SINGLE VARIABLE NEW FIRST-ORDER SHEAR DEFORMATION THEORY FOR ISOTROPIC PLATES

Abstract

THIS PAPER PRESENTS A SINGLE VARIABLE NEW FIRST-ORDER SHEAR DEFORMATION PLATE THEORY WITH ONLY ONE FOURTH-ORDER PARTIAL GOVERNING DIFFERENTIAL EQUATION. IT MAY BE NOTED THAT, FIRST-ORDER SHEAR DEFORMATION PLATE THEORY OF MINDLIN HAS THREE COUPLED PARTIAL GOVERNING DIFFERENTIAL EQUATIONS INVOLVING THREE UNKNOWN FUNCTIONS. EVEN A RECENTLY DEVELOPED NEW FIRST-ORDER SHEAR DEFORMATION PLATE THEORY HAS TWO UNCOUPLED PARTIAL GOVERNING DIFFERENTIAL EQUATIONS INVOLVING TWO UNKNOWN FUNCTIONS FOR STATIC PROBLEMS. THE DISPLACEMENT FUNCTIONS OF THE PROPOSED THEORY GIVE RISE TO CONSTANT TRANSVERSE SHEAR STRAINS THROUGH THICKNESS OF THE PLATE AND, AS IS THE CASE OF MINDLIN PLATE THEORY, THE PROPOSED THEORY ALSO REQUIRES A SHEAR CORRECTION FACTOR. THE GOVERNING DIFFERENTIAL EQUATION, EXPRESSIONS FOR MOMENTS AND SHEAR FORCES OF THE PROPOSED THEORY HAVE A STRIKING RESEMBLANCE TO THE CORRESPONDING EXPRESSIONS OF CLASSICAL PLATE THEORY. THE PROPOSED THEORY IS THE ONLY FIRST-ORDER SHEAR DEFORMATION PLATE THEORY WITH TWO DIFFERENT TYPES OF PHYSICALLY MEANINGFUL CLAMPED BOUNDARY CONDITIONS. TO OBTAIN SOLUTIONS FOR THE FLEXURE OF THE PLATE, EFFORTS REQUIRED USING THE PROPOSED THEORY ARE COMPARABLE TO THOSE INVOLVED IN THE CASE OF CLASSICAL PLATE THEORY. THE EFFECTIVENESS OF THE PROPOSED THEORY IS DEMONSTRATED THROUGH ILLUSTRATIVE EXAMPLES AND BY COMPARING RESULTS OBTAINED WITH OTHER PLATE THEORIES.