Thermoelastic Structures Research Articles

Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization

In this work, two different formulations that minimize the mean compliance and elastic strain energy of a structure as the objective function are comparatively investigated for topology optimization of thermoelastic problems. As thermal load is a design-dependent load compared with mechanical load, the particularity of the problem and the difference between both formulations are highlighted in terms of sensitivity analysis and related optimization results based on numerical tests. The concept of load sensitivity is used to interpret quantitatively the underlying influences of thermal and mechanical loads upon optimized results in both formulations.

Topology Optimization of Thermo-Mechanical Structure Using the Hybrid Celluar Automata Method

Topology optimization of thermo-elastic structures using the hybrid cellular automata method is investigated in this paper. The objective is to minimize the mean compliance of a structure with a single material volume constraint. The hybrid cellular automata method is used to solve the optimization problem. The local change in the design variable is determined by a local rule based on the proportional control law. The numerical example is presented to show the feasibility of the present approach.

Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material

The present paper studies multi-objective design of lightweight thermoelastic structure composed of homogeneous porous material. The concurrent optimization model is applied to design the topologie...

Interpolation/penalization applied for strength design of 3D thermoelastic structures

With design independent loads and only a constrained volume (no local bounds), the same optimal design leads simultaneously to minimum compliance and maximum strength. However, for thermoelastic structures this is not the case and a maximum volume may not be an active constraint for minimum compliance. This is proved for thermoelastic structures by sensitivity analysis of compliance that facilitates localized determination of sensitivities, and the compliance is not identical to the total elastic energy (twice strain energy). An explicit formula for the difference is derived and numerically illustrated with examples. In compliance minimization for thermoelastic structures it may be advantageous to decrease the total volume, but for strength maximization it is argued to keep the total permissible volume. Linear interpolation (no penalization) may to a certain extent be argued for 2D thickness optimized designs, but for 3D design problems interpolation must be included and not only from the penalization point of view to obtain 0---1 designs. Three interpolation types are presented in a uniform manner, including the well known one parameter penalizations, named SIMP and RAMP. An alternative two parameter interpolation in explicit form is preferred, and the influence of interpolation on compliance sensitivity analysis is included. For direct strength maximization the sensitivity analysis of local von Mises stresses is demanding. An applied recursive procedure to obtain uniform energy density is presented in details, and it is shown by examples that the obtained designs are close to fulfilling also strength maximization. Explicit formulas for equivalent thermoelastic loads in 2D and 3D finite element analysis are derived and applied, including the sensitivity analysis.

Strength optimized designs of thermoelastic structures

For thermoelastic structures the same optimal design does not simultaneously lead to minimum compliance and maximum strength. Compliance may be a questionable objective and focus for the present paper is on the important aspect of strength, quantified as minimization of the maximum von Mises stress. With compliance defined as the product of resulting displacements and their corresponding total loads, then for thermoelastic problems compliance is different from total elastic energy. An explicit formula for this difference is derived and numerically illustrated in the optimized examples. As an alternative to mathematical programming, which with a large number of both design variables and strength constraints, is found non-practical, we choose simple recursive iterations to obtain uniform energy density and find by examples that the obtained designs are close to fulfilling also strength maximization. In compliance minimization it may be advantageous to decrease the total volume, but for strength maximization it is argued that it is advantageous to keep the total permissible volume. With the thermoelastic analysis presented directly in a finite element formulation, simple explicit formulas for equivalent thermoelastic loads are appended.

A Uniform Optimum Material Based Model for Concurrent Optimization of Thermoelastic Structures and Materials

This paper presents an optimization technique for structures composed of uniform cellular materials in macro scale. The optimization aims at to obtain optimal configurations of macro scale structures and microstructures of material under certain mechanical and thermal loads with specific base material volume. A concurrent topology optimization me- thod is proposed for structures and materials to minimize compliance of thermoelastic structures. In this method macro and micro densities are introduced as the design variables for structure and material microstructure independently. Penalization approaches are adopted at both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material Penalization) in micro- scale and PAMP (Porous Anisotropic Material Penalization) in macro-scale. Optimizations in two scales are integrated into one system with homogenization theory and the distribution of base material between two scales can be decided automati- cally by the optimization model. Microstructure of materials is assumed to be uniform at macro scale to reduce manufactur- ing cost. The proposed method and computational model are validated by the numerical experiments. The effects of tem- perature differential, volume of base material, numerical parameters on the optimum results are also discussed. At last, for cases in which both mechanical and thermal loads apply, the configuration of porous material can help to reduce the system compliance.

