Thermoelastic Topology Optimization Research Articles

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.

Thermoelastic topology optimization of structural components at elevated temperatures considering transient heat conduction

Thermoelastic topology optimization of structural components at elevated temperatures considering transient heat conduction

Thermoelastic topology optimization for structures with temperature-dependent material properties

Thermoelastic topology optimization for structures with temperature-dependent material properties

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.

Thermo-elastic topology optimization of continuum structures subjected to load allocation constraints

Thermo-elastic topology optimization of continuum structures subjected to load allocation constraints

Stress-constrained thermo-elastic topology optimization of axisymmetric disks considering temperature-dependent material properties

The lightweight design of turbine disks is challenging due to the extreme thermomechanical service environment which leads to high stress and temperature-dependency of material properties. The simplified engineering design method which uses uniform material properties at fixed temperature would lead to either unsafe or conservative designs. In this article, a stress-constrained thermo-elastic topology optimization method is proposed for axisymmetric disks considering temperature-dependent material properties. The temperature-dependent property functions fitted from the material test data are used to determine the material properties of each element according to the element’s average temperature. The strain energy constraint is added into the optimization formulation in order to prevent isolated material and severe violation of stress constraint caused by abrupt volume change. The Helmholtz filter and Heaviside projection are utilized to eliminate the checkerboard pattern and ensure distinct solid/void interfaces in the optimization results, respectively. The geometry extraction from the optimization results is easily implemented by the Least Square Fitting with B-spline Method. In the illustrative examples, the effectiveness of the proposed method in obtaining lighter disk designs is demonstrated in comparison to the design obtained by the simplified engineering method and the traditional single-web disk design. The ability of the proposed method to deal with arbitrary nonuniform temperature field is also demonstrated and it is learned that lighter disk design can be obtained if the temperature field has a lower radial temperature gradient at the disk hub.

A multi-material topology optimization with temperature-dependent thermoelastic properties

This is a study on the development of a novel multi-material topology optimization scheme considering temperature-dependent thermoelastic properties for engineering structure design. Two cases, a three-point-bending beam under a uniform temperature field and a cantilever beam under a non-uniform temperature field, are investigated for the effects of thermoelastic properties on topology optimization. The proposed optimization scheme is compared with two existing topology optimization approaches: conventional topology optimization and thermoelastic topology optimization. The results show that the temperature-dependent elastic modulus dominantly influences the design optimization outcomes, in terms of material distribution, structural shape and compliance, while the temperature-dependent thermal expansion coefficient has a much more crucial impact on determining the material distribution and structural geometry than on compliance. Taken together, the findings demonstrate that the developed topology optimization scheme can be used to design thermally sensitive multi-materials in industrial applications, e.g. aerospace structures under high temperature and polymers in additive manufacturing.

An all-movable rudder designed by thermo-elastic topology optimization and manufactured by additive manufacturing

In high-speed vehicles, rudders often endure both aerodynamic pressure and thermal loads. The innovative design of rudders is of great importance for the performance of the whole vehicle. In this work, thermo-elastic topology optimization is adopted to design a typical all-movable rudder structure. The compliance of the rudder skin is considered to be a new objective and the moment of inertia of the rudder is constrained during optimization to ensure its fast response to instructions of the control system. Then sensitivity analysis of the structural compliance and the moment of inertia is carried out. Optimization results show that thermal load has a great effect on the optimized configuration and minimizing the compliance of the rudder skin gives much better design than minimizing the global compliance. Subsequently, an engineering-oriented post-processing is conducted to make the optimized design suitable for additive manufacturing. An appropriate printing direction is selected based on the layout of the optimized ribs and certain ribs are reshaped with fillets to make the rudder free of internal support structures. Besides, according to a secondary topology optimization of the ribs and the stress distribution, a set of powder-discharge holes are properly opened on the ribs so that all cavities within the rudder are connected and the metal powder inside the rudder can be discharged with little effort after manufacturing. Finally, the optimized design is successfully printed using Selective Laser Melting, demonstrating the proposed post-processing is effective for additive manufacturing.

Stress constrained thermo-elastic topology optimization based on stabilizing control schemes

This article proposes two effective stabilizing control schemes for addressing the stress constrained thermo-elastic topology optimization in a non-uniform temperature field. Based on the density interpolation scheme, two linear elastic equations for coupling a thermo-elastic problem are considered. For comparison, different topology problem formulations for minimizing compliance or volume subject to stress constraints are solved. By virtue of a stabilization transform method, two stabilizing control schemes combined with the grouped aggregation method are developed to handle the challenging difficulties stemming from the local nature of highly nonlinear stress constraints. Moreover, the adjoint method is adopted to perform the sensitivity analysis. The design variables are updated by utilizing the method of moving asymptotes. The results of several typical numerical examples verify the validity of the proposed methodology, including the present stabilizing control schemes which can be employed to obtain clear topological design and fast convergence rate for thermo-elastic coupling problems. Meanwhile, compliance minimization design with stress constraints is appropriate to achieve balance between stress level and stiffness.

