constitutive model is established for finite element analysis. By introducing the Tsai–Hill failure criteria, the strength constraint to evaluate the stress level of additively manufactured anisotropic components is formulated. The P-norm aggregation function is employed to approximate the maximum strength failure coefficient. Then, the aggregated strength constraint is augmented to the optimization objective through a Lagrange multiplier. Sensitivity analysis of the new objective function with respect to the elemental design variables is performed, and an analytical approach is proposed to optimize the print-off angle. To improve the stability of the optimization procedure, a series of numerical algorithms and parameter updating strategies are developed. The effectiveness of our proposed method is demonstrated through typical numerical examples, highlighting a desirable match between the structural topology and the print direction can greatly improve the structural performance.

Transient heat conduction in multi-material topology optimization of thermoelastic structures involving dynamic constraints

This work presents a modified solid isotropic material with penalization (SIMP) for conducting dynamic-constrained multi-material topology optimization (MMTO) of thermoelastic structures subjected to transient thermal conduction. The novelty of this study is the multi-material optimization of instantaneous temperature conduction under specific frequency constraints, which has never been studied before. The proposed method has been developed for general models of multi-material interpolations such as thermal stiffness, heat capacity, and thermal stress coefficient. The temperature environment is formulated by applying prescribed mechanical and thermal loads that are exposed over a period of time. In this work, we focus on the objective of minimizing compliance in a transient heat conduction structure while simultaneously imposing constraints on the dynamics. With high temperatures, the stiffness of the optimization results decreases while stability is still guaranteed. The sensitivity of the objective function is subsequently calculated using the discretize-then-differentiate approach for the dynamic problem as well as the adjoint variable method. This study examines the impact of thermal fields and different time increments in conjunction with dynamic criteria. The outcomes of heat conduction result in notable alterations under identical dynamic constraint levels.

Uncertainty‐oriented thermoelastic topology optimization with stress constraint

AbstractThe material redistribution abilities of traditional deterministic topology optimization are effective in addressing stress‐related design issues in thermal elastic structures. However, uncertainties are inevitable in real‐world. The structural strength of a design, achieved through deterministic topology optimization, is highly susceptible to these uncertainties, which may result in failure. This article introduces a novel method for topology optimization in stress‐constrained thermoelastic structures, taking into account the uncertainties associated with heat sources and loads. We employ the Kieisselmeier–Steinhauser function to aggregate the stress constraint when constructing the performance function. In order to improve optimization efficiency, the sequential optimization and reliability assessment method is used to decouple the double‐layer loop reliability‐based topology optimization. Initially, we derive the derivative of stress‐based performance functions with respect to heat source and load uncertainty variables, thereby facilitating the use of modified chaos control for assessing structural reliability and imposing constraints. The adjoint method and chain rule are utilized to obtain the derivative information of the performance function with respect to density variables, guiding the topology updates. We present five design examples to demonstrate the effectiveness of the presented method. Monte Carlo simulations for the optimized results are performed to show that the presented method can obtain a structure that meets reliability requirements.

Multi-objective topology optimization for thermo-elastic systems based on periodic constraints

Thermo-elastic systems have a wide range of applications in various engineering fields. Traditional single-objective topology optimization (TO) design of thermos-elastic structures is difficult to achieve the combined optimum of multiple properties, and the non-periodic TO design of results are complex and difficult to fabricate. This paper introduces a multi-objective TO formulation based on density for designing thermo-elastic structures with periodic constraints, aiming to overcome the aforementioned issues. This paper assesses two competing weighted objective functions, the first function corresponds to structural and thermal compliance, while the second pertains to regional temperature and global stress. To solve the optimization issue, we utilize the p-norm function with a modified coefficient for evaluating the maximum temperature and stress values. Additionally, the adjoint variable method is employed to evaluate the sensitivity of various objectives, while the method of moving asymptotes (MMA) is used to update the design variables. Then the influence of different weight coefficients and subregion numbers regarding thermos-elastic coupled analysis is demonstrated through numerical examples. The results show that the complexity of the subregion features decreases as the number of subregions increases, and that changing both the number of subregions and the weighting coefficients results in changes in the overall structural performance. Finally, the geometric model is reconstructed using the TO results, and the structural performance is validated through the simulation of the reconstructed model. The results indicate that the TO results obtained by the method of this paper have predefined performance.

