The Integral Equations of the Theory of Elasticity

1. Front Matter

   Pages 1-8

   PDF

2. Integral Equations

   1. General Results on Linear Integral Equations

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 9-27

   2. One-Dimensional Singular Integral Equations

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 28-75

   3. Two-Dimensional Singular Integral Equations

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 76-113

   4. Approximate Solution of Integral Equations

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 114-127

3. Problems of the Theory of Elasticity and Cracks Mechanics

   1. The Integral Equations of Classical Two-Dimensional Problems

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 128-164

   2. Potential Theory for Basic Three-Dimensional Problems

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 165-199

   3. The Contact Problems of the Theory of Elasticity

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 200-228

   4. Problems of the Theory of Cracks

      • Solomon G. Mikhlin, Nikita F. Morozov, Michael V. Paukshto

      Pages 229-272

4. Back Matter

   Pages 273-375

   PDF

The book is devoted to the methods and results of the integral equations theory for elasticity problems. It consists of two parts and appendix. The first part contains a survey of mathematical topics necessary for understanding the main aspects of this course.The mathematical background is presented within the first part in detail. The second part deals with the most important results in the theory of boundary integral equations. It also discusses some new aspects of this theory which have been suggested by the authors, including the following problems: the theory of elasticity for an anisotropic medium, new type of integral equations (Pobedria's type), contact problems, fracture mechanics and Cosserat spectrum. The applications in fracture mechanics go well beyond merely illustrating the methods: they yield new results in some classical problems. This book is of interest to applied mechanicians, engineers, mathematicians and students interested in boundary element method and its applications.

• Elastizität
• Integralgleichung

• Weierstraß Institute Berlin, Germany

  Herbert Gajewski

• University St. Petersburg, St. Petersburg, Russia

  Solomon G. Mikhlin, Nikita F. Morozov

• Marine Technical University St. Petersburg, Russia

  Michael V. Paukshto

Policies and ethics