Application of Ritz’s Method to Thin Elastic Shell Analysis

Abstract

This paper is concerned with finite-element analysis of thin elastic shells described by the Koiter-Sanders mathematical model. The middle surface of the shell is decomposed into curved finite triangular elements, which are mapped onto straight triangles in the plane of parameters of the surface. We show that with an appropriate approximation of the given surface, rigid-body motions may be represented exactly. Nine degrees of freedom are associated with each nodal point (the vertices of the elements) and the displacement functions fulfill the conditions of regularity required by Ritz’s method and assure convergence in energy. The derivation is quite general with respect to the geometry of the shell. A cylindrical shell analysis is presented as an illustrative numerical example.

On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures

“…The advantage of this formulation is a proper representation of the rigid-body motions when a finite element approach is used. A deep shell element based on this theory has been developed in [4].…”

A high precision triangular laminated anisotropic cylindrical shell finite element

“…The requirements upon valid minimum potential energy solutions in thin shell finite element analysis are extremely difficult to satisfy, and the satisfactory formulations are therefore relatively complicated. Further, for tackling problems involving description of arbitrary boundaries triangular and quadrilateral elements are obviously best suited, The most reliable and sophisticated triangular shell element formulations are those due to Dupuis [4], Cowper et al [5], Argyris and Scharph [6] and Dawe [7]. The formulation due to Cowper et al [5] has also been converted into a triangular cylindrical shell finite element by Lindberg and Olson [8].…”

Incremental Analysis of Nonlinear Structural Mechanics Problems with Applications to General Shell Structures

“…The triangular element developed by Dupuis [18], based on a previous formulation by Dupuis and Goel [19], has been used for a wide range of practical applications. The element has nine degrees of freedom at each node, and third order Lagrange polynomials are used to interpolate the displacements within the element.…”

“…There has been an extensive development of curved shell elements for axisymmetric and arbitrary shells [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The various approaches can best be described by discussing representative examples; the remaining elements are variations on these basic types.…”