Thermoelastic Structures Research Articles

Optimized high thermal insulation by the topological design of hierarchical structures

This study proposes a new method for the topological design of hierarchical structures with high performance in thermal insulation. Firstly, a three-layer design strategy including macro-, meso- and micro-layers is presented. The macroscopic structures are formed by periodically arranged mesoscopic structures, whose topological configurations are determined by the material microstructures provided at the micro-level. The microstructures and mesoscopic structures are independent of the optimization, to ensure an efficiency of the hierarchical design process. Secondly, four classical microstructures are considered to provide the normalized equivalent thermal conductivities with arbitrary densities between 0 and 1. Then, the floating projection technique is employed to find the optimal topologies of the thermoelastic structures. The objective function is defined by maximizing the thermal compliance, subjected to the volume constraint that is added to the objective function through the Lagrange multiplier. The sensitivity analysis and algorithm implementation are given in detail. Finally, numerical examples are presented to illustrate the advantages of the proposed method to obtain hierarchical structures with high performance in thermal insulation.

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

AbstractA 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 thermoelastic structures using MMV method

Thermoelastic problems refer to a coupled phenomenon existing in a wide range of practical applications where elastic responses are influenced by temperature variation. Meanwhile, Moving Morphable Void (MMV) approach receives extensive attentions owing to explicit topological geometric information. In MMV method, a closed B-spline curve defined by several design variables is adopted to describe void material in design domain. In present study, we intend to use the MMV method to topologically optimize the thermoelastic structures under uniform temperature increment and varying temperature field. The weak formulations of heat conduction and elasticity are combined to describe the thermoelastic problems. The optimization mathematical model with the aim of compliance minimization and volume constraint is constructed. The sensitivity of design variables is derived by material derivative method and adjoint sensitivity analysis method. The method of moving asymptote (MMA) algorithm is implemented to update the design variables for finding the best material distribution. Numerical examples are provided to demonstrate the effectiveness of the proposed method.

Robust topology optimization for thermoelastic hierarchical structures with hybrid uncertainty

This paper presents a robust topology optimization (RTO) framework for thermoelastic hierarchical structures with hybrid uncertainty. Firstly, the thermoelastic concurrent optimization model is established and the uncertainties with interval random parameters are integrated into the thermoelastic hierarchical structure. Then, a reliable and cost-effective hybrid uncertainty perturbation analysis method (HUPAM) is derived for a quick estimate of the robust objective function subject to the mechanical and thermal loads. Finally, by calculating the design variables sensitivities of macroscale and microscale, the robust topological design can be generated efficiently. To obtain clear and optimal topologies for both macro- and micro- structures, the bi-directional evolutionary structural optimization (BESO) method is adopted. Some 2D and 3D numerical examples are presented to demonstrate the influences of the hybrid uncertainties on the final designs. The results also show that the proposed method can effectively improve the thermoelastic structural performance when it comes to uncertainties.

Thermoelastic Structural Topology Optimization Based on Moving Morphable Components Framework

This study investigates structural topology optimization of thermoelastic structures considering two kinds of objectives of minimum structural compliance and elastic strain energy with a specified available volume constraint. To explicitly express the configuration evolution in the structural topology optimization under combination of mechanical and thermal load conditions, the moving morphable components (MMC) framework is adopted. Based on the characteristics of the MMC framework, the number of design variables can be reduced substantially. Corresponding optimization formulation in the MMC topology optimization framework and numerical solution procedures are developed for several numerical examples. Different optimization results are obtained with structural compliance and elastic strain energy as objectives, respectively, for thermoelastic problems. The effectiveness of the proposed optimization formulation is validated by the numerical examples. It is revealed that for the optimization design of the thermoelastic structural strength, the objective function with the minimum structural strain energy can achieve a better performance than that from structural compliance design.

Shape preserving design of thermo-elastic structures considering geometrical nonlinearity

Thermal stress is an important design factor that will influence structural responses and cause local warping deformations. In this paper, such temperature variation effect is considered in the structural optimization and the shape preserving design approach is extended into thermo-elastic problems to prevent local thermal damages. Based on the weak-coupled thermo-elastic system, nonlinear structural responses at large thermo-mechanical loads are accurately analyzed. The complementary elastic work is minimized to obtain a reasonable rigid structure. Corresponding integrated deformation energy is utilized to calculate the warping deformation accumulated in the incremental thermo-mechanical loading process. Shape preserving effect is then achieved by an additional constraint on the local deformation energy. Through the adjoint method, sensitivity analysis is derived in the coupled field with design-dependent heat conduction and geometrical nonlinearity. In the numerical implementation, an energy interpolation scheme is applied to circumvent numerical instability in low stiffness regions and further modified for multi-material design. Optimization results show that local distortions in thermo-elastic structures are effectively eliminated by the proposed shape preserving design approach.

