FLEXURE OF THICK ORTHOTROPIC PLATES BY EXPONENTIAL SHEAR DEFORMATION THEORY

Abstract

IN THE PRESENT PAPER, A VARIATIONALLY CONSISTENT EXPONENTIAL SHEAR DEFORMATION THEORY TAKING INTO ACCOUNT TRANSVERSE SHEAR DEFORMATION EFFECT IS PRESENTED FOR THE FLEXURAL ANALYSIS OF THICK ORTHOTROPIC PLATES. THE INPLANE DISPLACEMENT FIELD USES EXPONENTIAL FUNCTION IN TERMS OF THICKNESS COORDINATE TO INCLUDE THE SHEAR DEFORMATION EFFECT. THE TRANSVERSE SHEAR STRESS CAN BE OBTAINED DIRECTLY FROM THE CONSTITUTIVE RELATIONS SATISFYING THE SHEAR STRESS FREE SURFACE CONDITIONS ON THE TOP AND BOTTOM SURFACES OF THE PLATE, HENCE THE THEORY DOES NOT REQUIRE SHEAR CORRECTION FACTOR. GOVERNING EQUATIONS AND BOUNDARY CONDITIONS OF THE THEORY ARE OBTAINED USING THE PRINCIPLE OF VIRTUAL WORK. RESULTS OBTAINED FOR STATIC FLEXURE OF SIMPLY SUPPORTED ORTHOTROPIC PLATES ARE COMPARED WITH THOSE OF OTHER REFINED THEORIES AND ELASTICITY SOLUTION WHEREVER APPLICABLE. THE RESULTS OBTAINED BY PRESENT THEORY ARE IN EXCELLENT AGREEMENT WITH THOSE OF EXACT RESULTS AND OTHER HIGHER ORDER THEORIES. THUS THE EFFICACY OF THE PRESENT REFINED THEORY IS ESTABLISHED.