Multimaterial topology design for optimal elastic and thermal response with material-specific temperature constraints

We present an original method for multimaterial topology optimization with elastic and thermal response considerations. The material distribution is represented parametrically using a formulation in which finite element–style shape functions are used to determine the local material properties within each finite element. We optimize a multifunctional structure that is designed for a combination of structural stiffness and thermal insulation. We conduct parallel uncoupled finite element analyses to simulate the elastic and thermal response of the structure by solving the two-dimensional Poisson problem. We explore multiple optimization problem formulations, including structural design for minimum compliance subject to local temperature constraints so that the optimized design serves as both a support structure and a thermal insulator. We also derive and implement an original multimaterial aggregation function that allows the designer to simultaneously enforce separate maximum temperature thresholds based upon the melting point of the various design materials. The nonlinear programming problem is solved using gradient-based optimization with adjoint sensitivity analysis. We present results for a series of two-dimensional example problems. The results demonstrate that the proposed algorithm consistently converges to feasible multimaterial designs with the desired elastic and thermal performance.     

Shape, sizing optimization and material selection based on mixed variables and genetic algorithm

In this work, we explore simultaneous designs of materials selection and structural optimization. As the material selection turns out to be a discrete process that finds the optimal distribution of materials over the design domain, it cannot be performed with common gradient-based optimization methods. In this paper, material selection is considered together with the shape and sizing optimization in a framework of multiobjective optimization of tracking the Pareto curve. The idea of mixed variables is often introduced in the case of mono-objective optimization. However, in the case of multi-objective optimization, we still face some hard key points related to the convexity and the continuity of the Pareto domain, which underline the originality of this work. In addition to the above aspect, there is a lack in the literature concerning the industrial applications that consider the mixed parameters. Continuous variables refer to structural parameters such as thickness, diameter and spring elastic constants while material ID is defined as binary design variable for each material. Both mechanical and thermal loads are considered in this work with the aim of minimizing the maximum stress and structural weight simultaneously. The efficiency of the design procedure is demonstrated through various numerical examples.     

Overview of pool hydraulic design of Indian prototype fast breeder reactor

Thermal hydraulics plays an important role in the design of liquid metal cooled fast breeder reactor components, where thermal loads are dominant. Detailed thermal hydraulic investigations of reactor components considering multi-physics heat transfer are essential for choosing optimum designs among the various possibilities. Pool hydraulics is multi-dimensional in nature and simple one-dimensional treatment for the same is often inadequate. Computational Fluid Dynamics (CFD) plays a critical role in the design of pool type reactors and becomes an increasingly popular tool, thanks to the advancements in computing technology. In this paper, thermal hydraulic characteristics of a fast breeder reactor, design limits and challenging thermal hydraulic investigations carried out towards successful design of Indian Prototype Fast Breeder Reactor (PFBR) that is under construction, are highlighted. Special attention is paid to phenomena like thermal stratification, thermal stripping, gas entrainment, inter-wrapper flow in decay heat removal and multi-physics cellular convection. The issues in these phenomena and the design solutions to address them satisfactorily are elaborated. Experiments performed for special phenomena, which are not amenable for CFD treatment and experiments carried out for validation of the computer codes have also been described.     

Numerical and experimental design of graded cellular sandwich cores for multi-functional aerospace applications

The present contribution is concerned with a combined experimental and numerical design of graded cellular materials for multifunctional aerospace application performed in the context of an integrated research project funded by the European Commission. The primary objective is an exploration of the potential of functionally graded materials as sandwich cores for multifunctional application. With particulate advanced pore morphology (APM) foams and hollow spheres assemblies, two different types of particle-based cellular base materials are considered. Based on these constituent materials, functionally graded sandwich cores are designed in a combined numerical and experimental approach. Their properties and their performance in the desired application are investigated and optimized. The performance of the optimized material is compared to the performance of a non-graded sandwich core in the numerical simulation of a bird strike experiment.     

