Inverse and Crack Identification Problems in Engineering Mechanics

1. Front Matter

   Pages i-xiii

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2. Introduction. Problem Description

   1. Front Matter

      Pages 1-1

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   2. Direct and Inverse Problems in Mechanics and Applications

      • Georgios E. Stavroulakis

      Pages 3-7

3. Theoretical and Computational Tools

   1. Front Matter

      Pages 9-9

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   2. Computational Mechanics

      • Georgios E. Stavroulakis

      Pages 11-54

   3. Computational and Structural Optimization

      • Georgios E. Stavroulakis

      Pages 55-83

   4. Selected Soft Computing Tools

      • Georgios E. Stavroulakis

      Pages 85-104

4. Applications to Inverse Problems

   1. Front Matter

      Pages 105-105

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   2. Static Problems

      • Georgios E. Stavroulakis

      Pages 107-155

   3. Steady-State Dynamics

      • Georgios E. Stavroulakis

      Pages 157-186

   4. Transient Dynamics

      • Georgios E. Stavroulakis

      Pages 187-223

5. Back Matter

   Pages 221-226

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Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applications in civil, aeronautical, nuclear, and general mechanical engineering. Mathematical modeling and the numerical study of these problems require high competence in computational mechanics and applied optimization. This is the first monograph which provides the reader with all the necessary information. Delicate computational mechanics modeling, including nonsmooth unilateral contact effects, is done using boundary element techniques, which have a certain advantage for the construction of parametrized mechanical models. Both elastostatic and harmonic or transient dynamic problems are considered. The inverse problems are formulated as output error minimization problems and they are theoretically studied as a bilevel optimization problem, also known as a mathematical problem with equilibrium constraints. Beyond classical numerical optimization, soft computing tools (neural networks and genetic algorithms) and filter algorithms are used for the numerical solution.
The book provides all the required material for the mathematical and numerical modeling of crack identification testing procedures in statics and dynamics and includes several thoroughly discussed applications, for example, the impact-echo nondestructive evaluation technique.
Audience: The book will be of interest to structural and mechanical engineers involved in nondestructive testing and quality control projects as well as to research engineers and applied mathematicians who study and solve related inverse problems. People working on applied optimization and soft computing will find interesting problems to apply to their methods and all necessary material to continue research in this field.

• algorithm
• algorithms
• construction
• engineering mechanics
• genetic algorithms
• mathematical modeling
• mechanical engineering
• mechanics
• modeling
• optimization

• Institute of Applied Mathematics, Department of Civil Engineering, Technical University Carolo Wilhelmina, Braunschweig, Germany

  Georgios E. Stavroulakis

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