A B-spline multi-parameterization method for multi-material topology optimization of thermoelastic structures

A B-spline multi-parameterization method (MPM) is presented in this paper for topology optimization of thermoelastic structures. As thermoelastic topology optimization belongs to a kind of design-dependent problems that are complicated to deal with, this method is aimed to solve thermoelastic problems with multiple materials by means of B-spline parameterization that integrates together the recursive multiphase material interpolation (RMMI) and the uniform multiphase material interpolation (UMMI) schemes. The commonly used discrete pseudo-density variables related to the finite element model are thus replaced with continuous pseudo-density fields dominated by control parameters in the B-spline space. In this sense, B-spline multi-parameterization is used for the first time to represent multiple pseudo-density fields and multi-material properties including elasticity matrix and thermal stress coefficient. Compared with traditional pseudo-density method, the current method has the advantage of not only attaining a reduction of design variables in number but also achieving a regularized distribution of pseudo-density fields with a clear material layout over the whole structure domain. Numerical results show that the stable convergences are achieved with the avoidance of gray elements, checkerboards, and multi-material overlapping owing to the high continuity of B-spline preserved for multi-material distributions. Besides, it is found that the RMMI scheme distributes less stiff materials around stiff materials, while the UMMI scheme tends to gather less stiff materials together.

An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing

Combination of topology optimization and additive manufacturing technologies provides an effective approach for the development of light-weight and high-performance structures. A heavy-loaded aerospace bracket is designed by topology optimization and manufactured by additive manufacturing technology in this work. Considering both mechanical forces and temperature loads, a formulation of thermo-elastic topology optimization is firstly proposed and the sensitivity analysis is derived in detail. Then the procedure of numerical optimization design is presented and the final design is additively manufactured using Selective Laser Melting (SLM). The mass of the aerospace bracket is reduced by over 18%, benefiting from topology and size optimization, and the three constraints are satisfied as well in the final design. This work indicates that the integration of thermo-elastic topology optimization and additive manufacturing technologies can be a rather powerful tool kit for the design of structures under thermal-mechanical loading.

Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set

Engineering structures must often be designed to resist thermally induced stresses. Significant progress has been made on the design of such structures through thermo-elastic topology optimization. However, a computationally efficient framework to handle stress-constrained large-scale problems is lacking. The main contribution of this paper is to address this limitation. In particular, a unified topological-sensitivity (TS) based level-set approach is presented in this paper for optimizing thermo-elastic structures subject to non-uniform temperatures. The TS fields for various thermo-elastic objectives are derived, and, to address multiple constraints, an augmented Lagrangian method is developed to explore Pareto topologies. Numerical examples demonstrate the capability of the proposed framework to solve large-scale design problems. Comparison is made between pure elastic problems, and its thermo-elastic counterpart, shedding light on the influence of thermo-elastic coupling on optimized topologies.

Stress-based design of thermal structures via topology optimization

The design of thermal structures in the aerospace industry, including exhaust structures on embedded engine aircraft and hypersonic thermal protection systems, poses a number of complex design challenges. These challenges are particularly well addressed by the material layout capabilities of structural topology optimization; however, no topology optimization methods are readily available with the necessary thermoelastic considerations for these problems. This is due in large part to the emphasis on cases of maximum stiffness design for structures subjected to externally applied mechanical loads in the majority of topology optimization applications. In addition, while limited work in the literature has investigated thermoelastic topology optimization, a direct treatment of thermal stresses is not well documented. Such a treatment is critical in the design of thermal structures where excessive thermal stresses are a primary failure mode. In this paper, we present a method for the topology optimization of structures with combined mechanical and thermoelastic (temperature) loads that are subject to stress constraints. We present the necessary steps needed to address both the design-dependent thermal loads and accommodate the challenges of stress-based design criteria. A relaxation technique is utilized to remove the singularity phenomenon in stresses and the large number of stress constraints is handled using a scaled aggregation technique that has been shown previously to satisfy prescribed stress limits in mechanical problems. Finally, the stress-based thermoelastic formulation is applied to two numerical example problems to demonstrate its effectiveness.