Download or read book Parametric and Topology Optimization for Multidisciplinary Design Using a Decomposition Method to Address Nonlinear Boundary Conditions written by Tianliang Yu and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearities frequently appear in the field couplings and/or the boundary conditions in the multidisciplinary problems that are encountered in aerospace system design. Compared to linear analysis, nonlinear analysis involves higher computational costs to determine solutions and gradients. Efficient strategies are critical for multidisciplinary design optimization (MDO) problems, especially for those with nonlinearities. In this thesis, an MDO problem is solved in a hierarchical architecture that comprises two subproblems of optimization, namely discipline-level optimization, and design-level optimization. In the discipline-level optimization, a linearization method is proposed to decompose a multidisciplinary system with nonlinear boundary conditions into multiple subsystems, which can be modeled using systems of coupled linear equations. The multidisciplinary analysis problem the becomes equivalent to an optimization problem that minimizes the discrepancy between the shared boundary variables of each subsystem. In the design-level optimization, both gradient-based and heuristic algorithms can be used with respect to the global design variables subject to design constraints. Two diverse case problems with boundary nonlinearities, which are representative of aeronautical and astronautical applications, are investigated to validate the proposed method. The first case problem is a topology optimization for the design of a contact-aided heat valve structure for spacecraft passive thermal control. The thermal control is implemented based on variable thermal contact resistance (TCR), which depends on the contact pressure at an interface caused by material thermal expansion. The thermal contact resistance is a nonlinear function of the contact pressure; thus, the problem can be modeled as a thermo-mechanical coupled system with nonlinear boundary conditions. The optimization objective is maximizing the performance of the heat valve, which operates to minimize temperature variations of spacecraft electronic devices under different thermal loads. First, a one-dimensional model is developed to validate the feasibility of the thermal control mechanism. Second, a finite element method is formulated to address thermal conduction and thermal expansion of isotropic materials in a design domain of rectangular shape for the two-dimensional model. A topology optimization scheme based on the solid isotropic material with penalization (SIMP) approach is developed to explore the optimal material distribution. Using the proposed linearization method, the nonlinear thermal boundary conditions are transformed into Dirichlet boundary conditions. Then the coupled system can be solved by minimizing the difference of contact pressures computed from the thermal and mechanical systems in the discipline-level optimization. The method of moving asymptotes (MMA) is used to update design variables in the design-level topology optimization. Optimal topologies and corresponding temperature distributions are obtained using input parameters and constraints representing realistic situations. For the "hot" case, in which a uniform heat flux of 50,000W/m2 is input to the top surface, the top surface temperature remains lower than the maximum allowable temperature, 305K, for all optimal designs with material volume fraction higher than 0.2. For both the hot and cold cases, the top surface temperature never drops below the minimum allowable temperature, 275K. Results also show that the convergence of the analysis algorithm is sensitive to the initial guess of the Dirichlet boundary conditions. Although the algorithm lacks robustness for special cases, the linearization method and topology optimization scheme are generally effective for design optimization of the contact-aided heat valve structure. The second case problem is a parametric optimization for the design of a bimorph piezoelectric-driven synthetic jet actuator (SJA). SJAs are zero-net-mass-flux actuators which create non-zero-net momentum flux via periodic suction and ejection of fluid through an orifice. Resonant piezoelectric-diaphragm-type SJAs have been studied recently, yet the modeling remains a challenge due to the complexities and nonlinearities associated with both electro-elastic and fluid-structure couplings. The ultimate design objective is maximizing the time-averaged jet momentum. Lumped-element modeling has shown good capability to predict jet momentum but lacks accuracy for high-amplitude nonlinear response. Finite element methods yield accurate predictions but are computationally costly for design and optimization purposes. In this thesis, a low-order model is developed to capture electro-elastic and acoustic-structure couplings with adequate accuracy. In the initial approach, by matching the diaphragm mechanical resonance frequency with the cavity acoustic resonance frequency, the performance of optimal SJA design is determined by optimizing the structural proxies of the jet, such as blocking pressure and free displacement. An electro-elastic assumed-modes model is implemented to study the transverse motion of the piezoelectric diaphragms. In the improved approach, the performance of the jet is studied directly by coupling the electro-elastic model to a simplified cavity acoustic model, which is a one-degree-of-freedom spring-mass system. The linearity of the system is determined by the damping force associated with jet velocity. If the damping force is linear with velocity, the system is linear, and vice versa. For the case of a nonlinear jet damping force, a linearization method is implemented in a way that approximates the nonlinear periodic responses by the superposition of finite numbers of linear responses at odd harmonics of the driving frequency using truncated Fourier series. Therefore, the nonlinear viscous damping boundary condition can be transformed into Neumann boundary conditions at each odd harmonic frequency. The response of the nonlinear electro-elastic-acoustic coupled system can be solved using systems of linear equations at each of these frequencies. Then the discipline-level optimization minimizes the difference of the viscous damping forces obtained from the initial guess of the boundary conditions and the solutions of the coupled system equations. In the design-level optimization, a parametric optimization scheme based on a particle swarm optimization approach maximizes the time-averaged jet momentum. Optimal configurations based on the optimization results are obtained based on both linear and nonlinear models. For the linear model, the optimal design has a short-circuit resonance frequency of 1332 Hz, and an acoustic resonance frequency of 551 Hz. For the nonlinear model, the optimal design has a short-circuit resonance frequency of 1523 Hz, and an acoustic resonance frequency of 725 Hz. Although the optimal designs are different using linear and nonlinear models, both results show similar patterns, among them that the structural resonance frequency does not match but exceeds the acoustic resonance frequency. Using the nonlinear model, the best performance is found in the optimal configuration using PZT8, which has a driving frequency of 1270 Hz, a jet velocity of 390 m/s, a jet momentum flux of 4.79 m4/s2 driven at 10% of the material's coercive field. The linearization method and parametric optimization scheme are generally effective for the design optimization of the piezoelectric-driven synthetic jet actuators. Both case studies generally validate the feasibility of the proposed method for practical aerospace system designs.