Concurrent Two–Scale Topology Optimization of Thermoelastic Structures Using a M–VCUT Level Set Based Model of Microstructures

Concurrent Two–Scale Topology Optimization of Thermoelastic Structures Using a M–VCUT Level Set Based Model of Microstructures

Multiscale concurrent topology optimization for thermoelastic structures under design-dependent varying temperature field

Multiscale concurrent topology optimization for thermoelastic structures under design-dependent varying temperature field

Topology optimization for transient thermoelastic structures under time-dependent loads

Topology optimization for transient thermoelastic structures under time-dependent loads

An Efficient and Robust Topology Optimization Method for Thermoelastically Damped Microresonators

The challenges of computational cost and robustness are critical obstacles in topology optimization methods, particularly for the iterative process of optimizing large-scale multiphysical structures. This study proposes an efficient and robust topology optimization method for minimizing the thermoelastic damping of large-scale microresonators. An evolutionary structural optimization method is adopted to passively determine the search direction of optimizing large-scale thermoelastic structures. To efficiently reduce the computational cost of the iterative process of an optimizing process, a model reduction method is developed based on the projection-based model reduction method whose reduced basis is generated within the Neumann series subspace. However, the projection-based model reduction method may be unstable when topology modifications are made during an iteration optimization process. To ensure robustness, a modal validation technique is first implemented in the iterative process to stabilize the iteration and narrow down the search domain, and a posterior evaluation of the Neumann series expansion is then developed to retain the convergence of the projection-based model reduction method. Furthermore, the efficiency and accuracy of the proposed topology optimization method are validated through numerical examples. Two large-scale numerical models are also used to demonstrate the advantage of the proposed method. It is found that large-scale thermoelastic structures with a phase-lag heat conduction law can be designed passively, precisely, and efficiently by using the proposed topology optimization method.

Investigation of thermoelastic compliances considering finite strain

Topology optimization of thermoelastic structures is of significance in many engineering applications such as for additive manufacturing, metamaterials, and soft robotics. To ensure that a structure performs adequately over a wide range of thermoelastic loading conditions and thermal expansion, incorporating the finite strain theory in the design strategy is critical. In this study, we investigate the two energy-based objective functions, namely the end compliance and strain energy under thermomechanical conditions. The numerical examples considered indicate that the optimized layout is highly dependent on the selected objective function; such differences among the layouts can be attributed to the manner in which the structure accommodates the changing temperature. The end compliance is minimized by leveraging the direction of the thermal load to offset the mechanical load, while the minimization of the strain energy contributes to the strength of the structure by limiting the thermal contribution to the overall stress within the structure. Furthermore, we show the effects of different strain assumptions on the optimality of layouts. Thus, this study reveals the significance of adopting each thermoelastic compliance and highlights the importance of accounting for structural nonlinearity when considering the thermal effect.

Multidisciplinary Topology Optimization Using Generative Adversarial Networks for Physics-Based Design Enhancement

AbstractThe computational cost of traditional gradient-based topology optimization is amplified for multidisciplinary design optimization (MDO) problems, most notably when coupling between physics disciplines is accounted for. To alleviate this, we investigate new methods and applications of generative adversarial networks (GANs) as a surrogate for MDO. Accepting physical fields from each physics discipline as input, the trained network produces an optimal design that closely resembles that of the iterative gradient-based approach. With this model as a baseline, we introduce a novel architecture that performs physics-based design enhancement of optimal single-physics designs to produce multiphysics designs. By providing the network with boundary conditions from a secondary physics discipline, we obtain multiphysics structures while avoiding the need for costly coupled multiphysics analysis, thereby generating significant savings in computational effort. We demonstrate our approach by designing a series of structures optimized for both thermal and elastic performance. With the physics-based design enhancement GAN, we obtain thermoelastic structures that outperform those produced by the baseline multiphysics GAN architecture.

