عنوان

Applications of the topological derivative method /

3030054322

3030054330

9783030054328

9783030054335

3030054314

9783030054311

Applications of the topological derivative method /

[Book]

Antonio André Novotny, [and 2 others].

Cham, Switzerland :

Springer,

[2019]

1 online resource

Studies in systems, decision and control ;

volume 188

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.

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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.

Springer Nature

com.springer.onix.9783030054328

Applications of the Topological Derivative Method.

9783030054311

Topological dynamics.

Topological dynamics.

TEC004000

TJFM

TJFM

Novotny, Antonio André

20200823081532.0

pn

[Book]

Y