Numerical Methods In Sensitivity Analysis And Shape Optimization

Author : Emmanuel Laporte
Publisher : Springer Science & Business Media
ISBN 13 : 1461200695
Total Pages : 202 pages
Book Rating : 4.97/5 ( download)

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Download or read book Numerical Methods in Sensitivity Analysis and Shape Optimization written by Emmanuel Laporte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.

Author : Jan Sokolowski
Publisher : Springer Science & Business Media
ISBN 13 : 3642581064
Total Pages : 254 pages
Book Rating : 4.69/5 ( download)

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Download or read book Introduction to Shape Optimization written by Jan Sokolowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

Author : Zhiye Zhao
Publisher : Springer Science & Business Media
ISBN 13 : 3642843824
Total Pages : 203 pages
Book Rating : 4.22/5 ( download)

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Download or read book Shape Design Sensitivity Analysis and Optimization Using the Boundary Element Method written by Zhiye Zhao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the various aspects of shape optimization of two dimensional continuum structures, including shape design sensitivity analysis, structural analysis using the boundary element method (BEM), and shape optimization implementation. The book begins by reviewing the developments of shape optimization, followed by the presentation of the mathematical programming methods for solving optimization problems. The basic theory of the BEM is presented which will be employed later on as the numerical tool to provide the structural responses and the shape design sensitivities. The key issue of shape optimization, the shape design sensitivity analy sis, is fully investigated. A general formulation of stress sensitivity using the continuum approach is presented. The difficulty of the modelling of the ad joint problem is studied, and two approaches are presented for the modelling of the adjoint problem. The first approach uses distributed loads to smooth the concentrated adjoint loads, and the second approach employs the singu larity subtraction method to remove the singular boundary displacements and tractions from the BEM equation. A novel finite difference based approach to shape design sensitivity is pre sented, which overcomes the two drawbacks of the conventional finite difference method. This approach has the advantage of being simple in concept, and eas ier implementation. A shape optimization program for two-dimensional continuum structures is developed, including structural analysis using the BEM, shape design sensitiv ity analysis, mathematical programming, and the design boundary modelling.

Author : J. Haslinger
Publisher : SIAM
ISBN 13 : 9780898718690
Total Pages : 291 pages
Book Rating : 4.94/5 ( download)

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Download or read book Introduction to Shape Optimization written by J. Haslinger and published by SIAM. This book was released on 2003-01-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization comprehensively, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Applications include contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics. Audience: the book is written primarily for students of applied mathematics, scientific computing, and mechanics. Most of the material is directed toward graduate students, although a portion of it is suitable for senior undergraduate students. Readers are assumed to have some knowledge of partial differential equations and their numerical solution, as well as modern programming language such as C++ Fortran 90.

Author : K. K. Choi
Publisher : Springer Science & Business Media
ISBN 13 : 0387273069
Total Pages : 336 pages
Book Rating : 4.68/5 ( download)

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Download or read book Structural Sensitivity Analysis and Optimization 2 written by K. K. Choi and published by Springer Science & Business Media. This book was released on 2006-12-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Author : American Society of Mechanical Engineers. Winter Annual Meeting
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.70/5 ( download)

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Download or read book Sensitivity Analysis and Optimization with Numerical Methods written by American Society of Mechanical Engineers. Winter Annual Meeting and published by . This book was released on 1990 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Il Han Park
Publisher : Springer
ISBN 13 : 9811302308
Total Pages : 368 pages
Book Rating : 4.05/5 ( download)

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Download or read book Design Sensitivity Analysis and Optimization of Electromagnetic Systems written by Il Han Park and published by Springer. This book was released on 2018-08-27 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems. It treats the subject in a unified manner, providing numerical methods and design examples. The specific focus is on continuum design sensitivity analysis, which offers significant advantages over discrete design sensitivity methods. Continuum design sensitivity formulas are derived from the material derivative in continuum mechanics and the variational form of the governing equation. Continuum sensitivity analysis is applied to Maxwell equations of electrostatic, magnetostatic and eddy-current systems, and then the sensitivity formulas for each system are derived in a closed form; an integration along the design interface. The book also introduces the recent breakthrough of the topology optimization method, which is accomplished by coupling the level set method and continuum design sensitivity. This topology optimization method enhances the possibility of the global minimum with minimised computational time, and in addition the evolving shapes during the iterative design process are easily captured in the level set equation. Moreover, since the optimization algorithm is transformed into a well-known transient analysis algorithm for differential equations, its numerical implementation becomes very simple and convenient. Despite the complex derivation processes and mathematical expressions, the obtained sensitivity formulas are very straightforward for numerical implementation. This book provides detailed explanation of the background theory and the derivation process, which will help readers understand the design method and will set the foundation for advanced research in the future.

Author : Kyung K. Choi
Publisher : Springer Science & Business Media
ISBN 13 : 0387271694
Total Pages : 457 pages
Book Rating : 4.99/5 ( download)

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Download or read book Structural Sensitivity Analysis and Optimization 1 written by Kyung K. Choi and published by Springer Science & Business Media. This book was released on 2006-12-30 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.

Author : Lisa G. Stanley
Publisher : SIAM
ISBN 13 : 0898715245
Total Pages : 155 pages
Book Rating : 4.48/5 ( download)

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Download or read book Design Sensitivity Analysis written by Lisa G. Stanley and published by SIAM. This book was released on 2002-01-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrates some of the important issues inherent in using the sensitivity equation method for PDEs.

Author : Pekka Neittaanmäki
Publisher : Springer
ISBN 13 : 3319235648
Total Pages : 328 pages
Book Rating : 4.46/5 ( download)

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Download or read book Mathematical Modeling and Optimization of Complex Structures written by Pekka Neittaanmäki and published by Springer. This book was released on 2015-10-07 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimization algorithms; * Optimal control problems with distributed and discrete control; * Shape optimization and shape design problems in science and engineering; * Sensitivity analysis and parameters optimization of complex systems.