对流换热边界条件的多孔材料主动散热性能

通过推导2种不同换热边界条件下平板夹层多孔材料的散热指标, 研究了考虑对流换热因素的平板夹层多孔材料主动散热性能, 得到了影响材料散热性能的因素。分析了在确定的相对厚度下, 不同构型多孔材料的相对密度与散热指标的关系, 并得出正六边形构型的散热指数最大。随着相对厚度的增大, 最大散热指标和最优相对密度增大较快, 当相对厚度大于20时, 最大散热指标和最优相对密度变化较小并最终趋于定值。由上述结果可以得到相对应的最小质量, 随着最小质量的增大, 最大散热指标增大并最终趋于定值。在相同的最大散热指标下, 随着表面换热系数比值的增大, 最小质量逐渐减小。最后考虑承载因素对结构进行了优化分析, 正六边形构型的多孔材料具有明显的综合性能优势。      

Conceptual design of efficient heat conductors using multi-material topology optimization

Conductive heat transfer plays an important role in dissipating thermal energy to achieve lower operating temperatures in various devices. Topology optimization has the potential to provide efficient structural solutions for such devices. The traditional topology optimization approach considers a single material. Adding additional materials with unique properties not only can expand the design options but also may improve the structural performance of the final structure. In this work, a multi-resolution topology optimization approach is employed to design multi-material structures for efficient heat dissipation. The implementation blends an efficient multi-resolution approach to obtain high-resolution designs with an alternating active phase algorithm to handle multi-material giving greater design flexibility. It solves the steady-state heat equation using finite element analysis and iteratively minimizes thermal compliance (maximizes conductivity). Several examples are presented to show the efficacy of the numerical implementation, which involves benchmark problems. Results indicate good prospects when quantitatively compared with single-material structures.     

Thermal Applications of Open-Cell Metal Foams

The key structural and thermo-physical properties of reticulated metal foams (RMF) are reviewed. Analytical expressions relating such properties to basic structural parameters are developed through mathematical modeling and experimental studies. Conductive and convective aspects of thermal energy transfer through RMF-based heat exchangers are reviewed. A mathematical model is developed that calculates maximum thermal performance for such heat exchangers. Results of experimental and finite element analysis predicting thermal performance of test module using a thermal base plate, power device, RMF heat exchanger, and off-the-shelf external cold plate were compared. The superior performance of RMF-based heat exchangers is shown.     

On the reformulation of topology optimization problems as linear or convex quadratic mixed 0–1 programs

We consider equivalent reformulations of nonlinear mixed 0–1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. We show that the considered problems can equivalently be cast as either linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design of structures subjected to static or periodic loads, design of composite materials with prescribed homogenized properties using the inverse homogenization approach, optimization of fluids in Stokes flow, design of band gap structures, and multi-physics problems involving coupled steady-state heat conduction and linear elasticity. Several numerical examples of maximum stiffness design of truss structures are presented. The research is funded by the Danish Natural Science Research Council and the Danish Research Council for Technology and Production Sciences.     

Multi‐actuated functionally graded piezoelectric micro‐tools design: A multiphysics topology optimization approach

Micro‐tools offer significant promise in a wide range of applications such as cell manipulation, micro‐surgery, and micro/nanotechnology processes. Such special micro‐tools consist of multi‐flexible structures actuated by two or more piezoceramic devices that must generate output displacements and forces at different specified points of the domain and at different directions. The micro‐tool structure acts as a mechanical transformer by amplifying and changing the direction of the piezoceramics output displacements. The design of these micro‐tools involves minimization of the coupling among movements generated by various piezoceramics. To obtain enhanced micro‐tool performance, the concept of multifunctional and functionally graded materials is extended by tailoring elastic and piezoelectric properties of the piezoceramics while simultaneously optimizing the multi‐flexible structural configuration using multiphysics topology optimization. The design process considers the influence of piezoceramic property gradation and also its polarization sign. The method is implemented considering continuum material distribution with special interpolation of fictitious densities in the design domain. As examples, designs of a single piezoactuator, an XY nano‐positioner actuated by two graded piezoceramics, and a micro‐gripper actuated by three graded piezoceramics are considered. The results show that material gradation plays an important role to improve actuator performance, which may also lead to optimal displacements and coupling ratios with reduced amount of piezoelectric material. The present examples are limited to two‐dimensional models because many of the applications for such micro‐tools are planar devices. Copyright © 2008 John Wiley & Sons, Ltd.     

Kagome 蜂窝夹层平板的多功能优化设计

采用“等效介质模型”, 分析了复合材料夹层蜂窝平板的整体换热系数。在此基础上, 针对轻质蜂窝(相对密度小于0. 3) , 选取蜂窝面内等效剪切刚度表征夹层结构的承载能力, 综合考虑散热能力和结构承载能力, 比较了Kagome 蜂窝与传统的正三角形、正方形和正六边形蜂窝的性能。结果显示Kagome 蜂窝不但散热性能很好, 而且通过对蜂窝相对密度和尺寸的优化, 在结构质量相同的情况下, Kagome 蜂窝的综合性能比传统蜂窝具有明显优势。      

