An Ising machine formulation for design updates in topology optimization of flow channels

This article presents a topology optimization method for the design of the fluid flow channel of cold plate, aiming to solve the problem of heat dissipation for power devices in active phased array antenna (APAA). The density-based topology optimization method is used in the topology optimization design of flow path, in which the conjugate heat transfer analysis is performed. In the numerical experiment, we use the central plane of the cold plate to make a two-dimensional topology optimization, and then the result of two-dimensional topology optimization was used to build the three-dimensional flow channel of cold plate. The results of simulation show that the optimized flow channel has a better ability of heat dissipation compared with the traditional S style flow channel, which provides important reference for engineering application.

Study of the influence of objective functions on the topology optimization design of battery cold plate

The importance of computer aided engineering in product development processes and research has been increasing throughout the past years. As e.g. energy efficiency and therefore mechanical lightweight structures of new products plays a large role, optimization tools gained more and more importance. Weight reduction can be achieved by a change of the component’s design and by selection of adapted materials. Such an improved utilization of material can be implemented only if there is an accurate knowledge of the loads and the conditions on the material. As modern composite materials can make a clear weight reduction possible, appropriate tools and methods are necessary within the design process. Even for isotropic materials, the design of complex parts is not trivial. For the design of composites, additional parameters have to be considered, such as number and thickness of the plies and the orientation of fibers. Hence, design by intuition leads only in few cases to optimal parts. For the determination of the basic layout of a new design topology optimization can be used. It involves the determination of features such as the number, location and shape of holes and the connectivity of the domain. Today topology optimization is very well theoretically studied and also a very common tool in the industrial design process but is limited to isotropic materials. Several approaches for the determination of optimal fiber orientation have been presented in the past e.g. placing the fibers in the direction of the first main stress. Based on a finite element analysis, a method is presented that uses the orientation of main stresses to determine optimal orientations and thickness relations of plies. It is now applicable to complex 3D geometries. The result is a design proposal for the laminate structure (orientation and thicknesses of plies), taking multi-axial load cases into account. To determine a design proposal for complex 3D laminate structures, the application of both methods, topology and fiber optimization, is appropriate. Regarding an independent serial application of topology and fiber optimization it makes sense carrying out topology optimization in a first step and the determination of fiber orientations in a second step. An integrated approach might show even better results in certain cases. For that, we combined topology and fiber optimization in a two-level approach by optimizing laminate structure within each iteration of topology optimization process. In this paper topology and fiber orientation optimization are integrated into a straightforward, automatic way.

An important design challenge of modern vehicles is mass reduction. Hence in many cases, mechanical design of vehicle components covers different optimization processes. One important structural optimization technique which is highly utilised in weight reduction applications is the topology optimization. This paper contains a multi-stage optimization based on the topology and design optimizations. During this study, the mechanical design of a rear axle-chassis connection bracket is achieved. First of all, the design load of the bracket was determined through a multibody dynamics analysis. This load case was determined among various driving conditions and the most critical load case was indicated as the design load of the bracket. This process was executed by using Adams/Car™ software. Subsequently, a design volume for the bracket was decided, which specifies the domain of topology optimization that will be employed later on. The determination of the design domain was made by considering the structural position of the design component, the neighbor components of the rear axle and the chassis. In this manner, the basic shape and dimensions of the bracket were created. The unnecessary volume of the draft design, which is not properly loaded under the design conditions was determined and removed from the design by means of topology optimization. The topology optimization was run in topology optimization module of ANSYS® Workbench 18.2 finite element analysis (FEA) software package. In the light of the primary shape obtained from the topology optimization study, a producible initial design model was built. This model was then subjected to FE analysis under the same circumstances with the draft model, in order to perform strength and deformation assessments of the initial design. Correspondingly, the critical regions were determined where stress concentrations were observed. The model was updated in a way that the stress values were reduced in these regions through the response surface methodology (RSM). The comparisons between the result and the initial geometries reveal that the mass of the connection bracket was reduced by 63%. Besides, the total deformation which was dropped by the design optimization is 13% lower than the initial design that was generated with the influence of topology optimization result.

Topology and Structural Optimization methods have been applied in order to support the development of the A400M rear fuselage. This paper first gives an overview about the optimization assisted design process implemented at EADS Military Aircraft. The optimization models and the topology optimization results for A400M rear fuselage will be described afterwards. The topology optimization has been applied at a system level, in order to determine an optimum concept for the complete A400M rear fuselage. These results have then been refined for the internal support structure and further detailed for a single tail-plane frame. The sizing of a fuselage requires consideration of the post-buckling behavior. The. paper explains the post-buckling analysis capabilities, which have been implemented in the optimization procedure LAGRANGE. The sizing optimization models applied with the ongoing A400M sizing optimization activities are briefly discussed. Topology optimization methods and applications have experienced rapid development within the last few years. Several commercial codes offering topology optimization capabilities have been developed and mainly applied to structures in the mechanical engineering and automotive area. The tools have demo nstrated their power to determine optimum load paths and weight optimum designs for complex comp onents. The huge weight-saving potential and the relatively easy handling of the topology optimization tools have strongly supported their rapid dissemination. The number of applications in aerospace has been fairly l up to now. However, positive experiences have been gained with the application of t opology and structural optimization methods in different aerospace projects at EADS Military Aircraft. The development of the A400M Rear Fuselage has been supported by optimization methods during the concept- and pre-design phase. The paper gives an overview about the optimization process and the results achieved within this project.

