A posteriori local error estimation and adaptive time-stepping for newmark integration in dynamic analysis

1992 ◽  
Vol 21 (7) ◽  
pp. 555-571 ◽  
Author(s):  
L. F. Zeng ◽  
N.-E. Wiberg ◽  
X. D. Li ◽  
Y. M. Xie
Keyword(s):  
Dynamic Analysis ◽  
Error Estimation ◽  
Local Error ◽  
A Posteriori ◽  
Local Error Estimation ◽  
Time Stepping ◽  
Adaptive Time ◽  
Adaptive Time Stepping

AN ADAPTIVE TIME-STEPPING PROCEDURE BASED ON THE SCALED BOUNDARY FINITE ELEMENT METHOD FOR ELASTODYNAMICS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240007 ◽  
Author(s):  
Z. H. ZHANG ◽  
Z. J. YANG ◽  
GUOHUA LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Local Error ◽  
Error Estimator ◽  
Time Step ◽  
Time Stepping ◽  
Time Increment ◽  
Adaptive Time ◽  
Adaptive Time Stepping ◽  
Scaled Boundary Finite Element

This study develops an adaptive time-stepping procedure of Newmark integration scheme for transient elastodynamic problems, based on the semi-analytical scaled boundary finite element method (SBFEM). In each time step, a posteriori local error estimator based on the linear distributed acceleration is employed to estimate the error caused by the time discretization. The total energy of the domain, consisting of the kinetic energy and the strain energy, is calculated semi-analytically. The time increment is automatically adjusted according to a simple criterion. Three examples with stress wave propagation were modeled. The numerical results show that the developed method is capable of limiting the local error estimator within specified targets by using an optimal time increment in each time step.

A POSTERIORI ERROR ESTIMATION AND H-ADAPTIVE REFINEMENT TECHNIQUES FOR TRANSIENT DYNAMIC ANALYSIS OF STIFFENED PLATE/SHELL PANELS

2004 ◽  
Vol 04 (02) ◽  
pp. 259-277
Author(s):  
G. S. PALANI ◽  
NAGESH R. IYER ◽  
T. V. S. R. APPA RAO
Keyword(s):  
Dynamic Analysis ◽  
Posteriori Error ◽  
Adaptive Refinement ◽  
Error Estimator ◽  
A Posteriori ◽  
Transient Dynamic Analysis ◽  
A Posteriori Error ◽  
Transient Dynamic ◽  
Time Stepping ◽  
Adaptive Time

This paper presents a posteriori error estimation and h-adaptive refinement techniques for transient dynamic analysis of stiffened plates/shells using the finite element method (FEM). We furnish the formulation of stiffness and mass matrices for finite element (FE) models, QL9S2 and QUAD4S2 for dynamic analysis of plates/shells with arbitrarily-located concentric/eccentric stiffeners. Procedures for computing a posteriori errors for spatial and temporal errors have been presented for transient dynamic problems. An h-adaptive refinement strategy for stiffened plate/shell panels by employing QL9S2 and QUAD4S2 FE models has been discussed. An adaptive time stepping scheme, which is to be used with the time errors for quality control of the time steps, has also been presented. Numerical studies have been conducted to evaluate the efficacy of the error estimators and the adaptive mesh refinement and time stepping algorithm. The spatial error estimator for transient dynamic analysis is found to exhibit monotonic convergence at all time steps. The temporal error estimator for transient dynamic analysis in association with the adaptive time stepping is able to compute more accurate and reliable time steps to keep the time errors within the specified tolerance limits.

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