Adaptation of density distributions for optimising aluminium foam structures

Abstract

Metallic foams show some potential for being produced with controlled spatial variations in their density. This suggests employing them as graded materials in space filling lightweight structures designed in analogy to cortical bone, a natural cellular material, that displays increased density in regions of high loading. In the present study the influence of the mechanical properties of aluminium foams on the results of an optimisation of the foam density distribution with regard to structural strength and stiffness was examined. Regression formulae for the relationships between stiffness and strength of metallic foams on one hand and effective density on the other hand can be fitted to the results of uniaxial compression tests of a certain brand of metallic foam. These results and additional assumptions such as overall isotropy and a yield surface suitable for cellular materials can be implemented into a finite element program adapted for performing stiffness or strength optimisation on the basis of a density adaptation similar to the remodelling of bone. Some applications are presented that show how foams with gradients in the apparent density may be employed to obtain optimal structural behaviour for classical design problems.     

Extreme Specific Stiffness Through Interactive Cellular Networks in Bi-Level Micro-Topology Architected Metamaterials

Architected lattice materials, realized through artificial micro-structuring, have drawn tremendous attention lately due to their enhanced mechanical performances in multifunctional applications. However, the research area on the design of artificial microstructures for the modulation of mechanical properties is increasingly becoming saturated due to extensive investigations considering different possibilities of lattice geometry and beam-like network design. Thus, there exists a strong rationale for innovative design at a more elementary level. It can enhance and grow the microstructural space laterally for exploiting the potential of geometries and patterns in multiple length scales, and the mutual interactions thereof. A bi-level design is proposed, where besides having the architected cellular networks at an upper scale, the constituting beam-like members at a lower scale are further topology-engineered for most optimum material utilization. The coupled interaction of beam-level and lattice-level architectures can enhance the specific elastic properties to an extreme extent (up to ≈25 and 20 times, depending on normal and shear modes, respectively), leading to ultra-lightweight multifunctional materials for critical applications under static and dynamic environments.     

Some considerations of fracture mechanics applications in ships design,construction and operation

The structural performance demands placed on present day high performance ships and some types of shipboard liquid natural gas (LNG) cargo containment systems requires the use of new materials which can perform under higher loadings and severe service environments. Such critical designs must be accomplished while maintaining a high structural reliability and decreased life-cycle costs. For high performance ships these critical designs can be accomplished with damage-tolerant design procedures which provide for redundant load paths and/or crack arrest capabilities. The ship construction and maintenance requirements must also be included in the design because of their effect on the structural life performance of the high performance ship. For shipboard LNG cargo containment systems modified LEFM (linear elastic fracture mechanics) is used in the design phase.The paper discusses the philosophy of a fatigue and fracture control plan for high performance ships and the use of modified LEFM for shipboard LNG cargo containment systems. Current applications of a fatigue and fracture control plan are discussed. The types of shipboard cargo containment systems designed using the modified LNG approach are described.The paper addresses the need for an integrated life time quality assurance program. Such a program is shown to require a synthesis of materials characterization, structural analysis and nondestructive testing. A service performance feedback loop will assist the designers in continually improving the then governing design criteria. In addition, areas requiring further work and possible future applications for fatigue and fracture analysis will be discussed.     

正交各向异性蜂窝材料多功能优化设计

以矩形蜂窝为例 , 介绍了正交各向异性蜂窝填充的夹层蜂窝结构散热性能和散热2承载性能优化设计 ,给出了正交各向异性蜂窝相关系数的推导过程。从实际应用出发 , 针对常规以性能乘积形式构造的散热2承载性能指标对散热性能侧重程度的不足 , 给出了基于 2种双层规划模型的非确定性设计方法 , 得到了旨在强调散热性能设计意图的散热2承载多目标优化问题的有效解集。这种方法对结构敏感参数较多的正交各向异性蜂窝填充结构的多功能优化设计非常有效。最后讨论了不同尺寸效应下的蜂窝最优结构参数。     

Effective Thermal Conductivity and Heat Transfer Characteristics of a Series of Ceramic Triply Periodic Minimal Surface Lattice Structure

Triply periodic minimal surface (TPMS) structures with high surface area, high porosity, complex pore channels, and pore size distribution have great potential for application in thermal metamaterials and thermal engineering applications. To demonstrate the possibility of the use of TPMS structures as thermal metamaterials, the thermal insulation properties and heat transfer mechanisms of TPMS structures are investigated in detail. The results show that modulation of the volume fraction to within 15% by a rational geometric design indicates the possibility to obtain excellent lightweight properties. The effective thermal conductivity is within 0.25 W m⁻¹ K⁻¹, which is much lower than this component, indicating that the TPMS structure is designed to reduce the effective thermal conductivity and provide a lightweight design. However, in a high-temperature environment, reasonable structural parameters can shield the cavity radiation in the TPMS structure and play an effective role to provide high-temperature thermal insulation. Finally, based on the relationship between structural parameters and thermal insulation performance, a dynamic density TPMS-graded structure is proposed, which exhibits a better thermal insulation performance than the conventional TPMS structure both at room temperature and at high temperature.     

