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E-raamat: Boundary Integral Equatio Method in Axisymmetric Stress Analysis Problems

  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Engineering 14
  • Ilmumisaeg: 12-Mar-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642826443
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Boundary Integral Equatio Method in Axisymmetric Stress Analysis ProblemsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Engineering 14
  • Ilmumisaeg: 12-Mar-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642826443
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The Boundary Integral Equation (BIE) or the Boundary Element Method is now well established as an efficient and accurate numerical technique for engineering problems. This book presents the application of this technique to axisymmetric engineering problems, where the geometry and applied loads are symmetrical about an axis of rotation. Emphasis is placed on using isoparametric quadratic elements which exhibit excellent modelling capabilities. Efficient numerical integration schemes are also presented in detail. Unlike the Finite Element Method (FEM), the BIE adaptation to axisymmetric problems is not a straightforward modification of the two­ or three-dimensional formulations. Two approaches can be used; either a purely axisymmetric approach based on assuming a ring of load, or, alternatively, integrating the three-dimensional fundamental solution of a point load around the axis of rotational symmetry. Throughout this ~ook, both approaches are used and are shown to arrive at identi­ cal solutions. The book starts with axisymmetric potential problems and extends the formulation to elasticity, thermoelasticity, centrifugal and fracture mechanics problems. The accuracy of the formulation is demonstrated by solving several practical engineering problems and comparing the BIE solution to analytical or other numerical methods such as the FEM. This book provides a foundation for further research into axisymmetric prob­ lems, such as elastoplasticity, contact, time-dependent and creep prob­ lems.

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Springer Book Archives
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.- 2.3 Numerical
Implementation.- 2.4 Examples.- 3 Axisymmetric Elasticity Problems:
Formulation.- 3.1 Introduction.- 3.2 Analytical Formulation.- 3.3 Numerical
Implementation.- 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.- 5.4 Examples.- 6 Axisymmetric Centrifugal
Loading Problems.- 6.1 Introduction.- 6.2 Analytical Formulation.- 6.3
Numerical Implementation.- 6.4 Examples.- 7 Axisymmetric Fracture Mechanics
Problems.- 7.1 Introduction.- 7.2 Linear Elastic Fracture Mechanics.- 7.3
Numerical Calculation of the Stress Intensity Factor.- 7.4 Singularity
Elements.- 7.5 Examples.- 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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