The Scaled Boundary Finite Element MethodISBN: 978-0-471-48682-4
Hardcover
378 pages
March 2003
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FOREWORD.
PREFACE.
ACKNOWLEDGEMENTS.
FUNDAMENTALS OF NUMERICAL ANALYSIS.
NOVEL COMPUTATIONAL PROCEDURE.
PART I. MODEL PROBLEM: LINE ELEMENT FOR SCALAR WAVE EQUATION.
CONCEPTS OF SCALED BOUNDARY TRANSFORMATION OF GEOMETRY AND SIMILARITY.
WEDGE AND TRUNCATED SEMI-INFINITE WEDGE OF SHEAR PLATE.
SCALED-BOUNDARY-TRANSFORMATION-BASED DERIVATION.
MECHANICALLY-BASED DERIVATION.
MODELISATION WITH SINGLE LINE FINITE ELEMENT.
STATICS.
MASS OF WEDGE.
HIGH-FREQUENCY ASYMPTOTIC EXPANSION FOR DYNAMIC STIFFNESS OF TRUNCATED SEMI-INFINITE WEDGE.
NUMERICAL SOLUTION OF DYNAMIC STIFFNESS, UNIT-IMPULSE RESPONSE AND DISPLACEMENT OF TRUNCATED SEMI-INFINITE WEDGE.
ANALYTICAL SOLUTION IN FREQUENCY DOMAIN.
IMPLEMENTATION.
CONCLUSIONS.
APPENDIX A: SOLID MODELLING.
APPENDIX B: HARMONIC MOTION AND FOURIER TRANSFORMATION.
APPENDIX C: DYNAMIC UNBOUNDED MEDIUM-STRUCTURE INTERACTION.
APPENDIX D: HISTORICAL NOTE. PART II. TWO- AND THREE- DIMENSIONAL ELASTODYNAMICS, STATICS AND DIFFUSION.
FUNDAMENTAL EQUATIONS.
STATICS.
MASS MATRIX OF BOUNDED MEDIUM.
HIGH-FREQUENCY ASYMPTOTIC EXPANSION FOR DYNAMIC STIFFNESS OF UNBOUNDED MEDIUM.
NUMERICAL SOLUTION OF DYNAMIC STIFFNESS, UNIT-IMPULSE RESPONSE AND DISPLACEMENT OF UNBOUNDED MEDIUM.
ANALYTICAL SOLUTION IN FREQUENCY DOMAIN.
EXTENSIONS.
SUBSTRUCTURING.
EXAMPLES FOR BOUNDED MEDIA.
EXAMPLES FOR UNBOUNDED MEDIA.
ERROR ESTIMATION AND ADAPTIVITY.
CONCLUDING REMARKS.
REFERENCES.
INDEX.
PREFACE.
ACKNOWLEDGEMENTS.
FUNDAMENTALS OF NUMERICAL ANALYSIS.
NOVEL COMPUTATIONAL PROCEDURE.
PART I. MODEL PROBLEM: LINE ELEMENT FOR SCALAR WAVE EQUATION.
CONCEPTS OF SCALED BOUNDARY TRANSFORMATION OF GEOMETRY AND SIMILARITY.
WEDGE AND TRUNCATED SEMI-INFINITE WEDGE OF SHEAR PLATE.
SCALED-BOUNDARY-TRANSFORMATION-BASED DERIVATION.
MECHANICALLY-BASED DERIVATION.
MODELISATION WITH SINGLE LINE FINITE ELEMENT.
STATICS.
MASS OF WEDGE.
HIGH-FREQUENCY ASYMPTOTIC EXPANSION FOR DYNAMIC STIFFNESS OF TRUNCATED SEMI-INFINITE WEDGE.
NUMERICAL SOLUTION OF DYNAMIC STIFFNESS, UNIT-IMPULSE RESPONSE AND DISPLACEMENT OF TRUNCATED SEMI-INFINITE WEDGE.
ANALYTICAL SOLUTION IN FREQUENCY DOMAIN.
IMPLEMENTATION.
CONCLUSIONS.
APPENDIX A: SOLID MODELLING.
APPENDIX B: HARMONIC MOTION AND FOURIER TRANSFORMATION.
APPENDIX C: DYNAMIC UNBOUNDED MEDIUM-STRUCTURE INTERACTION.
APPENDIX D: HISTORICAL NOTE. PART II. TWO- AND THREE- DIMENSIONAL ELASTODYNAMICS, STATICS AND DIFFUSION.
FUNDAMENTAL EQUATIONS.
STATICS.
MASS MATRIX OF BOUNDED MEDIUM.
HIGH-FREQUENCY ASYMPTOTIC EXPANSION FOR DYNAMIC STIFFNESS OF UNBOUNDED MEDIUM.
NUMERICAL SOLUTION OF DYNAMIC STIFFNESS, UNIT-IMPULSE RESPONSE AND DISPLACEMENT OF UNBOUNDED MEDIUM.
ANALYTICAL SOLUTION IN FREQUENCY DOMAIN.
EXTENSIONS.
SUBSTRUCTURING.
EXAMPLES FOR BOUNDED MEDIA.
EXAMPLES FOR UNBOUNDED MEDIA.
ERROR ESTIMATION AND ADAPTIVITY.
CONCLUDING REMARKS.
REFERENCES.
INDEX.