Topology optimization of thermoelastic structures using level set method

This paper describes the topology optimization of thermoelastic structures, using level set method. The objective is to minimize the mean compliance of a structure with a material volume constraint. In level set method, free boundary of a structure is considered as design variable, and it is implicitly represented via level set model. Objective function of the optimization problem is defined as a function of the shape of a structure. Sensitivity analysis based on continuum model is conducted with respect to the free boundary, which suggests the steepest descent direction. A geometric energy term is introduced to ensure smooth structural boundary. Augmented Lagrangian multiplier method is adopted to enforce volume constraint. Numerical examples are provided for 2D cases, considering design independent temperature distribution.

Bloch–Floquet waves and controlled stop bands in periodic thermo-elastic structures

An algorithm for controlling the stop bands for elastic Bloch–Floquet waves within a periodic structure is proposed. Explicit asymptotic estimates of frequencies of translational and rotational standing waves, together with the numerical estimates of the stop band frequencies, are given. Thermal pre-stress is introduced and used to control the position of the stop bands on the dispersion diagram.

A wavelet-based methodology for monitoring thermoelastic structures

A wavelet-based methodology for detecting critical events in displacement and temperature histories, obtained by monitoring in-situ thermoelastic structures, is proposed. It is based on the wavelet analysis of thermoelastic potentials furnishing also the possibility to detect separately cases in which sudden jumps occur in the displacement history from those in which they occur on temperature history.

Photoacoustic elastic bending method in microelectronics – invited paper

The basic concept, development and application of the photoacoustic elastic bending method are given. The photoacoustic effect as a function of modulation frequency including the elastic bending contribution to the photoacoustic signal is investigated. The theoretical model for a typical detection configuration was given and the relations for elastic bending and photoacoustic signal were derived by the dynamic theory of the thin plate. The applications of the PA elastic bending method in investigation of thermal and electronic transport processes in semiconductors, plasmaelastic and thermoelastic effects, metal-semiconductor structures and ion-modified layers were presented.

STATIC SHAPE CONTROL OF FORCE-INDUCED INFINITESIMAL DEFORMATIONS SUPERIMPOSED ON LARGE DEFORMATIONS OF THERMOELASTIC BODIES

The present paper is concerned with the geometrically nonlinear static theory of anisotropic thermoelastic solids and structures. We consider infinitesimal incremental deformations superimposed on a given state of possibly large strain, the latter being called the intermediate state. Our goal is to derive a distribution of incremental thermal actuation stresses, which, when applied to the intermediate state together with a given set of incremental body forces and surface tractions, give zero incremental displacements everywhere in the body under consideration. This problem belongs to the field of static shape control, a notion originally introduced by Haftka and Adelman, who developed a procedure for determining temperatures in control elements to minimize the infinitesimal distortion of a large space antenna from its original shape. The present paper is concerned with the extension of shape control to infinitesimal force-induced static distortions from a large pre-deformation. Referring to the intermediate configuration as the reference configuration, we show that, in order to compensate the incremental force-induced deformations everywhere within the body, the incremental thermal actuation stress tensor must be equal to any statically admissible incremental first-order Piola–Kirchhoff stress tensor, a relation that is derived under the assumption that the intermediate state is infinitesimally superstable. We also discuss under which conditions it is possible to work with an isotropic thermal actuation stress. Finally, we present a formulation for shape control of infinitesimal deflections superimposed on a state of possibly large deflections of a slender beam.

A renorming method for thermoelastic models

We consider the coupled partial differential equations which arise in modeling linear thermoelastic structures. When this model is reformulated as an abstract Cauchy problem, it is known that the resulting solution semigroup is exponentially stable, and in certain cases it is analytic. In most cases, though, the infinitesimal generator of the semigroup does not satisfy a strict dissipative inequality. We construct a new norm, equivalent to the energy norm, for which a strict dissipative inequality is obtained. In the case of an analytic semigroup, the new norm allows the semigroup generator to become associated with a coercive esquilinear form.

