The Optimum Shape

The Optimum Shape
Author: James Bennett
Publisher: Springer Science & Business Media
Total Pages: 404
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461594839
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This book contains the papers presented at the International Symposium, "The Optimum Shape: Automated Structural Design," held at the General Motors Research Laboratories on September 3D-October 1, 1985. This was the 30th symposium in a series which the Research Laboratories began sponsoring in 1957. Each symposium has focused on a topic that is both under active study at the Research Laboratories and is also of interest to the larger technical community. While attempts to produce a structure which performs a certain task with the minimum amount of resources probably predates recorded civilization, the idea of coupling formal optimization techniques with computer-based structural analysis techniques was first proposed in the early 1960s. Although it was recognized at this time that the most fundamental description of the problem would be in terms of the shape or contours of the structure, much of the early work described the problem in terms of structural sizing parameters instead of geometrical descriptions. Within the past few years, several research groups have started to explore this more fundamental area of shape design. Initial research has raised many new questions about appropriate selection of design variables, methods of calculating derivatives, and generation of the underlying analysis problem.

Applied Shape Optimization for Fluids

Applied Shape Optimization for Fluids
Author: Bijan Mohammadi
Publisher: OUP Oxford
Total Pages: 296
Release: 2009-09-24
Genre: Mathematics
ISBN: 0199546908
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The fields of computational fluid dynamics (CFD) and optimal shape design (OSD) have received considerable attention in the recent past, and are of practical importance for many engineering applications.This new edition of Applied Shape Optimization for Fluids deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Strokes, but also those for microfluids) and with the numerical simulation of these problems. It presents the state of the art in shape optimization for an extended range of applications involving fluid flows. Automatic differentiation, approximate gradients, unstructured mesh adaptation, multi-modelconfigurations, and time-dependent problems are introduced, and their implementation into the industrial environments of aerospace and automobile equipment industry explained and illustrated.With the increases in the power of computers in industry since the first edition, methods which were previously unfeasible have begun giving results, namely evolutionary algorithms, topological optimization methods, and level set algortihms. In this edition, these methods have been treated in separate chapters, but the book remains primarily one on differential shape optimization.This book is essential reading for engineers interested in the implementation and solution of optimization problems using commercial packages or in-house solvers and graduates and researchers in applied mathematics, aerospace, or mechanical engineering, fluid dynamics, and CFD. More generally, anyone needing to understand and solve design problems or looking for new exciting areas for research and development in this area will find this book useful, especially in applying the methodology topractical problems.

Mesh Generation and Adaptation

Mesh Generation and Adaptation
Author: Rubén Sevilla
Publisher: Springer Nature
Total Pages: 328
Release: 2022-05-18
Genre: Mathematics
ISBN: 3030925404
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The developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.

