Boundary Methods: Elements, Contours, and Nodes (Hardcover)

INTRODUCTION TO BOUNDARY METHODSI SELECTED TOPICS IN BOUNDARY ELEMENTMETHODSBOUNDARY INTEGRAL EQUATIONSPotential Theory in Three DimensionsLinear Elasticity in Three DimensionsNearly Singular Integrals in Linear ElasticityFinite Parts of Hypersingular EquationsERROR ESTIMATIONLinear OperatorsIterated HBIE and Error EstimationElement-Based Error IndicatorsNumerical ExamplesTHIN FEATURESExterior BIE for Potential Theory: MEMSBIE for Elasticity: Cracks and Thin ShellsII THE BOUNDARY CONTOUR METHODLINEAR ELASTICITYSurface and Boundary Contour EquationsHypersingular Boundary Integral EquationsInternal Displacements and StressesNumerical ResultsSHAPE SENSITIVITY ANALYSISSensitivities of Boundary VariablesSensitivities of Surface StressesSensitivities of Variables at Internal PointsNumerical Results: Hollow SphereNumerical Results: Block with a HoleSHAPE OPTIMIZATIONShape Optimization ProblemsNumerical ResultsERROR ESTIMATION AND ADAPTIVITYHypersingular Residuals as Local Error EstimatorsAdaptive Meshing StrategyNumerical ResultsIII THE BOUNDARY NODE METHODSURFACE APPROXIMANTSMoving Least Squares (MLS) ApproximantsSurface DerivativesWeight FunctionsUse of Cartesian Coordinates POTENTIAL THEORY AND ELASTICITYPotential Theory in Three DimensionsLinear Elasticity in Three DimensionsADAPTIVITY FOR 3-D POTENTIAL THEORYHypersingular and Singular ResidualsError Estimation and Adaptive Strategy Progressively Adaptive Solutions: Cube ProblemOne-Step Adaptive Cell RefinementADAPTIVITY FOR 3-D LINEAR ELASTICITYHypersingular and Singular Residuals Error Estimation and Adaptive StrategyProgressively Adaptive Solutions: Pulling a Rod One-Step Adaptive Cell RefinementBibliographyIndex