THEORETICAL STRESS DISTRIBUTION IN AN ELASTIC MULTI-LAYERED SYSTEM

Abstract

A THEORETICAL MATHEMATICAL MODEL OF STRESS DISTRIBUTION IN A MULTI-LAYERED SYSTEM UNDER LOADS OF AXIAL SYMMETRY IS PRESENTED. THE MODEL IS GENERALIZED FOR ANY ARBITRARY NUMBER OF HORIZONTAL LAYERS AND EACH LAYER IS ASSUMED TO BE LINEARLY ELASTIC, HOMOGENEOUS, ISOTROPIC AND OF INFINITE EXTENT IN THE HORIZONTAL PLANE, THE LAST LAYER BEING SEMI- INFINITE. VERTICAL STRESS, VERTICAL DISPLACEMENT AND SHEAR STRESS ARE CONSIDERED TO BE CONTINUOUS ACROSS ANY INTERFACE. IN ADDITION, THE SHEAR STRESS AT AN INTERFACE IS ASSUMED TO BE PROPORTIONAL TO THE RELATIVE DISPLACEMENT. FIVE SETS OF CURVES, OBTAINED BY AN IBM 7074 COMPUTER, OF VERTICAL STRESS AND DISPLACEMENT AS A FUNCTION OF RELATIVE DEPTH UNDER PARABOLIC LOADS ARE PRESENTED. A COMPARISON OF VERTICAL STRESSES IS MADE TO THOSE CALCULATED BY THE THEORIES OF BURMISTER AND BOUSSINESQ. /AUTHOR/