Applications of the topological derivative method. ([2019])

• Record Type: Book
• Further Information: Note: Antonio André Novotny, [and 2 others].
• Authors: Novotny, Antonio André
• Contents: Intro; Foreword; Preface; Contents; 1 Introduction; 1.1 Theoretical Framework for Local Solutions; 1.2 Elementary Example of Topological Derivative; 1.3 Shape and Topology Optimization; 1.4 Evaluation of Topological Derivatives; 1.5 Open Problems for Topological Derivative Method; 1.6 Description of the Content of the Book; 2 Theory in Singularly Perturbed Geometrical Domains; 2.1 Preliminaries; 2.2 Asymptotic Expansions for the Domain Decomposition Technique; 2.2.1 Asymptotic Expansions of Steklov-Poincaré Operators 2.2.2 From Singular Domain Perturbations to Regular Perturbations of Bilinear Forms in Truncated Domains2.2.3 Signorini Problem in Two Spatial Dimensions; 2.2.4 Domain Decomposition Method for Elasticity; 2.3 Matched Asymptotic Expansions for Neumann Problem; 2.3.1 Asymptotic Expansion of the Steklov-Poincaré; 2.3.2 Asymptotic Expansion of the Linear Form; 2.3.3 Asymptotic Expansion of the Energy Functional; 2.4 Asymptotics of Steklov-Poincaré Operators in Multilayer Subdomains; 2.4.1 Multilayer Inclusions; 2.4.2 Steklov-Poincaré Operator in Multilayer Inclusion 2.4.3 Asymptotic Expansions in Multilayer Subdomain2.4.4 Multilayer Subdomains in Linear Elasticity; 3 Steklov-Poincaré Operator for Helmholtz Equation; 3.1 Representation of Solutions for Helmholtz Equation; 3.1.1 Case I: Coercive Operator; 3.1.2 Case II: Non-coercive Operator; 3.2 Numerical Testing of Approximate Formulas for Steklov-Poincaré Operators; 3.3 Solutions in the Ring for Helmholtz; 3.4 Precision of Formulas for Helmholtz in Both Cases; 4 Topological Derivatives for Optimal Control Problems; 4.1 Example in One Spatial Dimension; 4.2 Control Problem; 4.3 Topological Derivative 4.4 Numerical Example4.5 Final Remarks; 5 Optimality Conditions with Topological Derivatives; 5.1 Preliminaries; 5.2 Model Problem; 5.3 Double Asymptotic Expansion; 5.4 Topological Differential with Respect to Multiple Holes; 5.5 Dependence of Solutions on Boundary Variations; 5.6 Simultaneous Topology and Shape Modification; 5.7 Analytical Example; 6 A Gradient-Type Method and Applications; 6.1 Preliminaries; 6.2 First Order Topology Design Algorithm; 6.3 Shape and Topology Optimization; 6.3.1 Structural Topology Design; 6.3.2 Fluid Flow Topology Design; 6.3.3 Multiscale Material Design 6.3.4 Additional Applications6.4 Future Developments; 7 Synthesis of Compliant Thermomechanical Actuators; 7.1 Preliminaries; 7.1.1 Simple Example of a Bar Structure; 7.1.2 Topological Derivative for Inclusions; 7.2 Problem Formulation; 7.2.1 Unperturbed Problem; 7.2.2 Perturbed Problem; 7.3 Existence of the Topological Derivative; 7.4 Topological Asymptotic Analysis; 7.4.1 Contrast on the Elastic Coefficients; 7.4.2 Contrast on the Thermal Coefficients; 7.4.3 Topological Derivative; 7.5 Numerical Experiments; 7.5.1 Example 1: Amplifier; 7.5.2 Example 2: Inverter with Eccentricity Effect
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 512/.55; Topological dynamics; Electronic books
• Languages: English
• ISBNs: 9783030054328; 3030054322
• Notes: Note: Description based on online resource; title from digital title page (viewed on February 14, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.