TRANSIENT GREEN´S FUNCTIONS AND DISTRIBUTED LOAD AND SOLUTIONS FOR PLANE STRAIN, TRANSVERSELY ISOTROPIC AND VISCOELASTIC LAYERS

Abstract

THE PRESENT ARTICLE REPORTS THE NUMERICAL SYNTHESIS OF TRANSIENT GREEN'S FUNCTIONS AND DISTRIBUTED LOAD SOLUTIONS FOR TRANSVERSELY ISOTROPIC VISCOELASTIC LAYERS RESTING ON A RIGID BOTTOM UNDER PLANE STRAIN CONDITIONS. FREQUENCY DOMAIN SOLUTIONS ARE USED, IN CONJUNCTION WITH THE FAST FOURIER TRANSFORM (FFT) ALGORITHM, TO RENDER TRANSIENT TRANSVERSELY ISOTROPIC VISCOELASTIC RESPONSES. ACCURATE SOLUTIONS AT HIGH FREQUENCY RANGES ALLOW THE CALCULATION OF THE TRANSIENT RESPONSE AT VERY SMALL TIME STEPS. A SERIES OF ORIGINAL RESULTS ARE REPORTED. TRANSIENT DISPLACEMENT AND TRACTION GREEN'S FUNCTIONS AND TRANSIENT DISPLACEMENT ¯ELDS FOR DISTRIBUTED LOAD SOLUTIONS WERE DETERMINED. SHORT TIME AND LONG TERM RESPONSES WERE OBTAINED AND EXPLAINED IN TERMS OF THE WAVE PROPAGATION AND RE°ECTION PHENOMENA. SNAPSHOTS OF THE DISPLACEMENT ¯ELDS ARE FURNISHED, ALLOWING THE VISUALIZATION OF THE TRANSIENT PROPAGATION PHENOMENA. THE OBTAINED SOLUTIONS MAKE POSSIBLE TO ASSESS THE IN°UENCE OF VISCOELASTIC MODELS AND PARAMETERS, AS WELL AS THE DEGREE OF ANISOTROPY OF THE CONTINUUM ON THE LAYER TRANSIENT RESPONSE. THE CONSTANT HYSTERETIC AND THE KELVIN-VOIGT DAMPING MODELS ARE INVESTIGATED. THE E®ECTS OF THE VISCOELASTIC MODELS ON THE CAUSALITY OF THE TRANSIENT RESPONSE ARE ALSO ADDRESSED. THE TRANSIENT ANISOTROPIC VISCOELASTIC SOLUTIONS MAY BE INCORPORATED AS AUXILIARY STATES IN A BOUNDARY ELEMENT SOLUTION STRATEGY, ALLOWING, FOR INSTANCE, THE TRANSIENT SOLUTION OF RIGID OR °EXIBLE SURFACE FOUNDATIONS INTERACTING WITH A LAYER.