A dual boundary element formulation for three-dimensional fracture analysis

著者

    • Wilde, A

書誌事項

A dual boundary element formulation for three-dimensional fracture analysis

Andrew Wilde

（Topics in engineering, v. 37）

WIT Press, c2000

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注記

Bibliography: p. [205]-216

内容説明・目次

内容説明

This volume presents the dual boundary element formulation which uses continuous elements in three dimensions, and applies it to the analysis of geomechanical fracture problems and fatigue crack growth. The method overcomes the mathematical degeneration associated with the solitary use of the displacement boundary integral equation for cracked bodies by introducing an additional independent boundary integral equation on one of the crack surfaces. Effective implementation is achieved through the use of accurate algorithms for the singular and near-singular integrals in the dual equations. Two new approaches which enable discretisation of crack surfaces with continuous elements are considered, and special crack front elements to accurately model the square root variation of the displacement field near the crack front are developed. There is also discussion of implementation on MIMD computer architecture.The author then moves on to give two different techniques for the evaluation of stress intensity factors, both based on crack-opening-displacements, and to explore applications in seam extraction and in hydraulic fracture by the introduction of spring constraints between the crack surfaces. Finally, the method is extended to the analysis of fatigue crack growth, the accuracy and efficiency of which is demonstrated through a number of mixed-mode examples including both embedded and edge cracks. Contents: Introduction; Basic Elasticity and Fracture Mechanics; The Boundary Element Method; The Three-Dimensional Dual Boundary Element Method; Enriched Elements for the Evaluation of the Traction BIE; The Dual Boundary Element Method for Three-Dimensional Crack Analysis; Application of the DBEM to Crack Analysis in Geomechanics; Application of the DBEM to Three-Dimensional Crack Growth Analysis; Conclusions; Bibliography; Appendices.

目次

  • Introduction: General
  • Fracture Mechanics
  • Geomechanics
  • Numerical Methods
  • Boundary Element Methods in Fracture Mechanics. Basic Elasticity and Fracture Mechanics: Introduction
  • Three Dimensional Elasticity
  • Fracture Mechanics Fundamentals
  • Analysis of Crack Growth
  • Summary. The Boundary Element Method: Introduction
  • Historical Background
  • The Three-Dimensional BEM for Elasticity
  • Application to Cracked Bodies
  • Summary. The Three-Dimensional Dual Boundary Element Method: Introduction
  • Traction Boundary Integral Equation
  • Dual Boundary Element Formulation
  • Treatment of Singular Integral
  • Evaluation of the Traction BIE with Continuous Elements
  • Summary. Enriched Elements for the Evaluation of the Traction BIE: Introduction
  • The Displacement Derivative BIE
  • Continuity Requirements
  • Enriched Element
  • Evaluation of Free Term Coefficients
  • Conversion to the Traction BIE
  • Boundary Stress Evaluation
  • Summary. The Dual Boundary Element Method for Three-Dimensional Crack Analysis: Introduction
  • Near-Singular Integration
  • Dual Boundary Element Formulation
  • Implementation on MIMD Computer Architecture
  • Crack Front Elements
  • Stress Intensity Factor Evaluation
  • Numerical Examples
  • Summary. Application of the DBEM to Crack Analysis in Geomechanics: Introduction
  • Numerical Implementation
  • Summary. Application of the DBEM to Three-Dimensional Crack Growth Analysis: Introduction
  • Crack Propagation Simulation
  • Numerical Examples under Tension
  • Summary. Conclusions: Final Conclusions
  • Future Work.

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