A direct approach for boundary integral equations with high-order singularities

DOI<871::AID-NME979>3.0.CO;2-V 10.1002/1097-0207(20001110)49:7<871::AID-NME979>3.0.CO;2-VzbMath1013.74075OpenAlexW2080593894MaRDI QIDQ4525126

No author found.

Publication date: 5 July 2001

Full work available at URL: https://doi.org/10.1002/1097-0207(20001110)49:7<871::aid-nme979>3.0.co;2-v

zbMATH Keywords

boundary element methodplate bendingsingular integralsdirect approachhypersingularitystrong singularitysingular boundary integral equations

Mathematics Subject Classification ID

Plates (74K20) Boundary element methods applied to problems in solid mechanics (74S15) Stress concentrations, singularities in solid mechanics (74G70)

Related Items (31)

Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals ⋮ Projection plane method for evaluation of arbitrary high order singular boundary integrals ⋮ On the free terms of the dual BIE for \(N\)-dimensional Laplace problems ⋮ Evaluating hypersingular integrals of 3D acoustic problems on curved surfaces ⋮ An improved direct method for evaluating hypersingular stress boundary integral equations in BEM ⋮ The CPCT based CBIE and HBIE for potential problems in three dimensions ⋮ Implementation of CPCT based BIEs for 3D elasticity and its application in fracture mechanics ⋮ Solid analysis of micron-sized thin structures with BEM for steady-state heat conduction ⋮ An isogeometric boundary element method for three dimensional potential problems ⋮ Superconvergence of Newton-Cotes rule for computing hypersingular integral on a circle ⋮ Approximation of Hilbert and Hadamard transforms on \((0,+\infty)\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Regularization of divergent integrals: a comparison of the classical and generalized-functions approaches ⋮ Direct evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM. ⋮ An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals ⋮ An improved singular curved boundary integral evaluation method and its application in dual BEM analysis of two- and three-dimensional crack problems ⋮ Numerical evaluation of strain gradients in classical elasticity through the boundary element method ⋮ Numerical computation of hypersingular integrals on the real semiaxis ⋮ On the simultaneous approximation of a Hilbert transform and its derivatives on the real semiaxis ⋮ Evaluation of Green's boundary formula and its first- and second-order derivatives in Legendre series ⋮ The trapezoidal rule for computing supersingular integral on interval ⋮ Evaluation of second-order derivative of potential on boundary by discontinuous boundary element with exact integrations ⋮ Analytical integration of singular kernels in symmetric boundary element analysis of Kirchhoff plates ⋮ A boundary element numerical scheme for the two-dimensional convection-diffusion equation ⋮ High order projection plane method for evaluation of supersingular curved boundary integrals in BEM ⋮ Least‐square collocation and Lagrange multipliers forTaylor meshless method ⋮ Definitions, properties and applications of finite-part integrals ⋮ Numerical integration scheme for singular integrals based on polar coordinates free from angular quasi-singularities ⋮ Error bounds for a Gauss-type quadrature rule to evaluate hypersingular integrals ⋮ Trapezoidal rule for computing supersingular integral on a circle

Cites Work

• Unnamed Item
• The hypersingular integral equation for the bending moments \(m_{xx}\), \(m_{xy}\) and \(m_{yy}\) of the Kirchhoff plate
• Hypersingular boundary integral equations have an additional free term
• An efficient method to evaluate hypersingular and supersingular integrals in boundary integral equations analysis
• The direct boundary element method in plate bending
• A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method
• A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations
• A Galerkin symmetric and direct BIE method for Kirchhoff elastic plates: formulation and implementation
• Singular boundary elements for the analysis of cracks in plane strain
• Numerical integration schemes for the BEM solution of hypersingular integral equations
• Boundary element analysis of Kirchhoff plates with direct evaluation of hypersingular integrals

This page was built for publication: A direct approach for boundary integral equations with high-order singularities