This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself. Concerning the first topic, we investigate different means to improve the robustness of density-based numerical models including geometrical nonlinearities. The conventional approach (scaling the local material properties) can result in convergence problems due to excessive deformation in low-stiffness finite elements. To avoid excessive deformation, we combine the element connectivity parameterization method (adapting the connectivity between finite elements) with level-set-based topology optimization. Furthermore, we achieve greater robustness of analysis method using a second and improved approach called element deformation scaling. This approach eliminates the need for solving internal equilibrium equations (needed for the element connectivity parameterization method) via an explicit relation between the local internal and global external displacement field. The second focus of this thesis is on the optimization process of level-set-based topology optimization, and in particular its numerical consistency. We observe that signed-distance reinitialization of the level-set function affects the shape of a design in the optimization process. To minimize this effect, we propose a discrete level-set method that is based on an approximate Heaviside function and focusing on the implementation. Furthermore, we also propose a level-set-based topology optimization method using an exact Heaviside function and mathematical programming that effectively eliminates the need for reinitialization. We demonstrate that our density-based level-set method is closely related to conventional density-based topology optimization methods, while offering the advantage of more control over the geometrical complexity. On the other hand, we confirm that the dependence of the final result on the initial design which remains one of the big challenges for level-set-based topology optimization. The potential of the proposed level-set method is shown by applying it on problems with stress constraints and geometrical nonlinearities and performing manufacturing tolerant topology optimization. Finally, this thesis offers a review of level-set methods for structural topology optimization to identify and discuss the different approaches that are available in literature. We can distinguish between level-set methods by examination of their design parameterization, sensitivities, update procedures and regularization techniques. A level-set-based design parameterization offers the advantage of a crisp distinction between subdomains. For this reason, X-FEM approaches and conforming discretizations are an interesting option to retain the crisp nature of the level-set-based description of the design. Many level-set methods are combined with density-based numerical models and are, therefore, closely related to conventional density-based topology optimization methods. In particular, recently proposed projection methods have much in common with a level-set-based design description. The results of level-set-based TO methods often rely heavily on regularization techniques that introduce inconsistencies in the optimization process. Numerical consistency does not necessarily lead to the best search direction, but is essential to find a Karush-Kuhn-Tucker point of the discretized optimization problem.

To solve generalized shape optimization problems, material topology optimization is applied to determine the basic layout, i.e., to insert and eliminate holes in the design space. In addition, the inner and outer contours are optimized in detail by shape optimization. To improve the quality of the results and to increase the numerical efe ciency, the design model is adapted during the optimization process. Two aspects of design adaptivity are considered. On the one hand, the parametrization of the design space is varied during the material topology optimization process and, on the other hand, the kind of design model is adapted during the overall optimization process switching between material topology and shape optimization. The adaptive techniques are discussed, and adaptive design modeling is verie ed for topology optimization problems of shell structures.

To solve generalized shape optimization problems, material topology optimization is applied to determine the basic layout, i.e., to insert and eliminate holes in the design space. In addition, the inner and outer contours are optimized in detail by shape optimization. To improve the quality of the results and to increase the numerical efe ciency, the design model is adapted during the optimization process. Two aspects of design adaptivity are considered. On the one hand, the parametrization of the design space is varied during the material topology optimization process and, on the other hand, the kind of design model is adapted during the overall optimization process switching between material topology and shape optimization. The adaptive techniques are discussed, and adaptive design modeling is verie ed for topology optimization problems of shell structures.

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

Topology optimization methods application for viscous flow problems is currently an active area of research. A general approach to deal with shape and topology optimization design is based on the topological derivative. This relatively new concept represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes and inclusions. In previous topological derivative-based formulations for viscous fluid flow problems, the topology is obtained by nucleating and removing holes in the fluid domain which creates numerical difficulties to deal with the boundary conditions for these holes. Thus, we propose a topological derivative formulation for fluid flow channel design based on the concept of traditional topology optimization formulations in which solid or fluid material is distributed at each point of the domain to optimize the cost function subjected to some constraints. By using this idea, the problem of dealing with the hole boundary conditions during the optimization process is solved because the asymptotic expansion is performed with respect to the nucleation of inclusions --- which mimic solid or fluid phases --- instead of inserting or removing holes in the fluid domain, which allows for working in a fixed computational domain. To evaluate the formulation, an optimization problem which consists in minimizing the energy dissipation in fluid flow channels is implemented. Results from considering Stokes and Navier-Stokes are presented and compared, as well as two- (2D) and three-dimensional (3D) designs. The topologies can be obtained in a few iterations with well defined boundaries.

