SECOND–ORDER MODELS FOR THE BENDING ANALYSIS OF THIN AND MODERATELY THICK CIRCULAR CYLINDRICAL SHELLS

Abstract

THE SUITABILITY OF EMPLOYING THE SECOND-ORDER SHEAR DEFORMATION THEORY TO STATIC BENDING PROBLEMS OF THIN AND MODERATELY THICK ISOTROPIC CIRCULAR CYLINDRICAL SHELLS WAS INVESTIGATED. TWO VARIANT FORMS OF THE POLYNOMIAL SECOND-ORDER DISPLACEMENT MODELS WERE CONSIDERED. BOTH MODELS ACCOUNT FOR QUADRATIC EXPANSIONS OF THE SURFACE DISPLACEMENTS ALONG THE SHELL THICKNESS, ALTHOUGH THE SECOND MODEL (SSODM) WAS AUGMENTED BY THE INITIAL CURVATURE TERM. THE EQUILIBRIUM EQUATIONS WERE DERIVED BY USE OF THE PRINCIPLE OF VIRTUAL WORK. NAVIER ANALYTICAL SOLUTIONS WERE OBTAINED UNDER SIMPLY SUPPORTED BOUNDARY CONDITION. THE RESULTS OF THE DISPLACEMENTS AND STRESSES REVEALED THAT THE THEORY FORMULATED ON THE SSODM PROVIDES A GOOD DEPICTION OF THE BENDING BEHAVIOR OF THE THIN AND MODERATELY THICK SHELL AND ARE IN CLOSE AGREEMENT TO THOSE OF THE HIGHER-ORDER SHEAR DEFORMATION THEORY (HSDT). THE ABILITY OF THE THEORY FORMULATED ON THE FIRST DISPLACEMENT MODEL (FSODM) TO PREDICT ACCEPTABLE VALUES OF DISPLACEMENTS AND STRESSES IN THIN SHELLS WAS FOUND TO BE SIGNIFICANTLY AFFECTED BY CHANGES IN LENGTH TO RADIUS OF CURVATURE (L/A) RATIOS.