Analysis of finite element methods for the nonlinear dynamic analysis of shells
type: Item
instance of: scholarly article
title: Analysis of finite element methods for the nonlinear dynamic analysis of shells
zbMATH Open document ID: 0536.73065
DOI: 10.1007/BF01395312
author: Lois Mansfield
published in: Numerische Mathematik
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132872
review text: This paper gives a mathematical error analysis for different finite element methods for the nonlinear dynamic behaviour of shells. The authors demonstrate the convergence of the Galerkin method in time approach for damped and undamped problems. They extend the mixed finite element formulation - previously applied only to time independent problems - to time dependent problems. The formulation is considerably more efficient than the finite element displacement approach. The paper also presents new fully discrete methods which are unconditionally stable. This contribution is of interest to scientists who wish to solve dynamic problems - including nonlinearities - using a stable time integration technique.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K25
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 3852564
zbMATH Keywords: mathematical error analysis
zbMATH Keywords: nonlinear dynamic behaviour of shells
zbMATH Keywords: convergence of the Galerkin method in time approach
zbMATH Keywords: damped and undamped problems
zbMATH Keywords: mixed finite element formulation
zbMATH Keywords: time dependent problems
zbMATH Keywords: fully discrete methods
zbMATH Keywords: unconditionally stable
zbMATH Keywords: stable time integration technique
reviewed by: C. A. Brebbia
MaRDI profile type: Publication
cites work: Q4168022
cites work: Compatible triangular finite-elements
cites work: Q4148920
cites work: Finite element approximation of the Navier-Stokes equations
cites work: Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
cites work: Q4115572
cites work: On mixed finite element methods for elliptic equations
cites work: On the Solution of the Finite Element Equations for Nonlinear Shell Analysis
cites work: Q4135064
OpenAlex ID: W2016050979
Recommended article: Finite element procedures for the nonlinear dynamic stability analysis of arbitrary shell structures
Recommended article: Q5186856
Recommended article: Nonlinear dynamics of shells: Theory, finite element formulation, and integration schemes
Recommended article: Q4423280
Recommended article: Finite-element procedures for the stability analysis of nonlinear, parametric excited shell structures
Recommended article: Q4038134
Recommended article: Q3155535
Recommended article: Q4720886
Recommended article: A finite element analysis on random vibration of nonlinear shell structures
description: scientific article; zbMATH DE number 3852564