STRESSES AND DISPLACEMENTS IN VISCOELASTIC LAYERED SYSTEMS UNDER CIRCULAR LOADED AREAS

ANALYSIS IS CONDUCTED OF STRESSES AND DISPLACEMENTS IN VISCOELASTIC LAYERED SYSTEMS. THE ANALYSIS IS BASED ON THE ELASTIC-VISCOELASTIC CORRESPONDENCE PRINCIPLE IN WHICH THE LA PLACE TRANFORM IS APPLIED TO REPLACE THE TIME VARIABLE WITH A TRANSFORMED VARIABLE AND THUS CHANGE THE VISCOELASTIC PROBLEM INTO AN ASSOCIATED ELASTIC PROBLEM. THE SOLUTION OF THE ASSOCIATED ELASTIC PROBLEM, WHEN TRANSFORMED BACK INTO THE REAL TIME VARIABLE, WILL GIVE THE DESIRED VISCOELASTIC SOLUTION. TWO METHODS, ONE BASED ON A DIRECT METHOD OF LA PLACE INVERSION AND THE OTHER ON AN APPROXIMATE METHOD OF COLLOCATION WERE DEVELOPED TO DETERMINE NUMERICALLY THE STRESSES AND DISPLACEMENTS IN TWO AND FOUR-LAYER SYSTEMS MADE OF LINEAR VISCOELASTIC MATERIALS. IT WAS DETERMINED, AT THE INITIAL TIME, THAT THE STRESSES ARE DETERMINED BY THE VISCOSITY RATIO OF THE TWO DASHPOTS. AT THE INFINITE TIME THEY ARE GOVERNED BY THE ELASTICITY RATIO OF THE TWO SPRINGS. THE VARIATION OF STRESSES BETWEEN THESE TWO LIMITING TIMES CAN BE PREDICTED FROM THE ELASTIC SOLUTIONS. WHEN BOTH LAYERS HAVE THE SAME RETARDATION TIME, THE STRESSES ARE INDEPENDENT OF TIME AND REMAIN CONSTANT. LIKE THE KELVIN MODEL ITSELF, THE SURFACE AND INTERFACE DISPLACEMENTS AT THE AXIS OF SYMMETRY GENERALLY INCREASE WITH TIME, THOUGH A SLIGHT DECREASE MAY OCCUR AT THE FINAL STAGE. AWAY FROM THE AXIS OF SYMMETRY, THE DISPLACEMENTS CHANGE WITH TIME IN AN ERRATIC MANNER.