Index
Adjoint operator, 112
Approximate boundary solutions, 187
Bessel functions, 51
Hankel functions, 51, 187
Boundary conditions, 2, 12
Boundary methods, 17
Bromwich integral, 158
Cell collocation, 5
Cells (numerical integration), 45
Combination of finite and boundary ele-
ments, 203
Complementary function, 152
Constant elements, 39, 129
Cubic elements, 64
Dipoles, 32
Dirac delta function, 3, 4
for bounded region, 82
Direct method, 17
Eigenfunctions, 80
infinite region, 43
Equilibrium condition, 41
Error functions, 2
Exponential integral function, 172
Finite elements, 1, 201
Fourier expansion, 88, 89
Fourier transforms, 154
Fundamental solutions, 26-29
explicit forms, 115
finite region, 89
Green's functions, 80-119
Helmholtz, 51, 53, 187
infinite region, 95
Laplace, Poisson, 24, 35
numerical, 100
orthotropic media, 49
semi-infinite space, 103
Fundamental tensor, 99
Galerkin method, 7, 16, 111
Gauss quadrature, 39
Gauss' theorem, 28
Green's functions (see Fundamental
solutions)
Green's theorem, 18
Harbour resonance, 194
Helmholtz equation, 50-53, 91, 187
Homogeneous coordinates, 76
Images, 102
Indirect formulation, 32
Infinite elements, 148
Influence coefficients, 56
Inverse problem, 14
Jacobian, 63, 68
Kelvin solution, 100
Krönecker delta, 82
209
210 INDEX
Laplace transform, 152, 156
Limit on boundary, 31
Linear elements, 36
two-dimensional problems, 55
Linear operator, 80
Localised functions, 4
Matrix formulation, 37
Method of moments, 6
Mindlin solution, 106
Natural boundary conditions, 33
Navier's equation, 98
Norm, 81
Orthonormalisation infinite region, 93
finite region, 82
Orthotropic medium, 47, 48
Particular integral, 153
Plasticity, 175
Poisson's equation,
18-21,
25, 45
Potential problems, 25
Quadratic elements, 36, 62, 70
triangular elements, 75
Quadrilateral elements, 65, 69
Saint Venant torsion, 57
Scalar product, 82
Self-adjoint operators, 33
Sommerfeld radiation condition, 53, 192
Source formulation, 40
Stress, 120
Subregions, 181
Three dimensional elements, 76
problems, 65
Time-dependent fundamental solution,
164
Time integration, 167
Transient elastodynamics, 160
Triangular coordinates, 74
elements, 65, 72
Viscoelasticity, 165
Weak formulations, 10
Weighted residuals, general, 1, 3
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