A New Boundary Element Formulation in Engineering

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.- 2.5.1 Definition of Fundamental Solution.- 2.5.2 Approximation for the Domain Variable.- 2.5.3 Approximations for the Boundary Variables.- 2.5.4 Final System of Equations.- 2.5.5 Solution on the Boundary.- 2.5.6 Solution at Internal Points.- 2.6 Symmetry of the Stiffness Matrix.- 3 Numerical Aspects in Potential Problems.- 3.1 Introduction.- 3.2 The Constant Element.- 3.2.1 Matrix F for Constant Elements.- 3.2.2 Matrix G for Constant Elements.- 3.2.3 Matrix L for Constant Elements.- 3.2.4 Equivalent Nodal Fluxes.- 3.3 The Quadratic Element.- 3.3.1 Matrix F for Quadratic Elements.- 3.3.2 Matrix G for Quadratic Elements.- 3.3.3 Matrix L for Quadratic Elements.- 3.3.4 Equivalent Nodal Fluxes.- 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.- 4.4.1 Fundamental Solution.- 4.4.2 Approximation for the Domain Variable.- 4.4.3 Approximation for Boundary Variables.- 4.4.4 Final System of Equations.- 4.4.5 Solution on the Boundary.- 4.4.6 Solution at Internal Points.- 4.4.7 Symmetry of the Stiffness Matrix.- 5 Numerical Aspects in Elastostatics Problems.- 5.1 Introduction.- 5.2 The Constant Element.- 5.2.1 Matrix F for Constant Elements.- 5.2.2 Matrix G for Constant Elements.- 5.2.3 Matrix L for Constant Elements.- 5.2.4 Load Vector.- 5.3 The Quadratic Element.- 5.3.1 Matrix F for Quadratic Elements.- 5.3.2 Matrix G for Quadratic Elements.- 5.3.3 Matrix L for Quadratic Elements.- 5.3.4 Load Vector.- 5.4 Computation of the Submatrices Fii.- 5.5 Body Forces.- 5.5.1 Transformation of the Domain Integrals into Boundary Integrals.- 6 Numerical Applications.- 6.1 Introduction.- 6.2 Examples for Potential Problems.- 6.2.1 Constant Elements.- 6.2.2 Quadratic Elements.- 6.3 Elasticity Problems.- 6.3.1 Constant Elements.- 6.3.2 Quadratic Elements.- 7 Conclusions.- 8 Bibliography.