Stress-based topology optimization of thermoelastic structures considering self-support constraints

A thermoelastic topology optimization method considering stress and manufacturing constraints is developed for engineering structures under thermo-mechanical coupled field in this paper. A design dependent non-uniform temperature field is considered for the heat conduction and the thermoelastic analysis during the topology optimization. Based on the solid isotropic material with penalization (SIMP), a topology optimization model is formulated to minimize the structural compliance under stress and overhang angle constraints. The overhang angle constraint to achieve the self-support property in additive manufacturing is established by connecting the elemental density values between the printing element and the corresponding support elements in the lower layer. The stress aggregation function is built to approximate the maximum stress value and an improved adaptive normalization scheme is applied to deal with the highly nonlinearity of the optimization. The sensitivity of the objective function and constraints with respect to the design variables are derived by the adjoint method, and the design variables are updated by the gradient-based optimization method. Moreover, a robustness scheme is proposed for the thermoelastic topology optimization to eliminate possible manufacturing issues such as “single node connection” and “thin rod” phenomena. Several typical numerical examples are provided to demonstrate the effectiveness of the proposed method in stress value reduction and overhang angle control. Meanwhile, the topology optimization with robustness scheme is also proved to result in more robust designs for manufacturing.

Reliability based topology optimization of thermoelastic structures using bi-directional evolutionary structural optimization method

The aim of this paper is to propose a novel computational technique of applying reliability-based design to thermoelastic structural topology optimization. Therefore, the optimization of thermoelastic structures' topology based on reliability-based design is considered by utilizing geometrical nonlinearity analysis. For purposes of introducing reliability-based optimization, the volume fraction parameter is viewed as a random variable with a normal distribution having a mean value and standard deviation. The Monte Carlo simulation approach for probabilistic designs is used to calculate the reliability index, which is used as a constraint related to the volume fraction constraint of the deterministic problem. A new bi-directional evolutionary structural optimization scheme is developed, in which a geometrically nonlinear thermoelastic model is applied in the sensitivity analysis. The impact of changing the constraint of a defined volume of the required design in deterministic problems is examined. Additionally, the impact of altering the reliability index in probabilistic problems is investigated. The effectiveness of the suggested approach is shown using a benchmark problem. Additionally, this research takes into account probabilistic thermoelastic topology optimization for a 2D L-shaped beam problem.

Topology optimization of thermoelastic structures under transient thermal loads limited to stress constraints

Topology optimization of thermoelastic structures under transient thermal loads limited to stress constraints

Multi-Head Self-Attention Generative Adversarial Networks for Multiphysics Topology Optimization

Machine learning surrogates for topology optimization must generalize well to a large variety of boundary conditions and volume fractions to serve as a stand-alone model. However, when analyzing design performance using physics-based analysis, many of the recently published methods suffer from low reliability, with a high percentage of the generated structures performing poorly. Disconnected regions of solid material between boundary conditions lead to unstable designs with significant outliers skewing the performance on test data. In this work, multi-head self-attention generative adversarial networks are introduced as a novel architecture for multiphysics topology optimization. This network contains multi-head attention mechanisms in high-dimensional feature spaces to learn the global dependencies of data (i.e., connectivity between boundary conditions). The model is demonstrated on design of coupled thermoelastic structures and its performance is evaluated with respect to the physics-based objective function used to generate training data. The proposed network achieves over a 36 times reduction in mean objective function error and an eight times reduction in volume fraction error compared to a baseline approach without attention mechanisms.

Efficient Design of Thermoelastic Structures Using a Krylov Subspace Preconditioner and Parallel Sensitivity Computation

The repeated updating of parametric designs is computationally challenging, especially for large-scale multi-physics models. This work is focused on proposing an efficient modal modification method for gradient-based topology optimization of thermoelastic structures, which is essential when dealing with their complex eigenproblems and global sensitivity analysis for a huge number of design parameters. The degrees of freedom of the governing equation of thermoelastic structures is very huge when its parametric partial differential equation is discretized using the numerical technique. A Krylov subspace preconditioner is constructed based on the Neumann series expansion series so that the thermoelastic eigenproblem can be solved in an efficient low-dimension solver, rather than its original high-fidelity solver. In the construction of Krylov reduced-basis vectors, the computational cost of the systemic matrix inverse becomes a critical issue, which is solved efficiently by means of constructing a diagonal systemic matrix with the lumped mass and heat generation submatrices. Then, the reduced-basis preconditioner can provide an efficient optimal solver for both the thermoelastic eigenproblem and its eigen sensitivity. Furthermore, a master-slave pattern parallel method is developed to reduce the computational time of computing the global sensitivity numbers, and therefore, the global sensitivity problem can be efficiently discretized into element-scale problems in a parallel way. The sensitivity numbers can thus be solved at the element scale and aggregated to the global sensitivity number. Finally, two case studies of the iterative topology optimization process, in which the proposed modal modification method and the traditional method are implemented, are used to illustrate the effectiveness of the proposed method. Numerical examples show that the proposed method can reduce the computational cost remarkably with acceptable accuracy.