Download or read book Multidisciplinary Design Optimization written by Natalia M. Alexandrov and published by SIAM. This book was released on 1997-01-01 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidisciplinary design optimization (MDO) has recently emerged as a field of research and practice that brings together many previously disjointed disciplines and tools of engineering and mathematics. MDO can be described as a technology, environment, or methodology for the design of complex, coupled engineering systems, such as aircraft, automobiles, and other mechanisms, the behavior of which is determined by interacting subsystems.

Download or read book Topology Optimization written by Martin Philip Bendsoe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition, has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also materials and MEMS.

Download or read book Domain Decomposition Methods in Science and Engineering XXVI written by Susanne C. Brenner and published by Springer Nature. This book was released on 2023-03-15 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.

Download or read book Learning Topology Optimization Process for Compliance Minimization with Data driven Method written by Qiaochu Ma and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology optimization is a method of structural design that addresses the engineering challenge of optimally distributing material within a specified design domain to achieve peak performance. Over the past several decades, the method has experienced rapid advancements and remains a vibrant area of research, with ongoing enhancements in both theory and application. However, while topology optimization has gained increasing traction in real-world applications, the substantial computational cost associated with conventional methods hinders its broader applicability. The computational cost in the conventional topology optimization method is heavy due to the intrinsic nature of the Finite Element Analysis(FEA) and sensitivity analysis, coupled with the iterative nature of the optimization process. FEA is employed to evaluate the performance of a design. This involves discretizing the design domain into a large number of elements and nodes. The computational cost of FEA increases dramatically with the number of elements because for each design iteration, stiffness matrices need to be recomputed, and systems of equations must be solved. After evaluating the performance using FEA, sensitivity analysis is conducted to understand how small changes in the design variables affect the performance objectives and constraints. This is essential to guide the optimization algorithm in the right direction. Sensitivity analysis requires additional computations, often involving derivatives of the objective and constraints with respect to design variables. These computations can become computationally intensive, especially for intricate or nonlinear problems. To improve computational efficiency, a subset of studies has explored the use of machine learning frameworks in addressing challenges within topology optimization. Broadly speaking, machine learning models applied to topology optimization fall into two main categories. The first approach substitutes the iterative process with a non-iterative neural network. The primary advantage of this approach is its ability to bypass the iterative procedure, enabling rapid generation of optimal topologies in mere seconds. However, this method presents challenges, including limited generalization capabilities-particularly in scenarios with unseen boundary conditions-and the potential generation of disconnect structures. The second approach endeavors to optimize topologies by finding surrogate representations of geometric shape, which are then parametrized and optimized using deep learning. The primary strength lies in retaining the iterative process inherent to topology optimization, which facilitates the generation of intermediate results, and it does not suffer from generalization issues. However, a significant drawback is its reliance on FEA and sensitivity analyses in every iteration. Consequently, the gains in computational efficiency are marginal. The objective of this dissertation is to address the topology optimization for compliance minimization problems in both 2D and 3D using machine learning methods that possess superior generalization capabilities and yield high-quality results. To achieve this, it is imperative to develop a new deep learning framework capable of producing high-quality intermediate outcomes while eliminating the need for external FEA and sensitivity analyses in each iteration. To secure intermediate results without the reliance on FEA and sensitivity analyses, the dissertation recasts the iterative procedure in topology optimization as a recursive process. This process is modeled using a recurrent neural network. Notably, the network achieves exemplary performance in predicting scenarios with unseen boundary conditions. This is accomplished by compelling the neural network to adhere to the optimization trajectory inherent in the conventional optimization procedure. Building upon the foundation of the recurrent neural network, the dissertation posits that the topology optimization process can be conceptualized as an iterative sequence of simple differential equations, reminiscent of the numerical solution for a definite integral. The dynamics governing the updates to the design variables are articulated as outcomes from the neural network. Consequently, the structural configurations at every iterative juncture can be derived through integration from the onset to the present step. This model showcases exceptional prowess in terms of scalability and also excels in addressing scenarios with unseen boundary conditions. The dissertation further endeavors to ensure high-quality outcomes by integrating a 2-layer Generative Adversarial Neural Network, specifically aimed at eradicating issues of disconnected structures. Additionally, the dissertation expands the application of the recurrent neural network to address 3D challenges. Given the inherent complexities that arise with increased dimensionality, a temporal multi-attention model has been devised. This model facilitates the flow of information across multiple updates into the neural network. The result is a commendable performance in charting the complete trajectory of topology optimization in 3D, particularly in scenarios with unseen boundary conditions.

