# A New Boundary Element Formulation in Engineering

• Tania G. B. DeFigueiredo
Book

Part of the Lecture Notes in Engineering book series (LNENG, volume 68)

1. Front Matter
Pages N1-IX
2. Tania G. B. DeFigueiredo
Pages 1-15
3. Tania G. B. DeFigueiredo
Pages 16-43
4. Tania G. B. DeFigueiredo
Pages 44-81
5. Tania G. B. DeFigueiredo
Pages 82-106
6. Tania G. B. DeFigueiredo
Pages 107-148
7. Tania G. B. DeFigueiredo
Pages 149-180
8. Tania G. B. DeFigueiredo
Pages 181-185
9. Tania G. B. DeFigueiredo
Pages 186-196
10. Back Matter
Pages 197-203

### Introduction

1. 1 The Hybrid Displacement Boundary Element Model This work is concerned with the derivation of a numerical model for the solution of boundary-value problems in potential theory and linear elasticity. It is considered a boundary element model because the final integral equation involves some boundary integrals, whose evaluation requires a boundary discretization. Furthermore, all the unknowns are boundary vari­ ables. The model is completely new; it differs from the classical boundary element formulation ·in the way it is generated and consequently in the fi­ nal equations. A generalized variational principle is used as a basis for its derivation, whereas the conventional boundary element formulation is based on Green's formula (potential problems) and on Somigliana's identity (elas­ ticity), or alternatively through the weighted residual technique. 2 The multi-field variational principle which generates the formulation in­ volves three independent variables. For potential problems, these are the potential in the domain and the potential and its normal derivative on the boundary. In the case of elasticity, these variables are displacements in the domain and displacements and tractions on the boundary. For this reason, by analogy with the assumed displacement hybrid finite element model, ini­ tially proposed by Tong [1] in 1970, it can be called a hybrid displacement model. The final system of equations to be solved is similar to that found in a stiffness formulation. The stiffness matrix for this model is symmetric and can be evaluated by only performing integrations along the boundary.

### Keywords

Boundary Elements Numerical Methods Numerische Methoden Randelement Variational Principles Variationsprinzip development

#### Authors and affiliations

• Tania G. B. DeFigueiredo
• 1
1. 1.Departamento de Engenharia CivilUniversidade de Brasilia Campus UniversitarioBrasiliaia-DFBrazil

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-84504-8
• Copyright Information Springer-Verlag Berlin Heidelberg 1991
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-54030-4
• Online ISBN 978-3-642-84504-8
• Series Print ISSN 0176-5035
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