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A New Boundary Element Formulation in Engineering

Tania G.B. DeFigueiredo (Autor)

Buch | Softcover

IX, 198 Seiten

1991 | 1. Softcover reprint of the original 1st ed. 1991
Springer Berlin (Verlag)
978-3-540-54030-4 (ISBN)

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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.

1 Introduction.- 1.1 The Hybrid Displacement Boundary Element Model.- 1.2 Historical Development of Variational Principles.- 1.3 Variational Principles and Finite Element Models.- 1.4 Boundary Element Method Fundamentals.- 1.5 Boundary Element Variational Formulations.- 2 Potential Problems.- 2.1 Introduction.- 2.2 Indicial Notation.- 2.3 Basic Equations.- 2.4 Generalized Variational Principle.- 2.5 Derivation of the Model.- 2.6 Symmetry of the Stiffness Matrix.- 3 Numerical Aspects in Potential Problems.- 3.1 Introduction.- 3.2 The Constant Element.- 3.3 The Quadratic Element.- 3.4 The Vector B.- 4 Elastostatics.- 4.1 Introduction.- 4.2 Basic Relations in Linear Elastostatics.- 4.3 Modified Variational Principle.- 4.4 Derivation of the Model.- 5 Numerical Aspects in Elastostatics Problems.- 5.1 Introduction.- 5.2 The Constant Element.- 5.3 The Quadratic Element.- 5.4 Computation of the Submatrices Fii.- 5.5 Body Forces.- 6 Numerical Applications.- 6.1 Introduction.- 6.2 Examples for Potential Problems.- 6.3 Elasticity Problems.- 7 Conclusions.- 8 Bibliography.

Erscheint lt. Verlag	25.7.1991
Reihe/Serie	Lecture Notes in Engineering
Zusatzinfo	IX, 198 p.
Verlagsort	Berlin
Sprache	englisch
Maße	170 x 242 mm
Gewicht	378 g
Themenwelt	Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Chemie ► Physikalische Chemie
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Technik ► Maschinenbau
Schlagworte	boundary elements • Development • Numerical Methods • numerische Methoden • Randelement • Variational Principles • Variationsprinzip
ISBN-10	3-540-54030-X / 354054030X
ISBN-13	978-3-540-54030-4 / 9783540540304
Zustand	Neuware