Unconstrained finite element for geometrical nonlinear dynamics of shells
type: Item
instance of: scholarly article
title: Unconstrained finite element for geometrical nonlinear dynamics of shells
zbMATH Open document ID: 1179.74140
DOI: 10.1155/2009/575131
author: Humberto B. Coda
author: Rodrigo R. Paccola
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45863
review text: Summary: This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark \(\beta \) algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K25
zbMATH DE Number: 5632505
Wikidata QID: Q58649406
MaRDI profile type: Publication
OpenAlex ID: W1984265737
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description: scientific article; zbMATH DE number 5632505