A variational formulation of the topology optimization problem is presented. A strain energy functional, being an equivalent of compliance, was minimized while constraints were imposed on the body mass. A global mass constraint and a local constraint on the amount of mass accumulated in a single material point of the body were adopted. A penalization procedure was defined and implemented in the optimization process to speed up the latter. The procedure in the successive optimization process steps translocates mass within the design domain, from the less strained areas to the more strained ones. The optimization process was described as a series of sequences of topologies determined using various control parameters, including different threshold functions. This means that the optimization process is characterized by a sequence of objective functional values approaching a minimal value. Various functions updating Young’s modulus were considered. Primarily the updating method referred to as SIMP was adopted. Three ways of using the discrete strain energy value to update Young's modulus in the considered material point were taken into account. These were: the amount of energy accumulated in the preceding step, the sum of the amounts of energy from all the preceding steps and the average amount of energy from the last two steps. In order to ensure the global limiting condition a mass constancy satisfaction procedure was incorporated into the algorithm. The algorithm procedures are described in detail. Finally, the algorithm was used to analyze selected problem relating to the pavement structure and the structure of tall buildings.

Fabrication and characterization of thermal conductivity detectors (TCDs) of different flow channel and heater designs

MorphoGen: Topology optimization software for Extremely Modular Systems

Preface. List of Participants. Program. Part I: Basic aspects of topology optimization. Some recent results on topology optimization of periodic composites M.P. Bendsoe, et al. Problem classes, solution strategies and unified terminology of FE-based topology optimization G.I.N. Rozvany. Comparative study of optimizing the topology of plate-like structures via plate theory and 3-D theory of elasticity N. Olhoff. A formulation for optimal structural design with optimal materials J.E. Taylor. On the influence of geometrical non-linearities in topology optimization O. Sigmund, et al. Part II: Special techniques and problem classes in topology optimization. Structural reanalysis for topological modifications - a unified approach U. Kirsch, P.Y. Papalambros. Topological derivative and its application in optimal design of truss and beam structures for displacement, stress and buckling constraints Z. Mroz, D. Bojczuk. Transmissible loads in the design of optimal structural topologies M.B. Fuchs and E. Moses. New formulation for truss topology optimization problems under buckling constraints G. Cheng, et al. Part III: Treatment of computational difficulties in topology optimization. On Singular topologies and related optimization algorithm G. Cheng, Y. Wang. An efficient approach for checkerboard and minimum member size control and its implementation in a commercial software M. Zhou, et al. Some intrinsic difficulties with relaxation- en penalization methods in topology optimization K. Svanberg, M. Stolpe. Topology optimization subject to design-dependent validity of constraints W. Achtziger. Part IV: Emerging methods in topology optimization. Evolutionarycomputing and structural topology optimization -- a state of the art assessment P. Hajela, S. Vittal. Stress ratio type methods and conditional constraints -- a critical review G.I.N. Rozvany. Advances in evolutionary structural optimization: 1992-2000 O.M. Querin, et al. Part V: Mathematical aspects of topology optimization. Shape optimization with general objective functions using partial relaxation G. Allaire, et al. Equally stressed structures: two-dimensional perspective A.V. Cherkaev, I. Kucuk. Part VI: Practical applications of topology optimization. Practical aspects of commercial composite topology optimization software development H.L. Thomas, et al. Topology optimisation of the porous coating distribution in non-cemented hip prostheses H. Rodrigues, et al. A formulation in design for optimal energy absorption A.R. Diaz, et al. Part VII: Miscellaneous topics. Optimal design with non-linear elastic materials P. Pedersen. Damage tolerant topology optimization under multiple damage configurations M.A. Akgun, R.T. Haftka. On topology aspects of optimal bi-material physically non-linear structures S.V. Selyugin. Brief contributions (Extended abstracts). Model of functional adaptation of bone and design of composite structureal elements P. Bednarz, L. Lekszycki. On optimal design problems for unilaterally supported plates subjected to buckling I. Bock. Shape truss optimization in Java multithreaded genetic program S. Czarnecki. Optimal design of material and topology based on an energy model J. Du, J.E. Taylor. Modelling and optimization of porous materials deformation process B.M. Efros, et al. Topology optimization

A three-dimensional full-cell CFD model used to investigate the effects of different flow channel designs on PEMFC performance