Displacement minimization of thermoelastic structures by evolutionary thickness design

Structural optimization aims at finding an appropriate material distribution to achieve the best structural performance. In this paper, the evolutionary structural optimization method is further developed to deal with thermoelastic optimization, where structural material is progressively redistributed so as to minimize the displacement under thermal and mechanical loading. To evaluate the effects of material removal or addition on the displacement of thermoelastic structures, a sensitivity number is proposed on the basis of the thickness variation of an element. The method proves to be very simple in its mathematical operations and suitable for computer implementation. The numerical examples are compared against those by the homogenization method to verify and validate this method of solving thermoelastic optimizations. In addition, the effect of various temperature distributions on the final optimum structures is investigated in detail.

Shape Design Optimization of Thermoelastic Structures for Durability

Shape design sensitivity analysis (DSA) and optimization methods for the fatigue life of thermoelastic structural components are presented in this paper. A multiaxial fatigue life prediction method is used for crack initiation. The crack initiation life prediction is modeled using constant amplitude strain-life data and cyclic stress-strain curves. A hybrid DSA method is used for the fatigue life. The design sensitivities of the dynamic stress and the temperature field are obtained using analytical approaches. The design sensitivity is used to predict the dynamic stress and temperature of the perturbed design. Using predicted stress and temperature, the fatigue life of the perturbed structural design component is predicted. The predicted fatigue life is then used to obtain the design sensitivity of the fatigue life by utilizing the finite difference method. The proposed DSA method is applied to design optimization of an automotive exhaust manifold of an automotive vehicle, considering crack initiation lives as design constraints.

Shaping of Piezoelectric Sensors/Actuators for Vibrations of Slender Beams: Coupled Theory and Inappropriate Shape Functions

Flexural vibrations of smart slender beams with integrated piezoelectric actuators and sensors are considered. A spatial variation of the sensor/actuator activity is achieved by shaping the surface electrodes and/or varying the polarization profile of the piezoelectric layers, and this variation is characterized by shape functions. Seeking shape functions for a desired purpose is termed a shaping problem. Utilizing the classical lamination theory of slender composite beams, equations for shaped sensors and actuators are derived. The interaction of mechanical, electrical and thermal fields is taken into account in the form of effective stiffness parameters and effective thermal bending moments. Self-sensing actuators are included. From these sensor/actuator equations, shaping problems with a practical relevance are formulated and are cast in the form of integral equations of the first kind for the shape functions. As a practical interesting aspect of these inverse problems, shape functions which fail to measure or to induce certain structural deformations are investigated in the present paper. Such inappropriate shape functions are termed nilpotent solutions of the shaping problems. In order to derive an easy-to-obtain class of such nilpotent solutions, the homogeneous versions of the integral equations for the shaping problems are compared to orthogonality relations valid for redundant beams. Hence, by analogy, the presented nilpotent solutions are shown to correspond to solutions of the basic theory of thermoelastic structures, namely to thermally induced static bending moment distributions. This result beautifully reflects the close connection between the theory of thermally loaded structures and the theory of smart structures. A particular result for a nilpotent shape function previously investigated in the literature is explained in the context of the present theory, and examples of nilpotent shape functions for various structural systems are presented.

A material based model for topology optimization of thermoelastic structures

AbstractThis paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2‐D linear‐elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analysed.

Shape optimization of two-dimensional thermoelastic structures using boundary integral equation formulation

A general method for shape design sensitivity analysis as applied to two-dimensional uncoupled thermoelasticity problem is developed using the material derivative concept and adjoint variable method. The method for deriving sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. The sensitivity of a general functional is considered which depends on thermal and mechanical quantities such as temperature, heat flux, displacement, stress and surface traction. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the sensitivity is studied with two thermoelastic shape optimization problems of a fillet and a hole. Optimal shapes for the two problems of weight minimization are presented to show numerical applications. It is shown through the fillet design problem that optimal shape under stress constraint is highly dependent on thermal boundary conditions, indicating that the shape optimization based on thermoelasticity is crucial when thermal field is sensitive to boundary shape.

Thermoelastic sloping thin-walled shell structures deformed without bending

We have derived a nonlinear integrodifferential equation to find the unbent shape of the middle surface of a sloping shell of constant thickness, subjected to a given temperature and force field.

Simultaneous material/load/shape variations of thermoelastic structures

A continuous approach is adopted in order to find the total variation of a general performance criterion. The present analysis may find important physical applications in the simultaneous shape optimization and control of large space structures in time by applied thermal and/or mechanical loads. The adjoint variable method and the material derivative concept are used to find the sensitivity expressions