Multi-material thermomechanical topology optimization with applications to additive manufacturing: Design of main composite part and its support structure

This paper presents a density-based topology optimization formulation for the design of multi-material thermoelastic structures. The formulation is written in the form of a multi-objective topology optimization problem that considers two competing objective functions, one related to mechanical performance (mean compliance) and one related to thermal performance (either thermal compliance or temperature variance). To solve the optimization problem, we present an efficient design variable update scheme, which we have derived in the context of the Zhang–Paulino–Ramos (ZPR) update scheme by Zhang et al. (2018). The new update scheme has the ability to solve non-self-adjoint topology optimization problems with an arbitrary number of volume constraints, which can be imposed either to a subset of the candidate materials, or to sub-regions of the design domain, or to a combination of both. We present several examples that explore the ability of the formulation to obtain candidate Pareto fronts and to design support structures for additive manufacturing. Enabled by the ZPR update scheme, we are able to control the complexity and the length scale of the support structures by means of regional volume constraints.

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.

Analyticity of hybrid systems arising in visco and thermo elastic structures

We consider two systems arising in a two-dimensional viscoelastic fluid-structure interaction, one of them coupled with a wave equation with interior damping of Kelvin–Voigt type. In the second model, the acoustic vibrations of the viscous fluid which fills the two-dimensional interior cavity are coupled with the mechanical vibrations of a one-dimensional thermoelastic beam. Therefore, the systems are related to the problem of the active control of noise in a cavity. Our main results are that the corresponding semigroups are analytic. In particular we show the exponential stability of the models.

Two-dimensional thermal shock problem of generalized thermoelastic multilayered structures considering interfacial conditions

ABSTRACTA two-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting nondimensional coupled equations together with the Laplace and Fourier transform techniques are applied to a specific problem of multilayered structures considering thermal resistance subjected to thermal shock and traction-free surface. The solutions in the transformed domain are obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transform. Numerical results are represented graphically to estimate the effects of the thermal resistance and thermal conductivities on the temperature, displacement, and stress distributions.

Thermomechanical behavior of sandwich panels with graphitic-foam cores

Structural sandwich panels with graphitic-foam cores are considered for applications where extraordinary thermal conductivity of the core material may offer unique benefits for challenging thermoelastic structures. Sandwich panels constructed with carbon-fiber facesheets and graphitic-foam cores could provide a viable solution for “optical benches,” which require high stiffness and thermal stability; such panels should exhibit lower susceptibility to thermal distortion than sandwich panels constructed with traditional honeycomb cores or monolithic plates of materials having low thermal conductivity.Specimens of sandwich panels were fabricated with graphitic-foam cores, aluminum facesheets and carbon-fiber facesheets, as well as with honeycomb cores for the purpose of comparing behaviors. Measurements of plate bending behavior and through-thickness thermal conductivity were performed with these specimens; resulting data were used to validate analytical models. Separate testing was conducted to measure the shear modulus of graphitic foam in simple shear, as that strongly influences the bending behavior of sandwich panels, and has not appeared previously in the published literature.Out-of-plane distortion of sandwich panels subjected to asymmetric thermal loading was measured using an optical surface profilometer. Results of these measurements demonstrate that the use of graphitic foam as core material in sandwich panels greatly reduces their tendency to experience thermal distortion.

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.

A procedure for the approximated response history analysis of linear thermoelastic structures

ABSTRACTThis article presents a procedure for the approximated response history analysis of linear thermoelastic structures subjected to pure thermal loading based on eigenvalue analysis. The underlying assumption is that the mechanical system response does not affect heat transfer. Typically, the mechanical response of a structure subjected to pure thermal loading is such that inertia forces can be neglected but there are instances, however, where this is not the case. An approach to make this determination is also presented for a generic pair of retained mechanical and thermal modal coordinates and then extended to the multiple degree-of-freedom case.

Topology optimization of thermo-elastic structures with multiple materials under mass constraint

This work addresses the complicated design problem in which a structure of multiple materials is topologically optimized under the conditions of steady-state temperature and mechanical loading. First, the general thermal stress coefficient (GTSC) is introduced to relate the thermal stress load to the design variables and address an engineering practice need by breaking down the previous assumption that the Poisson’s ratios of all candidate materials are the same. Second, the Uniform Multiphase Materials Interpolation (UMMI) scheme and the Rational Approximation of Material Properties (RAMP) scheme are combined to parameterize material properties (e.g., the elasticity matrix and GTSC). In the problem formulation, mass constraint is adopted to automatically determine the optimal match of candidate materials instead of imposing the standard volume constraint to each material phase. An improved optimization formulation with an artificial penalty term is also proposed to avoid a possible mixed material status in the numerical results. Numerical tests illustrate the validity of the proposed method.

