Error estimation and adaptivity in elastodynamics
type: Item
instance of: scholarly article
title: Error estimation and adaptivity in elastodynamics
zbMATH Open document ID: 0802.73076
DOI: 10.1016/0045-7825(92)90030-N
author: Juan-Miguel Gracia
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1993-10-17T00:00:00Z
review text: The authors try to apply mesh adaptive techniques to elastodynamics. There are few papers concerning the problem of mesh adaptation for hyperbolic problems. This paper summarizes the recent works of the authors. The excellent introduction gives the reader the view to mesh adaptation techniques and error estimation. Both spatial and temporal discretization is considered. \(h\) and \(p\) version of adaptive techniques are presented with references to the most characteristic literature contributions. Error analysis proves the lower error order for time discretization than for space one. That is why only error indicator related to spatial variables is significant for mesh modification. The mesh is modified according to the error distribution in spatial domain. Since the phenomenon observed changes in time, the mesh is also changed in each several steps of time integration of the differential equation of motion. The mesh regeneration is performed with the use of the smoothed field of characteristic parameters of the problem (for example, stress). Nodal parameters are transferred between two different meshes in that way. However, the error introduced by this procedure is not considered or evaluated. For vibration analysis, regeneration of the mesh with different geometry may be difficult provided the smoothing procedure is applied both to space and time. Such a discussion could eliminate doubts in individual applications. Examples of eigenvalue analysis and direct integration of the motion equation demonstrate the efficiency of the approach. It allows to reduce the number of variables in the problem and finally decrease the computational effort. Although the problem of mesh adaptation in elastodynamics is still open, the paper can be interesting for people working in the domain of applications of computer methods to structural dynamics.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M50
zbMATH DE Number: 429036
zbMATH Keywords: Newmark method
zbMATH Keywords: spatial and temporal discretization
zbMATH Keywords: error indicator
zbMATH Keywords: vibration analysis
zbMATH Keywords: eigenvalue analysis
reviewed by: C. I. Bajer
MaRDI profile type: Publication
cites work: Basic principles of feedback and adaptive approaches in the finite element method
cites work: Adaptive approximations in finite element structural analysis
cites work: The hierarchical concept in finite element analysis
cites work: Formulation and solution of hierarchical finite element equations
cites work: Q3813123
cites work: The h-p version of the finite element method. II. General results and applications
cites work: Adaptive h-p procedures for high accuracy finite element analysis of two-dimensional linear elastic problems
cites work: The p- and h-p versions of the finite element method in solid mechanics
cites work: Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation
cites work: A simple error estimator and adaptive procedure for practical engineerng analysis
cites work: Adaptivity and mesh generation
cites work: An Adaptive Finite Element Method for Linear Elliptic Problems
cites work: Adaptive and hierarchical weighted residual and least-squares time integration of convection-diffusion problems
cites work: An adaptive procedure for eigenvalue problems using the hierarchical finite element method
cites work: An adaptive finite element technique for structural dynamic analysis
cites work: A variable-step central difference method for structural dynamics analysis. I. Theoretical aspects
cites work: An automatic time-stepping algorithm for dynamic problems
cites work: Spatial mesh adaptation in semidiscrete finite element analysis of linear elastodynamic problems
cites work: Q4341567
cites work: Adaptive mesh in dynamic problems by the space-time approach
cites work: An adaptive finite element procedure for 2D dynamic transient analysis using direct integration
cites work: Superconvergence recovery technique anda posteriori error estimators
cites work: Note on an approximate method for computing consistent conjugate stresses in elastic finite elements
cites work: A unified set of single step algorithms. Part 1: General formulation and applications
cites work: A simple local error estimator and an adaptive time-stepping procedure for direct integration method in dynamic analysis
description: scientific article; zbMATH DE number 429036