The boundary integral equation method in axisymmetric stress analysis problems

A.A. Bakr


  • 1 Introduction and Aims.- 1.1 Introduction.- 1.2 Literature Survey - Axisymmetric Problems.- 1.3 Layout of Notes.- 2 Axisymmetric Potential Problems.- 2.1 Introduction.- 2.2 Analytical Formulation.- 2.2.1 The axisymmetric fundamental solution.- 2.2.2 The boundary integral identity.- 2.2.3 The axisymmetric potential kernels.- 2.2.4 Treatment of the axis of rotational symmetry.- 2.3 Numerical Implementation.- 2.3.1 Isoparametric quadratic elements.- 2.3.2 Numerical integration of the kernels.- 2.3.3 Calculation of the elliptic integrals.- 2.3.4 Solutions at internal points.- 2.3.5 Treatment of non-homogeneous problems.- 2.4 Examples.- 2.4.1 Hollow cylinder.- 2.4.2 Hollow sphere.- 2.4.3 Effect of element curvature.- 2.4.4 Compound sphere.- 2.4.5 Reactor pressure vessel.- 2.4.6 Externally grooved hollow cylinder.- 3 Axisymmetric Elasticity Problems: Formulation.- 3.1 Introduction.- 3.2 Analytical Formulation.- 3.2.1 Basic equations of elasticity.- 3.2.2 Solution of the Navier equations.- 3.2.3 The boundary integral identity.- 3.2.4 Treatment of the axis of rotational symmetry.- 3.2.5 Treatment of non-homogeneous problems.- 3.3 Numerical Implementation.- 3.3.1 Isoparametric quadratic elements.- 3.3.2 Numerical integration of the kernels.- 3.3.3 Surface stresses.- 3.3.4 Solutions at internal points.- 4 Axisymmetric Elasticity Problems: Examples.- 4.1 Introduction.- 4.2 Hollow Cylinder.- 4.3 Hollow Sphere.- 4.4 Thin Sections.- 4.5 Compound Sphere.- 4.6 Spherical Cavity in a Solid Cylinder.- 4.7 Notched Bars.- 4.8 Pressure Vessel with Hemispherical End Closure.- 4.9 Pressure Vessel Clamp.- 4.10 Compression of Rubber Blocks.- 4.11 Externally Grooved Hollow Cylinder.- 4.12 Plain Reducing Socket.- 5 Axisymmetric Thermoelasticity Problems.- 5.1 Introduction.- 5.2 Analytical Formulation.- 5.3 Numerical Implementation.- 5.3.1 Isoparametric quadratic elements.- 5.3.2 Numerical integration of the kernels.- 5.3.3 Solutions at internal points.- 5.4 Examples.- 5.4.1 Hollow cylinder.- 5.4.2 Hollow sphere.- 5.4.3 Compound sphere.- 5.4.4 Comparison with other numerical methods.- 5.4.5 Reactor pressure vessel.- 5.4.6 Externally grooved hollow cylinder.- 6 Axisymmetric Centrifugal Loading Problems.- 6.1 Introduction.- 6.2 Analytical Formulation.- 6.3 Numerical Implementation.- 6.3.1 Isoparametric quadratic elements.- 6.3.2 Numerical integration of the kernels.- 6.4 Examples.- 6.4.1 Rotating disk of uniform thickness.- 6.4.2 Rotating tapered disk.- 6.4.3 Rotating disk of variable thickness.- 7 Axisymmetric Fracture Mechanics Problems.- 7.1 Introduction.- 7.2 Linear Elastic Fracture Mechanics.- 7.3 Numerical Calculation of the Stress Intensity Factor.- 7.3.1 The displacement method.- 7.3.2 The stress method.- 7.3.3 Energy methods.- 7.4 Singularity Elements.- 7.5 Examples.- 7.5.1 Circumferential crack in a round bar.- 7.5.2 Penny-shaped crack in a round bar.- 7.5.3 Internal circumferential crack in a hollow cylinder.- 7.5.4 Flat toroidal crack in a hollow cylinder.- 7.5.5 Pressurised penny-shaped crack in a solid sphere.- 7.5.6 Circumferential cracks in grooved round bars.- 7.5.7 Modelling both faces of the crack.- 8 Conclusions.- References.- Appendix B Numerical Coefficients for the Evaluation of the Elliptical Integrals.- Appendix C Notation for Axisymmetric Vector and Scalar Differentiation.- Appendix D Components of the Traction Kernels.- Appendix E Derivation of the Axisymmetric Displacement Kernels from the Three-Dimensional Fundamental Solution.- Appendix G Differentials of the Displacement and Traction Kernels.- Appendix H The Thermoelastic Kernels.- Appendix I Differentials of the Thermoelastic Kernels.

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書名 The boundary integral equation method in axisymmetric stress analysis problems
著作者等 Bakr, A. A.
Bakr Adib A.
Bakr A A
シリーズ名 Lecture notes in engineering
出版元 Springer-Verlag
刊行年月 c1986
版表示 Softcover reprint of the original 1st ed. 1986
ページ数 xi, 213 p.
大きさ 25 cm
ISBN 3540160302
NCID BA01066369
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言語 英語
出版国 ドイツ