Theory of Elasticity and Stress Concentration

Since July 2006, under the auspices of the "Fundamental Research Project on Advanced Hydrogen Science", a 7-year-long project adopted by NEDO, Professor Murakami has managed and pursued research on hydrogen and material property as the project leader in collaboration with National Institute of Advanced Industrial Science and Technology (AIST) and is tirelessly working toward the realization of a hydrogen society. His research interests are: strength of materials; metal fatigue; fracture mechanics; hydrogen embrittlement; stress analysis; and tribology. He has published 13 books and over 400 papers. He has been a Director of the Research Center for Hydrogen Industrial Use and Storage (HYDROGENIUS), National Institute of Advanced Industrial Science and Technology since July 2006. He is currently the Special advisor to Director of International institute for Carbon-Neutral Energy Research (I2CNER), Kyushu University. He has lectured Strength of materials, theory of Elasticity for undergraduate courses and Fatigue and fracture for post graduate. He has supervised more than 35 PhD students.

• Part IPreface for the bookPreface for the partChapter 1 Stress1.1 Stress at the surface of a body1.2 Stress in the interior of a body1.3 Two-dimensional (2D) stress state, three-dimensional (3D) stress state and stress transformationChapter 2 Strains2.1 Strains in two-dimensional problems2.2 Strains in three-dimensional problems2.3 Strains in an arbitrary direction2.4 Principal strains2.5 Conditions of compatibilityChapter 3 The Relationship between Stresses and Strains: The Generalized Hooke's lawChapter 4 Equilibrium EquationsChapter 5 Saint Venant's Principle and Boundary Conditions5.1 Saint Venant's Principle5.2 Boundary conditionsChapter 6 Two-Dimensional Problems6.1 Plane stress and plane strain6.2 Basic conditions for exact solutions: Nature of solutions6.3 Airy's stress function6.4 Hollow cylinder6.5 Stress concentration at a circular hole6.6 Stress concentration at an elliptical hole6.7 Stress concentration at a hole in a finite width plate6.8 Stress concentration at a crack6.9 Stress field due to a point force applied at the edge of a semi-infinite plate6.10 Circular disk subjected to a concentrated forceChapter 7 Torsion of a Bar with Uniform Section7.1 Torsion of cylindrical bars7.2 Torsion of bars having thin closed section7.3 Saint Venant's torsion problems7.4 Stress function in torsion7.5 Membrane analogy: Solution of torsion problems by using the deformation of pressurized membrane7.6 Torsion of bars having thin unclosed section7.7 Comparison of torsional rigidity between a bar with an open section and a bar with a closed sectionChapter 8 Energy Principles8.1 Strain energy8.2 Uniqueness of the solutions of elasticity problems8.3 Principle of the virtual work8.4 Principle of the minimum potential energy8.5 Castigliano's theorem8.6 The reciprocal theoremChapter 9 The Finite Element Method, FEM9.1 FEM for one-dimensional problems9.2 Analysis of plane stress problems by the finite element methodChapter 10 Bending of Plates10.1 Simple examples of plate bending10.2 General problems of plate bending10.3 Transformation of bending moment and torsional moment10.4 Differential equations for a plate subjected to loads on the surface and their applications10.5 Boundary conditions in plate bending problems10.6 Polar coordinate expression of the quantities of plate bending10.7 Stress concentration in plate bending problems10.8 Bending of a circular plateChapter 11 Deformation and Stress in Cylindrical Shells11.1 Basic equations11.2 Various problems of cylindrical shellsChapter 12 Thermal Stress12.1 Thermal stress in a rectangular plate – Simple examples of thermal stress12.2 Thermal stress in a circular plate12.3 Thermal stress in a cylinderChapter 13 Contact Stress13.1 Two-dimensional contact stress13.2 Three-dimensional contact stressProblems of Chapter 13AppendixAppendix 1 Rule of direction cosinesAppendix 2 Green's theorem and Gauss' divergence theoremAnswers and Hints for the Problems