Scaled Boundary Finite Element Method

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.

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element; fundamental; finite; solutionless; scaled boundary; method; discretisation; advantages; one; satisfied; spatial; boundary; infinity; condition; crack; boundaries; faces; interfaces; certain