Download or read book Domain Decomposition Methods in Science and Engineering written by Ralf Kornhuber and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Download or read book Domain Decomposition Methods in Science and Engineering XVI written by Olof Widlund and published by Springer Science & Business Media. This book was released on 2007-07-30 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Download or read book Isogeometric Topology Optimization written by Jie Gao and published by Springer Nature. This book was released on 2022-04-26 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic description about the development of Isogeometric Topology Optimization (ITO) method using the density, and then addresses the effectiveness and efficiency of the ITO method on several design problems, including multi-material structures, stress-minimization structures, piezoelectric structures and also with the uniform manufacturability, ultra-lightweight architected materials with extreme bulk/shear moduli, auxetic metamaterials and auxetic meta-composites with the NPRs behavior in microstructures. A detailed MATLAB implementation of the ITO method with an in-house code “IgaTop” is also presented.

Download or read book Topology Design of Structures written by Martin P Bendse and published by Kluwer Academic Pub. This book was released on 1993 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: The efficient use of materials is of great importance, and the choice of the basic topology for the design of structures and mechanical elements is crucial for the performance of sizing of shape optimization. This volume provides a comprehensive review of the state of the art in topology design, spanning fundamental mathematical, mechanical and implementation issues. Topology design of discrete structures involves large scale computational problems and the need to select structural elements from a discrete set of possibilities. The formulation and solution of discrete design problems are described, including new applications of genetic algorithms and dual methods. For continuum problems the emphasis is on the `homogenization method', which employs composite materials as the basis for defining shape in terms of material density, unifying macroscopic structural design optimization and micromechanics. All aspects of this field are covered, including computational aspects and the use of the homogenization method in a computer-aided design environment.

Download or read book Domain Decomposition Methods in Science and Engineering XXI written by Jocelyne Erhel and published by Springer. This book was released on 2014-10-10 with total page 931 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.