Математическая модель нестационарного термоупругого деформирования многослойных демпфирующих покрытий в радиоэлектронной аппаратуре

Generation of new multilayer coatings of units and blocks in electronics for effective damping of thermo-mechanical impact loads requires the development of mathematical models suitable for engineering practice. Mathematical model and calculation method proposed in this paper allows investigate the passing and reflection of thermo-elastic waves in a multilayer body excited by non-stationary magnetic field at the conductive layer boundary. Also, the problem of estimating relative influence of volume forces induced by the magnetic field in the electrically conductive nonferromagnetic layer on the wave propagation in thermo-elastic polymer compounds was considered. It is assumed that the velocity of heat propagation is finite. Assumptions are introduced to simplify the fully coupled system of magneto-thermo-elastic equations that allow applying the numerical solution based on the method of characteristics for obtaining concrete results. A method for finding required quantities at the nodal points of the boundary between the layers is indicated. The suggested mathematical model and calculation method makes it possible, without making any significant changes in the computing system, to carry out numerical experiments on researching the damping properties of multilayer coatings with different geometrical and mechanical parameters under the conditions of the thermo-mechanical loadings. This calculation method of heterogeneous multilayer thermo-elastic structures can be used to identify the areas most disposed to the damage.

Minimum Compliance Optimization of a Thermoelastic Lattice Structure with Size-Coupled Effects

The minimum compliance design of thermoelastic structures forced by mechanical and thermal loads simultaneously composed of periodic lattice materials is studied in this paper. The Extended Multi scale Finite Element Method (EMsFEM) is utilized to connect the macro structural and material microstructural scales. In the optimization, sectional areas of the microcomponents are set as design variables under volume constraints. In numerical examples, we discuss the influence of the geometrical dimensions of the material microstructure, the amount of base material and the different ratios of thermal load over the mechanical load on the optimization results.

異種材料で構成される3次元熱弾性構造体の界面形状同定

異種材料で構成される3次元熱弾性構造体の界面形状同定

Material interface effects on the topology optimizationof multi-phase structures using a level set method

A level set method is used as a framework to study the effects of including material interface properties in the optimization of multi-phase elastic and thermoelastic structures. In contrast to previous approaches, the material properties do not have a discontinuous change across the interface that is often represented by a sharp geometric boundary between material regions. Instead, finite material interfaces with monotonic and non-monotonic property variations over a physically motivated interface zone are investigated. Numerical results are provided for several 2D problems including compliance and displacement minimization of structures composed of two and three materials. The results highlight the design performance changes attributed to the presence of the continuously graded material interface properties.

Inner thermal resonance in thermoelastic geological structures

When investigating heterogeneous media such as composite materials or geological structures, it is convenient to replace them by macroscopic equivalent media, which simplifies computations a lot. In the paper, we look for the equivalent macroscopic model for describing seismic wave propagation and transient heat transfers in thermoelastic periodic geological structures made of rock or soil. We follow the route described in Auriault (2012), to investigating thermoelastic composite media. We use the method of multi-scale asymptotic expansions. By estimating the dimensionless numbers in the momentum and energy balances, we show that an equivalent macroscopic model exists for describing seismic waves at very low frequencies only. The model then shows a damping which is due to thermal resonance at the heterogeneity scale. At higher frequencies, such an equivalent macroscopic model does not exist. Macroscopic models for describing transient heat transfers do not exist.

Topology optimization of thermoelastic structures using the guide-weight method

The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper. First, the solid isotropic microstructure with penalization (SIMP) with different penalty factors is selected as a material interpolation model for the thermal and mechanical fields. The general criteria of the guide-weight method is then presented. Two types of iteration formulas of the guide-weight method are applied to the topology optimization of thermoelastic structures, one of which is to minimize the mean compliance of the structure with material constraint, whereas the other one is to minimize the total weight with displacement constraint. For each type of problem, sensitivity analysis is conducted based on SIMP model. Finally, four classical 2-dimensional numerical examples and a 3-dimensional numerical example considering the thermal field are selected to perform calculation. The factors that affect the optimal topology are discussed, and the performance of the guide-weight method is tested. The results show that the guide-weight method has the advantages of simple iterative formula, fast convergence and relatively clear topology result.