| Course objectives: |
| The main objective of this graduate course is to provide the students with an introduction to the subject Boundary element method. To this end we present the fundamental concepts, principles and methodologies in such a way which will make possible for the students to understand and use commercial boundary element packages in their engineering practice with the intention of solving various mechanical problems numerically. |
| Course content and structure: |
| Classification of boundary value problems for the plane Poisson’s equation. The fundamental solution and its properties. The Green identity with proof.The first, second and third Green formulas for inner regions. Regular functions in finite and at infinity. Integral equations of the indirect method.Gradient of the scalar field u(Q) using the first Green formula. Single and double layer potentials – definitions and properties. Integral equations of the direct method. Determination of the constant c in the integral equation.Boundary elements and with linear and quadratic approximations of the geomtry and the unknown quantities. Triangular elements on the inner domain. Numerical solution of the integral equation of the direct method – reduction of the solution to a system of linear equtions.Problems of numerical integration. Methods of calculating weakly (logarithmic singularity) and strongly singular integrals. Corner points and discontinuous elements.Equations of plane elasticity. Derivation of uncoupled equations – Galjorkin functions and fundamental solutions of order one and two. Somigliana identity and the first, second and third Somiglian formulas for inner regions. Equations of the direct method. Numerical handling of weakly and strongly singular integrals.Somigliana formulas for outer regions. Solution techniques for solving the integral equations of the direct method. Examples. |
| Evaluation method: |
| Performance of a student during term time is evaluated via four homeworks. In addition there is a final exam (an oral one) to be taken in the examination period at the end of the semester. |
| Required reading: |
| Brebbia, C.A., Dominguez : Boundary element, an Introductory Course, McGraw-Hill Book Company, 1989, ISBN 0-905451-76-7 |
| Suggested reading: |
| John T. Katsikadels: Boundary elements: Theory and Applications Elsevier, 2002, ISBN: 0-080-44107-6 |