Download or read book Topology Design Methods for Structural Optimization written by Osvaldo M. Querin and published by Butterworth-Heinemann. This book was released on 2017-06-09 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Design Methods for Structural Optimization provides engineers with a basic set of design tools for the development of 2D and 3D structures subjected to single and multi-load cases and experiencing linear elastic conditions. Written by an expert team who has collaborated over the past decade to develop the methods presented, the book discusses essential theories with clear guidelines on how to use them. Case studies and worked industry examples are included throughout to illustrate practical applications of topology design tools to achieve innovative structural solutions. The text is intended for professionals who are interested in using the tools provided, but does not require in-depth theoretical knowledge. It is ideal for researchers who want to expand the methods presented to new applications, and includes a companion website with related tools to assist in further study. Provides design tools and methods for innovative structural design, focusing on the essential theory Includes case studies and real-life examples to illustrate practical application, challenges, and solutions Features accompanying software on a companion website to allow users to get up and running fast with the methods introduced Includes input from an expert team who has collaborated over the past decade to develop the methods presented

Download or read book Multiscale Structural Topology Optimization written by Liang Xia and published by Elsevier. This book was released on 2016-04-27 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain. Presents the first attempts towards topology optimization design of nonlinear highly heterogeneous structures Helps with simultaneous design of the topologies of both macroscopic structure and microscopic materials Helps with development of computer codes for the designs of nonlinear structures and of materials with extreme constitutive properties Focuses on the simultaneous design of both macroscopic structure and microscopic materials Includes a reduce database model from a set of numerical experiments in the space of effective strain

Download or read book Decomposition Techniques in Mathematical Programming written by Antonio J. Conejo and published by Springer Science & Business Media. This book was released on 2006-04-28 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.

Download or read book Robust Optimization Directed Design written by Andrew J. Kurdila and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust design—that is, managing design uncertainties such as model uncertainty or parametric uncertainty—is the often unpleasant issue crucial in much multidisciplinary optimal design work. Recently, there has been enormous practical interest in strategies for applying optimization tools to the development of robust solutions and designs in several areas, including aerodynamics, the integration of sensing (e.g., laser radars, vision-based systems, and millimeter-wave radars) and control, cooperative control with poorly modeled uncertainty, cascading failures in military and civilian applications, multi-mode seekers/sensor fusion, and data association problems and tracking systems. The contributions to this book explore these different strategies. The expression "optimization-directed” in this book’s title is meant to suggest that the focus is not agonizing over whether optimization strategies identify a true global optimum, but rather whether these strategies make significant design improvements.

Download or read book Topology Optimization Design of Heterogeneous Materials and Structures written by Daicong Da and published by John Wiley & Sons. This book was released on 2019-12-30 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue. The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high industrial and practical relevance. Part 1 starts by testing the limits of the homogenization-based approach when the size of the representative volume element is non-negligible compared to the structure. The book then introduces a non-local homogenization scheme to take into account the strain gradient effects. Using a phase field method, Part 2 offers three significant contributions concerning optimal placement of the inclusion phases. Respectively, these contributions take into account fractures in quasi-brittle materials, interface cracks and periodic composites. The topology optimization proposed has significantly increased the fracture resistance of the composites studied.

Download or read book Shape Optimization and Free Boundaries written by Michel C. Delfour and published by Springer. This book was released on 2014-10-09 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape optimization deals with problems where the design or control variable is no longer a vector of parameters or functions but the shape of a geometric domain. They include engineering applications to shape and structural optimization, but also original applications to image segmentation, control theory, stabilization of membranes and plates by boundary variations, etc. Free and moving boundary problems arise in an impressingly wide range of new and challenging applications to change of phase. The class of problems which are amenable to this approach can arise from such diverse disciplines as combustion, biological growth, reactive geological flows in porous media, solidification, fluid dynamics, electrochemical machining, etc. The objective and orginality of this NATO-ASI was to bring together theories and examples from shape optimization, free and moving boundary problems, and materials with microstructure which are fundamental to static and dynamic domain and boundary problems.

Download or read book Topology Optimization of Compliant Mechanisms written by Xianmin Zhang and published by Springer. This book was released on 2018-05-02 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers various topics regarding the design of compliant mechanisms using topology optimization that have attracted a great deal of attention in recent decades. After comprehensively describing state-of-the-art methods for designing compliant mechanisms, it provides a new topology optimization method for finding new flexure hinges. It then presents several attempts to obtain distributed compliant mechanisms using the topology optimization method. Further, it discusses a Jacobian-based topology optimization method for compliant parallel mechanisms, and introduces readers to the topology optimization of compliant mechanisms, taking into account geometrical nonlinearity and reliability. Providing a systematic method for topology optimization of flexure hinges, which are essential for designing compliant mechanisms, the book offers a valuable resource for all readers who are interested in designing compliant mechanism-based positioning stages. In addition, the methods for solving the de facto hinges in topology optimized compliant mechanisms will benefit all engineers seeking to design micro-electro-mechanical system (MEMS) structures.