2 edition of **Shape optimisation of solids in contact using variational inequalities.** found in the catalog.

Shape optimisation of solids in contact using variational inequalities.

Maher Y. Al-Dojayli

- 78 Want to read
- 20 Currently reading

Published
**2003**
.

Written in English

**Edition Notes**

Thesis (Ph.D.) -- University of Toronto, 2003.

The Physical Object | |
---|---|

Pagination | 124 leaves. |

Number of Pages | 124 |

ID Numbers | |

Open Library | OL19732276M |

ISBN 10 | 0612784053 |

Greg Turk and James F. O'Brien. "Shape Transformation Using Variational Implicit Functions". In Proceedings of ACM SIGGRAPH , pages –, August Supplemental Material 3D shape transformation. 3D shape transformation. 3D shape transformation. 3D shape transformation with a torus as an influence shape. Transformation with warping #1. variational inequalities. For the applications of variational inequalities in in nite-dimensional spaces, the reader can refer to the book of Kinderlehrer and Stam-pacchia [41]. For the detail of a numerical treatment of variational inequalities, the reader can refer to an early book .

Variational inequalities provide a general mathematical framework for many problems arising in optimization. For example, constrained optimization problems like LP and NLP are special cases of VI, and systems of equations and complementarity problems can be cast as VI. Optimal Shape Proxies Together with the regions and proxies defined previously, we now define the total distortion over all the partitions: Optimal shape proxies: a set of proxies associated to the regions of a partition of that minimizes the total distortion above.

KeywordsOptimal shape problem, Convexity, Approximation, Speed method, Sobolev space, Variational inequalities, Finite element method. 1. INTRODUCTION The purpose of this paper is to develop an optimal shape design, which governed by the variational inequalities of the fourth order for the design of the shape for elastic-plastic problem. Abstract. Contact problems with given friction are considered for plane elasticity in the framework of shape-topological optimization. The asymptotic analysis of the second kind variational inequalities in plane elasticity is performed for the purposes of shape-topological optimization.

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Myśliński A. () Shape optimization of contact problems using mixed variational formulation. In: Davisson L.D. et al. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol Cited by: 4. This paper is concerned with the development of a mixed variational formulation and computational procedure for the shape optimization problem of linear elastic solids in possible contact with a rigid foundation.

The objective is to minimize the maximum value of the von Mises equivalent stress in a body (non-differentiable objective function), subject to a constraint on its volume and bound Cited by: 8. The shape of the free boundary arising from the solution of a variational inequality is controlled by the shape of the domain where the variational inequality is defined.

Shape and topological. strained shape optimization problems is discussed in [9, 36]. E.g., in [36, Chap. 4], shape derivatives of elliptic variational inequality problems are presented in the form of solutions to again variational inequalities.

In [29], shape optimization for 2D graph-like domains are investigated. Also [25, 26] present existence results for. In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems.

In this paper, we consider shape optimization problems constrained by variational inequalities of the first kind, so-called obstacle-type problems. Under appropriate assumptions, we prove existence of adjoints for regularized problems Cited by: 2. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems.

Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in.

Motivated and inspired by the growing contribution with respect to iterative approximations from some researchers in the literature, we design and investigate two types of brand-new semi-implicit viscosity iterative approximation methods for finding the fixed points of nonexpansive operators associated with contraction operators in complete {\operatorname{CAT}(0)}spaces and for solving related.

Variational Inequalities and Related Problems VI’s are closely related with many general problems of Nonlinear Analysis, such as complementarity, xed point and optimization problems. The simplest example of VI is the problem of solving a system of equations. It is easy to see that if U = Rn in.

Lions [ 1 I]; applications to a wide variety of free-boundary problems are discussed in the book of Duvaut and Lions[8]. Numerical methods based on variational inequalities are discussed in the two-volume text of Glowinski, Lions and TrCmolieres[6] and in the monograph of Theory of variational inequalities, flow through porous media - [ [.

Variational Inequalities On the other hand, in the case where a certain symmetry condition holds, the variational inequality problem can be reformulated as an optimization problem. In other words, in the case that the variational inequality formulation of the equilibrium conditions underlying a speciﬁc.

That chapter also discusses the merits and demerits of those approaches. In chapter 3, we describe a relaxed projection method, and a descent method for solving variational inequalities with some examples.

An application of the descent framework to a game theory problem leads to an algorithm for solving box constrained variational inequalities. () A Level Set Method in Shape and Topology Optimization for Variational Inequalities. International Journal of Applied Mathematics and Computer Science() Topological sensitivity analysis for three-dimensional linear elasticity problem.

A level set method in shape and topology optimization for variational inequalities 3. Shape Derivative The shape derivatives of solutions for the Signorini prob-lem can be evaluated by an application of the abstract re-sult on Hadamard differentiability of the projection op-erator onto convex sets in Hilbert spaces (Jarusek et al., ).

a.e. in Q admits analytic apply assume boundary value bounded called Chapter choose coercive compact conclude connected Consequently consider constant continuous convex set Corollary defined Definition denote the solution depends derivatives differential dimensional discuss domain dx dy elliptic equation estimate example exists extend fact.

which by the duality relation J(u) =I*(p*) coincides with ().In Chapter 6, we obtained an estimate of J(v) -J(u) invoking the dual problem and using its properties in order to find a directly computable and physically meaningful upper bound of J(v) -I*(q*).

For variational inequalities, deviation estimates are obtained in a similar way, but with some complications caused by the fact that. The present contribution investigates shape optimization problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions.

Sensitivity estimates and material derivatives are first derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. A shape-topological control of singularly perturbed variational inequalities is considered in the abstract framework for state-constrained optimization problems.

First quasi-variational inequality was introduced by Bensoussan and Lions in Many problems leading to v.i.-s are considered here: G. Duvaut and J.-L. Lions, \Inequalities in Mechanics and Physics", J.-F. Rodrigues, \Obstacle Problems in Mathematical Physics", The classical book on numerical methods for v.i.-s is.

This is almost a quite general fact: many problems of applied mathematics (e.g., static and dynamic traffic equilibrium problems, Cournot-Nash equilibrium problems, etc) involving minimality condition are equivalent to suitable variational inequalities.

This makes variational inequalities worth studying. present a novel approach where shape approximation is tackled as a discrete, variational partitioning problem, for which provably-good heuristics are readily available.

Related Work Many techniques have been specically designed to exploit an ob-ject’s local planarity, symmetry and features in order to optimize its geometric representation. ated using shape transformation, much in the same way as with contour interpolation for medical imaging.

Because of the smooth-ness properties of variational interpolation methods, we consider them a natural tool to explore for shape transformation in CAD. Finally, animated shape transformations have been used to cre.Since the early s, the mathematical theory of variational inequalities has been under rapid development, based on complex analysis and strongly influenced by 'real-life' application.

Many, but of course not all, moving free (Le., a priori un known) boundary problems originating from."The book under review deals with some variational methods to treat shape optimization problems.

The book contains a complete study of mathematical problems for scalar equations and eigenvalues, in particular regarding the existence of solutions in shape optimization.

The main goal of the book is to focus on the existence of an optimal Reviews: 1.