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The book presents a new boundary element formulation for the solution of boundary-value problems in potential theory and linear elastostatics. The basis of the approach is a multi-field variational principle. A stiffness type of formulation is generated, involving a symmetric stiffness matrix, which is only evaluated on the boundary. The formulation is completely developed and its implementation in computer code is explained in detail. Se- veral numerical examples are shown and the solutions are compared to analytical and to other approximate solutions. Further a study of the convergence of the solutions is presented.
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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.
Reseña del editor
The book presents a new boundary element formulation for the solution of boundary-value problems in potential theory and linear elastostatics. The basis of the approach is a multi-field variational principle. A stiffness type of formulation is generated, involving a symmetric stiffness matrix, which is only evaluated on the boundary. The formulation is completely developed and its implementation in computer code is explained in detail. Se- veral numerical examples are shown and the solutions are compared to analytical and to other approximate solutions. Further a study of the convergence of the solutions is presented.
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A New Boundary Element Formulation in Engineering.
Verlag:
Berlin, Heidelberg, New York u.a., Springer, 1991
ISBN 10: 354054030X
ISBN 13: 9783540540304
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Gr.-8°, Original-Broschur. Zustand: Akzeptabel. IX, 198 SS. Lecture Notes in Engineering, 68. - Ehemaliges Bibliotheksexemplar mit den üblichen Stempeln und Signaturen, Rücken mit Signaturschildchen. Seiten papierbedingt ganz leicht gebräunt. Sonst gutes Exemplar. / Ex library copy with the usual label, stamps and markings. Light browning. Else well preserved. Sprache: Englisch Gewicht in Gramm: 550. Artikel-Nr. 51346
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A New Boundary Element Formulation in Engineering (Lecture Notes in Engineering)
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Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1991
ISBN 10: 354054030X
ISBN 13: 9783540540304
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A New Boundary Element Formulation in Engineering
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Springer Berlin Heidelberg, 1991
ISBN 10: 354054030X
ISBN 13: 9783540540304
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A New Boundary Element Formulation in Engineering
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9783540540304
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A New Boundary Element Formulation in Engineering (Lecture Notes in Engineering, 68)
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