AN EFFICIENT GENERAL CURVILINEAR COORDINATES FINITE ELEMENT METHOD FOR THE LINEAR DYNAMIC STUDY OF THICKNESS-INDEPENDENT SHELLS

Abstract

TO DATE, A LARGE NUMBER OF FINITE ELEMENT METHODS HAVE BEEN DEVELOPED TO STUDY THE DYNAMICS OF SHELL STRUCTURES. MOST OF THEM ARE GENERALLY BASED ON THE DEGENERATED SOLID APPROACH AND OTHER LESS IN SHELL THEORIES, BUT INTRODUCING, IN THIS LAST CASE, SOME ASSUMPTIONS TO ANALYZE THIS PROBLEM: SOME OF THEM REFER TO SHALLOW SHELLS (SLIGHTLY CURVED SHELLS), OR CONSIDER THIN SHELLS NEGLECTING SHEAR DEFORMATION, OR DISPENSE SOME TERMS IN THEIR STRESS-STRAIN DEVELOPMENTS LIKE THE OFF-DIAGONAL COMPONENTS OF THE CURVATURE OR METRIC TENSORS (ORTHOGONAL COORDINATES). IN THE PRESENT WORK, WE PRESENT AN IMPROVED FINITE ELEMENT METHOD FOR THE DYNAMIC ANALYSIS OF MODERATELY THICK AND THICK SHELLS DEVELOPED IN GENERAL CURVILINEAR COORDINATES, BASED ON A REFINED SHEAR DEFORMATION SHELL THEORY AND FREE OF THE WELL-KNOWN SHEAR AND MEMBRANE LOCKING EFFECTS. EXACT CONSTITUTIVE EQUATIONS, INCLUDING HIGHER ORDER MOMENTS – STRAINS RELATIONS, ARE ALSO DEDUCED. TO CIRCUMVENT THE SHEAR LOCKING PROBLEMS, THE MIXED INTERPOLATION OF THE TENSORIAL COMPONENTS (MITC) OF THE GREEN-LAGRANGE DEFORMATION TENSOR IS USED. AN EXHAUSTIVE STUDY OF DIFFERENT SURFACES IS PERFORMED, ESPECIALLY IN DOUBLY CURVED SHELLS, AND INTERESTING CONCLUSIONS OF THE HIGHER ORDER MODES OF VIBRATION AND THE STRAIN ENERGY OF THE ELEMENT ARE DERIVED. OTHER DESIRABLE FEATURES LIKE A LOW COMPUTATIONAL EFFORT, A STRAIGHTFORWARD EXTENSION TO NONLINEAR FORMULATION AND APPLICATIONS FOR COMPOSITE SHELLS ARE FOUND IN THIS NOVEL AND GENERAL FORMULATION.