An Alternative Positional FEM Formulation for Geometrically Non-linear Analysis of Shells: Curved Triangular Isoparametric Elements

Abstract

This work presents an alternative finite element shell formulation based on non-conventional nodal parameters. The considered parameters are nodal positions (not displacements) and generalized vector components that comprise both director cossines and shell thickness variation at the same time. Although any objective strain measure could be adopted to develop the proposed formulation, non-linear engineering strain is chosen in order to take advantage of well know linear engineering stress-strain relations and to complement the easy geometrical appeal of positional formulation. The resulting formulation presents six degrees of freedom by each node and considers constant thickness variation. Consequently, the formulation fulfills a three dimensional compatible mapping and requires a relaxed three-dimensional constitutive relation to avoid thickness locking. Curved triangular elements with cubic approximation are adopted following a very simple notation. Several numerical simulations illustrate and confirm the accuracy and applicability of the proposed formulation.

Fiber-matrix Contact Stress Analysis for Elastic 2D Composite Solids

“…The 2D solid finite element applied here to discretize the continuum is isoparametric of any order (Coda, 2009;Coda and Paccola, 2008;Pascon and Coda, 2013). Curved high order fiber elements are developed to be embedded in the continuum.…”

“…The deformation gradient A can be derived directly from 0 A and 1 A as (Bonet et al, 2000;Coda and Paccola, 2007):…”

A shell finite element formulation to analyze highly deformable rubber-like materials

“…Despite the computational effort required, the use of fully integrated finite elements of higher orders tends to mitigate most types of locking, increasing the reliability of the formulation (see, for instance, [2], [3], [4] and [5]). High-order shell finite elements are successfully employed, for example, in [5][6][7][8][9][10].…”

“…An alternative procedure, which avoids the abovementioned difficulties, is the positional version of the FEM (see, for instance, [15], [16] and [9]). In this case, the seven nodal degrees of freedom of the shell are: three components of the current shell reference surface; three components of the final deformed unconstrained director; and the final linear strain rate across the thickness.…”

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“…Adota-se o elemento finito de casca NLG com cinemática de Reissner originalmente proposto por Coda & Paccola (2008). Para este elemento, o mapeamento de pontos pertencentes ao corpo sólido é feito primeiramente pela sua superfície média.…”