Analysis and optimization of thermoelastic structures with tension–compression asymmetry

Many engineering and biological materials have been found to have tension–compression asymmetry properties. An extension of the linear thermoelastic behavior called a bi-modulus constitutive model is proposed to study the impact of thermo-mechanical coupling in such materials and structures. The well-posedness of the corresponding bi-modulus thermoelasticity problems is confirmed via a variational approach. An efficient numerical analysis method is developed for such nontrivial material behavior and is further employed for structural topology optimization. The importance of the proposed analysis and design framework is demonstrated by the significant impact of the tension–compression asymmetry and thermal effect on structural responses and optimum structural configurations.

Multi-Material Topology Optimization of Thermo-Elastic Structures with Stress Constraint

This paper proposes a multi-material topology optimization formulation for thermo-elastic structures considering coupled mechanical and uniform thermal loads. The ordered-SIMP multiple materials interpolation model is introduced, combined with examples considering structural volume minimization under stress constraints. The p-norm function with the adjusted coefficient was adopted to measure the global maximum stress. The adjoint variable method is presented to discuss the sensitivity of stress constraints, and the method of moving asymptotes (MMA) is utilized to update the design variables. The results demonstrate that clear topologies are obtained for complicated multiple material combinations with various temperature values. Meanwhile, the optimized configuration with stress constraints has clear sensitivity to uniform temperature variations. Therefore, the proposed model demonstrates the necessity of a thermo-elastic model influenced by temperature in optimization.

Reliability-Based Topology Optimization of Thermo-Elastic Structures with Stress Constraint

Traditional topology optimization of thermo-elastic structures is based on deterministic conditions, without considering the influence of uncertainty factors. To address the impact uncertainty on structural strength, a reliability-based topology optimization of thermo-elastic structure with stress constraint is proposed. The probabilistic uncertainty quantities are associated with the structural material property, mechanical loads and the thermal stress coefficient with the topology optimization formulation considering volume minimization and stress constraint. The relaxation stress method combined with normalized p-norm function is adopted to condense whole element stresses into the global stress measurement that approximates the maximum stress. The adjoint variable method is utilized to derive the sensitivity of the stress constraint and the optimization problem is solved by the method of moving asymptote (MMA). Finally, several numerical examples are presented to demonstrate the effectiveness and validity of the proposed approach. Compared with the deterministic design, the reliability design has distinct topological configurations and the optimized structures maintain a higher reliability level.

Sensitivity analysis and design optimization of 3T rotating thermoelastic structures using IGBEM

<abstract> <p>In this study, the isogeometric boundary element method (IGBEM) based on non-uniform rational basis spline (NURBS) is used to perform shape design sensitivity and optimization of rotating three-temperature (3T) thermoelastic structures. During the optimization process, the shape design sensitivity within the IGBEM formulation was derived to include precise geometries and greater continuities. It was found through the application of the IGBEM that the shape design velocity has a significant effect on accuracy of the obtained shape design sensitivity. As a result, the developed shape design sensitivity analysis (SDSA) technique based on the considered IGBEM formulation outperforms the computational solution based on the traditional SDSA method. The isogeometric shape sensitivity and optimal design for a complicated three-temperature thermoelastic problem in rotating structures are investigated. The impact of rotation on the thermal stress sensitivity, optimal three-temperature, optimal displacement and optimal three temperature thermal stress distributions are established. It is shown that the SDSA derived using IGBEM is efficient and applicable for most three-temperature thermoelastic optimization problems.</p> </abstract>