Boundary Collocation Techniques and Their Application in Engineering 1st Edition by Jan Adam Kolodziej, Andrzej Piotr Zielinski ISBN 1845643941 9781845643942
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ISBN 10: 1845643941
ISBN 13: 9781845643942
Author: Jan Adam Kolodziej, Andrzej Piotr Zielinski
Methods of mathematical modelling applied in contemporary computational mechanics can be divided into purely numerical and analytical-numerical procedures. Purely analytical solutions loose their popularity because of strong limitations connected with simple regions and mostly linear equations to which they can be applied. Obviously, the fundamental monographs like for example elastic solids, in fluid mechanics or for heat exchange are always popular and often quoted, but rather as sources of comparative benchmarks confirming correctness and accuracy of computer solutions.This volume can be divided into two parts. In the first part a general presentation of the boundary collocation approach and its numerous variants is enclosed. In the second part the method is applied to many different engineering problems, showing its properties, accuracy and convergence. Both evident advantages and also limitations of the approach are clearly presented. The observations are based mainly on investigations by the authors and their co-operators carried out in the last two decades. The monograph includes figures and tables that present results of numerical examples. A considerable number (above 1000) of papers and monographs concerning the discussed approach are quoted. They are listed separately in each chapter, which makes the literature survey easier to use.
Table of contents:
Chapter 1. General Information
Chapter 2. Analytical Trial T-Functions Applied in the Boundary Collocation Method
Chapter 3. Substructuring and T-Elements
Chapter 4. Basic Numerical Investigations of the Boundary Collocation Method
Chapter 5. Two-Dimensional Harmonic Problems: Laplace-Type Equations
Chapter 6. Problems Described by Two-Dimensional Biharmonic Equations
Chapter 7. Two-Dimensional Problem of Elastostatics
Chapter 8. Inverse Problems in 2D Elasticity
Chapter 9. Three-Dimensional Problems Described by Elliptic Equations
Chapter 10. Non-Homogeneous Equations and Nonlinear Boundary Conditions
Chapter 11. Physically Nonlinear Elastic–Plastic Problems
Chapter 12. Problems Described by Parabolic Equations
Chapter 13. Eigenvalue Problems
Chapter 14. Final Remarks, Conclusions and Perspectives
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Tags: Jan Adam Kolodziej, Andrzej Piotr Zielinski, Boundary, Collocation, Techniques, Application, Engineering