Topological Derivatives In Shape Optimization
Download Topological Derivatives In Shape Optimization full books in PDF, epub, and Kindle. Read online free Topological Derivatives In Shape Optimization ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Antonio André Novotny |
Publisher | : Springer Nature |
Total Pages | : 120 |
Release | : 2020-01-21 |
Genre | : Mathematics |
ISBN | : 3030369153 |
This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis. This new concept in shape optimization has applications in many different fields such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms. Some exercises are offered at the end of each chapter, helping the reader to better understand the involved concepts.
Author | : Antonio André Novotny |
Publisher | : Springer Science & Business Media |
Total Pages | : 423 |
Release | : 2012-12-14 |
Genre | : Technology & Engineering |
ISBN | : 3642352456 |
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.
Author | : Jan Sokolowski |
Publisher | : Springer Science & Business Media |
Total Pages | : 254 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642581064 |
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 | : Dorin Bucur |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2006-09-13 |
Genre | : Mathematics |
ISBN | : 0817644032 |
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
Author | : Antonio André Novotny |
Publisher | : Springer |
Total Pages | : 222 |
Release | : 2018-12-28 |
Genre | : Technology & Engineering |
ISBN | : 3030054322 |
The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.
Author | : Martin Philip Bendsoe |
Publisher | : Springer Science & Business Media |
Total Pages | : 602 |
Release | : 2006-10-03 |
Genre | : Technology & Engineering |
ISBN | : 1402047525 |
This volume offers edited papers presented at the IUTAM-Symposium Topological design optimization of structures, machines and materials - status and perspectives, October 2005. The papers cover the application of topological design optimization to fluid-solid interaction problems, acoustics problems, and to problems in biomechanics, as well as to other multiphysics problems. Also in focus are new basic modelling paradigms, covering new geometry modelling such as level-set methods and topological derivatives.
Author | : M. C. Delfour |
Publisher | : SIAM |
Total Pages | : 638 |
Release | : 2011-01-01 |
Genre | : Mathematics |
ISBN | : 0898719828 |
This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.
Author | : Vadim Komkov |
Publisher | : Academic Press |
Total Pages | : 399 |
Release | : 1986-05-01 |
Genre | : Technology & Engineering |
ISBN | : 0080960006 |
The book is organized into four chapters. The first three treat distinct types of design variables, and the fourth presents a built-up structure formulation that combines the other three. The first chapter treats finite-dimensional problems, in which the state variable is a finite-dimensional vector of structure displacements and the design parameters. The structual state equations are matrix equations for static response, vibration, and buckling of structures and matrix differential equations for transient dynamic response of structures, which design variables appearing in the coefficient matrices.
Author | : Tamal Krishna Dey |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 2022-03-10 |
Genre | : Mathematics |
ISBN | : 1009103199 |
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Author | : Harbir Antil |
Publisher | : Springer |
Total Pages | : 435 |
Release | : 2018-10-12 |
Genre | : Mathematics |
ISBN | : 1493986368 |
This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs). As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.