The collocation Trefftz method for biharmonic equations with crack singularities

DOI10.1016/S0955-7997(03)00094-8zbMath1106.74418OpenAlexW2002161418MaRDI QIDQ597583

Hsin-Yun Hu, Tzon-Tzer Lu, Zi Cai Li

Publication date: 6 August 2004

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0955-7997(03)00094-8

zbMATH Keywords

Green functionBiharmonic equationBoundary conditionBoundary approximation methodCollocation Trefftz methodsCorner conditionSingular problems

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Brittle fracture (74R10) Boundary element methods applied to problems in solid mechanics (74S15)

Related Items (11)

Perturbation and stability analysis of strong form collocation with reproducing kernel approximation ⋮ Models of corner and crack singularity of linear elastostatics and their numerical solutions ⋮ Construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order ⋮ Stability analysis of Trefftz methods for the stick-slip problem ⋮ The singular function boundary integral method for a two-dimensional fracture problem ⋮ The singular function boundary integral method for biharmonic problems with crack singularities ⋮ Effective condition number of the Hermite finite element methods for biharmonic equations ⋮ Simple iterative method for solving problems for plates with partial internal supports ⋮ The Trefftz method using fundamental solutions for biharmonic equations ⋮ Corner and crack singularity of different boundary conditions for linear elastostatics and their numerical solutions ⋮ Modified nonlocal boundary value problem method for an ill-posed problem for the biharmonic equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary approximation methods for solving elliptic problems on unbounded domains
• The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities
• Applications to multi-region Trefftz-collocation to fracture mechanics
• Error and Stability Analysis of Boundary Methods for Elliptic Problems with Interfaces
• The hybrid-Trefftz finite element model and its application to plate bending
• Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
• Unified formulation of numerical methods. I. Green's formulas for operators in discontinuous fields
• Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities
• Trefftz method for Kirchhoff plate bending problems
• A highly accurate numerical solution of a biharmonic equation
• Indirect methods of collocation: Trefftz-Herrera collocation
• The treatment of singularities of partial differential equations by relaxation methods
• Trefftz method: An overview

This page was built for publication: The collocation Trefftz method for biharmonic equations with crack singularities