Introduction to Shape Optimization

Introduction to Shape Optimization
Author: Jan Sokołowski
Publisher: Springer Science & Business Media
Total Pages: 0
Release: 1992
Genre: Control theory
ISBN: 9783540541776
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1 Introduction to shape optimization.- 1.1. Preface.- 2 Preliminaries and the material derivative method.- 2.1. Domains in ?N of class Ck.- Surface measures on ?.- 2.3. Functional spaces.- 2.4. Linear elliptic boundary value problems.- 2.5. Shape functionals.- 2.6. Shape functionals for problems governed by linear elliptic boundary value problems.- 2.6.1. Shape functionals for transmission problems.- 2.6.2. Approximation of homogenuous Dirichlet problems.- 2.7. Convergence of domains.- 2.8. Transformations Tt of domains.- 2.9. The speed method.- 2.10. Admissible speed vector fields Vk(D).- 2.11. Eulerian derivatives of shape functionals.- 2.12. Non-differentiable shape functionals.- 2.13. Properties of Tt transformations.- 2.14. Differentiability of transported functions.- 2.15. Derivatives for t > 0.- 2.16. Derivatives of domain integrals.- 2.17. Change of variables in boundary integrals.- 2.18. Derivatives of boundary integrals.- 2.19. The tangential divergence of the field V on ?.- 2.20. Tangential gradients and Laplace-Beltrami operators on ?.- 2.21. Variational problems on ?.- 2.22. The transport of differential operators.- 2.23. Integration by parts on ?.- 2.24. The transport of Laplace-Beltrami operators.- 2.25. Material derivatives.- 2.26. Material derivatives on ?.- 2.27. The material derivative of a solution to the Laplace equation with Dirichlet boundary conditions.- 2.28. Strong material derivatives for Dirichlet problems.- 2.29. The material derivative of a solution to the Laplace equation with Neumann boundary conditions.- 2.30. Shape derivatives.- 2.31. Derivatives of domain integrals (II).- 2.32. Shape derivatives on ?.- 2.33. Derivatives of boundary integrals.- 3 Shape derivatives for linear problems.- 3.1. The shape derivative for the Dirichlet boundary value problem.- 3.2. The shape derivative for the Neumann boundary value problem.- 3.3. Necessary optimality conditions.- 3.4. Parabolic equations.- 3.4.1 Neumann boundary conditions.- 3.4.2 Dirichlet boundary conditions.- 3.5. Shape sensitivity in elasticity.- 3.6. Shape sensitivity analysis of the smallest eigenvalue.- 3.7. Shape sensitivity analysis of the Kirchhoff plate.- 3.8. Shape derivatives of boundary integrals: the non-smooth case in ?2.- 3.9. Shape sensitivity analysis of boundary value problems with singularities.- 3.10. Hyperbolic initial boundary value problems.- 4 Shape sensitivity analysis of variational inequalities.- 4.1. Differential stability of the metric projection in Hilbert spaces.- 4.2. Sensitivity analysis of variational inequalities in Hilbert spaces.- 4.3. The obstacle problem in H1 (?).- 4.3.1. Differentiability of the Newtonian capacity.- 4.3.2. The shape controlability of the free boundary.- 4.4. The Signorini problem.- 4.5. Variational inequalities of the second kind.- 4.6. Sensitivity analysis of the Signorini problem in elasticity.- 4.6.1. Differential stability of solutions to variational inequalities in Hilbert spaces.- 4.6.2. Shape sensitivity analysis.- 4.7. The Signorini problem with given friction.- 4.7.1. Shape sensitivity analysis.- 4.8. Elasto-Plastic torsion problems.- 4.9. Elasto-Visco-Plastic problems.- References.

Liquid Film Coating

Liquid Film Coating
Author: P.M. Schweizer
Publisher: Springer Science & Business Media
Total Pages: 794
Release: 2012-12-06
Genre: Science
ISBN: 9401153426
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This multi-authored volume provides a comprehensive and in-depth account of the highly interdisciplinary science and technology of liquid film coating. The book covers fundamental principles from a wide range of scientific disciplines, including fluid mechanics aand transport phenomena, capillary hydrodynamics, surface and colloid science. The authors, all acknowledged eperts in their fields, represent a balance between industrial and academic points of view. Throughout the text, many case studies illustrate how scientific principles together with advanced experimental and theoretical methods are applied to develop and optimize manufacturing processes of eve increasing sophiatication and efficiency. In the first part of the book, the authors systematically recount the underlying physical principles and important material properties. The second part of the book gives a comprehensive overview of the most advanced experimental, mathematical and computational methods available today to investigate coating processes. The third part provides an overview and critical literature review for all major classes of liquid film coating processes of industrial importance.

Optimization of Structural Topology, Shape, and Material

Optimization of Structural Topology, Shape, and Material
Author: Martin P. Bendsoe
Publisher: Springer Science & Business Media
Total Pages: 278
Release: 2013-03-14
Genre: Technology & Engineering
ISBN: 3662031159
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In the past, the possibilities of structural optimization were restricted to an optimal choice of profiles and shape. Further improvement can be obtained by selecting appropriate advanced materials and by optimizing the topology, i.e. finding the best position and arrangement of structural elements within a construction. The optimization of structural topology permits the use of optimization algorithms at a very early stage of the design process. The method presented in this book has been developed by Martin Bendsoe in cooperation with other researchers and can be considered as one of the most effective approaches to the optimization of layout and material design.