A NEW 48 D.O.F. QUADRILATERAL SHELL ELEMENT WITH VARIABLE-ORDER POLYNOMIAL AND RATIONAL B-SPLINE GEOMETRIES WITH RIGID BODY MODES (DEGREE OF FREEDOM)

CARLETON JOHN MOORE, Purdue University

Abstract

A 48 degree of freedom quadrilateral thin elastic shell finite element using variable-order polynomial function, B-spline functions, and rational B-spline functions to model the shell surface is developed for linear and geometrically nonlinear analyses. This development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems. The displacement functions are those of bicubic Hermitian polynomials. The displacement functions and degrees of freedom are expressed and investigated in both the curvilinear and Cartesian forms. The simpler curvilinear form is shown to provide the proper solution for a number of problems such as cylinders, spherical caps, hypars, and oval shells. For certain highly curved shells such as bellows, however, the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions. It was found in this study that this difficulty can be circumvented and the rigid body modes can be properly included if a Cartesian form is used for displacement functions. The strain-displacement equations for both stiffness formulations are expressed in curvilinear coordinates. Thus the Cartesian displacement functions require a transformation to curvilinear displacements at each numerical integration point in the derivation of the element stiffness.

Degree

Ph.D.

Subject Area

Mechanics

COinS