On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells
type: Item
instance of: scholarly article
title: On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells
zbMATH Open document ID: 0848.73060
DOI: 10.1007/BF00350723
author: F. B. Damjanić
author: Boštjan Brank
author: D. Perić
published in: Computational Mechanics
publication date: 1996-10-31T00:00:00Z
review text: The authors present a simple nonlinear stress resultant four node shell finite element. The underlying shell theory is developed from three-dimensional continuum theory via standard assumptions on the displacement field. A model for thin shell is obtained by approximating terms describing the shell geometry. The rotation of the shell director is parameterized by two Euler angles, although other approaches can also be easily accomodated. A procedure is provided to extend the presented approach by including the through-thickness variable material properties. These may include a general nonlinear elastic material with varying degree of orthotropy, which is typical for fibre reinforced composites. Thus a simple and efficient model suitable for analysis of multilayered composite shells is obtained. Shell kinematics is consistently linearized, leading to the Newton-Raphson numerical procedure, which preserves quadratic rate of asymptotic convergence. A range of linear and nonlinear tests is provided and compared with available solutions to illustrate the approach.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74E30
zbMATH DE Number: 833534
zbMATH Keywords: rotation of shell director
zbMATH Keywords: three-dimensional continuum theory
zbMATH Keywords: Euler angles
zbMATH Keywords: through-thickness variable material properties
zbMATH Keywords: general nonlinear elastic material
zbMATH Keywords: fibre reinforced composites
zbMATH Keywords: Newton-Raphson numerical procedure
zbMATH Keywords: quadratic rate of asymptotic convergence
reviewed by: Ladislav Prášek
MaRDI profile type: Publication
cites work: EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements
cites work: A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
cites work: Shell theory versus degeneration—a comparison in large rotation finite element analysis
cites work: Q4304280
cites work: Interpolation of curved shell geometries by low order finite elements—errors and modifications
cites work: Q5537118
cites work: The influence of the reference geometry on the response of elastic shells
cites work: An investigation of a finite rotation four node assumed strain shell element
cites work: Rational approach for assumed stress finite elements
cites work: An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation
cites work: On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
cites work: On a stress resultant geometrically exact shell model. II: The linear theory; computational aspects
cites work: On a stress resultant geometrically exact shell model. III: Computational aspects of the nonlinear theory
cites work: On the Variational Foundations of Assumed Strain Methods
cites work: Q5722857
cites work: Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation
cites work: A general procedure for the direct computation of turning and bifurcation points
description: scientific article; zbMATH DE number 833534