Stress concentration at notches

• Main Authors: Savruk, Mykhaylo P. (Author), Kazberuk, Andrzej (Author)
• Format: Electronic eBook
• Language: English
• Published: Switzerland : Springer, [2017]
• Subjects: Fracture mechanics > Mathematical models.; Stress concentration.; Integral equations.; elektronické knihy; electronic books
• ISBN: 9783319445557; 9783319445540
• Physical Description: 1 online resource : illustrations

This book compiles solutions of linear theory of elasticity problems for isotropic and anisotropic bodies with sharp and rounded notches. It contains an overview of established and recent achievements, and presents the authors? original solutions in the field considered with extensive discussion. Th...

Table of Contents:

• Preface; Contents; Acronyms; 1 Method of Singular Integral Equations in Application to Problems of the Theory of Elasticity; 1.1 Basic Relationships of the Plane Theory of Elasticity; 1.1.1 Basic Equations; 1.1.2 Complex Representation of General Solution for Equations of Plane Theory of Elasticity; 1.2 System of Curvilinear Cracks in Elastic Plane; 1.2.1 Selected Information Concerning the Theory of Analytical Functions; 1.2.2 Single Curvilinear Crack; 1.2.3 System of Curvilinear Cracks; 1.3 System of Curvilinear Holes and Cracks in Elastic Body; 1.3.1 Multiply Connected Region with Holes
• 1.3.2 Multiply Connected Region with Holes and Cracks1.4 Numerical Solution of Singular Integral Equations; 1.4.1 Quadrature Formulas; 1.4.2 Integral Equation on an Open Contour; 1.4.3 Integral Equation on a Closed Contour; References; 2 Stress Distribution in Elastic Plane with a Semi-infinite Notch; 2.1 Methods for Stress Analysis in Notched Bodies; 2.2 Eigensolutions of Elasticity Theory Plane Problem for Wedge; 2.2.1 Characteristic Equations; 2.2.2 Stress Intensity Factors in V-Notch Tip; 2.2.3 Constructing General Solution Using Eigenfunctions
• 2.3 Semi-infinite Curvilinear Notches in Elastic Plane2.3.1 Parabolic Notch; 2.3.2 Hyperbolic Notch; 2.3.3 Curvilinear Notch of Special Shape; 2.4 Rounded V-Notch Under Symmetrical Loading; 2.4.1 Problem Definition and Reduction to Singular Integral Equation; 2.4.2 Symmetrical Stress Distribution in Plane with Rounded V-Notch; 2.5 Rounded V-Notch Under Mixed Loading; 2.5.1 Antisymmetric Stress Distribution; 2.5.2 Complex-Stressed State; References; 3 Elastic Plane with Semi-infinite Notch and Cracks; 3.1 Elastic Wedge with Edge Crack at Notch Tip
• 3.1.1 Solutions Obtained Using Wiener
• Hopf Method3.1.2 Approximate Closed-Form Solution for Symmetrical Loading; 3.2 Edge Crack System in Semi-infinite Rounded V-Notch Tip; 3.2.1 Reduction of Problem to Singular Integral Equations; 3.2.2 Numerical Solution of Singular Integral Equations; 3.3 Symmetrical Edge Crack in Rounded V-Notch Tip; 3.4 Two Symmetrical Edge Cracks in Rounded V-Notch Tip; References; 4 Deformation Fracture Criterion for Bodies with Notches; 4.1 Fracture Criteria for Notched Solid Bodies; 4.2 Model of Plasticity Bands in Fracture Mechanics; 4.2.1 Plane Stress State
• 4.2.2 Plane Strain State4.3 Infinite Wedge with Plasticity Bands; 4.3.1 Plane Stress State; 4.3.2 Plane Strain State; 4.4 Plasticity Band Near Rounded V-Notch; 4.5 Two Plasticity Bands Near Rounded V-Notch; References; 5 Stress Concentration Near Hole in Elastic Plane; 5.1 Elliptical Hole; 5.1.1 Stress Concentration Near Elliptical Hole; 5.1.2 Limit Transition to Parabolic Notch; 5.1.3 Stress Distribution Around Notch Tip; 5.2 Oval Hole; 5.2.1 Stress Concentration Near Narrow Slot; 5.2.2 Stress Concentration Near Oval Hole; 5.2.3 Limit Transition to Two-Tip Lens-Like Hole; 5.3 Rhombic Hole