On design of multi-functional microstructural materials

The design of periodic microstructural composite materials to achieve specific properties has been a major area of interest in material research. Tailoring different physical properties by modifying the microstructural architecture in unit cells is one of the main concerns in exploring and developing novel multi-functional cellular composites and has led to the development of a large variety of mathematical models, theories and methodologies for improving the performance of such materials. This paper provides a critical review on the state-of-the-art advances in the design of periodic microstructures of multi-functional materials for a range of physical properties, such as elastic stiffness, Poisson’s ratio, thermal expansion coefficient, conductivity, fluidic permeability, particle diffusivity, electrical permittivity and magnetic permeability, etc.     

A review on application of carbonaceous materials and carbon matrix composites for heat exchangers and heat sinks

Carbonaceous materials and carbon matrix composites (CAMCs) have potential to be used in heat exchangers and heat sinks for a number of thermal management applications related to HVAC&R systems, especially in high-temperature and corrosive environments. Recent developments in carbonaceous materials, such as new, natural graphite, carbon foam, carbon nanotubes, and CAMCs, open opportunities for new heat exchanger designs for compact and lightweight applications. The property data of various monolithic carbonaceous materials and CAMCs and their applications in liquid-to-liquid heat exchangers, liquid-to-gas heat exchangers, gas-to-gas heat exchangers and heat sinks are reviewed in this paper. While it is clear that these materials do hold promise for use in the construction of heat exchangers in different applications, additional research is still required in material properties, life-time behavior, structural design and manufacturing cost reduction.     

二维多孔材料散热性能分析与设计

二维多孔材料存在一个易于流动的方向并具有较大的面密度 , 因此在具有良好的比刚度和比强度的同时也具有良好的散热性能 , 研究强迫对流下的散热性能对其多功能化设计具有重要意义。本文中利用数值方法求解考虑二维多孔材料内部流体流动规律、 热传导和对流换热影响的流固耦合热传输问题 , 分析了多孔率和微结构尺寸对散热性能的影响并进行了最优参数设计 ; 通过分析比较 5种具有典型微结构形式的二维多孔材料的散热性能 , 给出了微结构形式对散热性能的影响。提出了以需要满足的散热性能为约束条件 , 以满足需求的设计参数的可调范围(设计参数的允许变化范围)为设计目标的最优散热结构设计理念。以此理念得到的设计结果 , 更有利于根据其他性能的要求对材料进行多功能化设计。分析表明 , 具有正六边形微结构的二维多孔材料的散热性能最优 , 并有利于实现轻质多功能化设计。     

DESIGN SENSITIVITY ANALYSIS AND OPTIMAL DESIGN OF COMPOSITE STRUCTURES USING HIGHER ORDER DISCRETE MODELS

This paper deals with the structural optimization of multilaminated composite plate structures of arbitrary geometry and layup, using single layer higher order shear deformation theory discrete models. The structural and sensitivity analysis formulation is developed for a family of C° Lagrangian elements. The design sensitivities of static response for objective and/or constraint functions, such as maximum displacements, stress failure criterion and elastic strain energy, with respect to ply angles and ply thickness are presented. The objectives of the design are the minimization of the structural elastic strain energy, minimization of maximum deflection and/or the minimization of the structure volume. The accuracy and relative performance of the proposed discrete models are compared and discussed among developed elements and alternative models. Several test designs are optimized to show the applicability of the proposed refined discrete models.     

基于混合单元建模的复合板热诱导结构振动研究

针对复合板的热诱导结构振动问题，提出一种新的混合单元计算模型，将三维和二维单元组成混合单元，利用不同类型单元体现复合结构中不同的材料特性，实现对真实复合结构物理特征的高精度模拟。在此基础上基于虚功原理建立了三维形式的复合板瞬态热弹性动力学方程，利用该方法对空间大尺度复合薄板的热诱导扰动进行研究。仿真结果表明，结构固有频率和热容是决定热诱导振动发生的主要内囚，对于一些刚度较大的空间复合薄板，由于空间约束环境弱，整体频率低易发生热诱导结构振动。本研究对于空间大尺度复合平板结构的工程设计具有一定的参考价值。