Unilateral contact, dynamic analysis of beams by a time-stepping, quadratic programming procedure

Meccanica ◽  
1983 ◽  
Vol 18 (4) ◽  
pp. 254-265 ◽  
Author(s):  
Efthimia Mitsopoulou
Keyword(s):  
Quadratic Programming ◽  
Dynamic Analysis ◽  
Unilateral Contact ◽  
Time Stepping

Augmented Time-Stepping by Step-Size Adjustment and Extrapolation

2007 ◽  
Author(s):  
Christian Studer ◽  
Christoph Glocker
Keyword(s):  
Time Evolution ◽  
Integration Method ◽  
Switching Time ◽  
Mechanical Systems ◽  
Unilateral Contact ◽  
Step Size ◽  
Frictional Contacts ◽  
Time Stepping ◽  
Size Adjustment ◽  
Integration Order

Time-stepping schemes are widely used when integrating non-smooth systems. In this paper we discuss an augmented time-stepping scheme which uses step-size adjustment and extrapolation. The time evolution of non-smooth systems can be divided in different smooth parts, which are separated by switching points. We deduce the time-stepping method of Moreau, which is a common order-one integration method for non-smooth systems. We formulate the method using contact inclusions, and show how these inclusions can be solved by a projection. We show how time-steps which contain a switching point can be detected by observing the projection behaviour, and propose a step-size adjustment, which treats these switching time-steps with a minimal step-size Δtmin. Time-steps in smooth parts of the motion are run with a larger step-size, and an extrapolation method, which is based on the time-stepping scheme, is used to increase the integration order. The presented method is suitable for mechanical systems with unilateral and frictional contacts. For simplicity, we deduce the method considering solely mechanical systems with one unilateral contact.

A new algorithm of time stepping in the non-linear dynamic analysis

2001 ◽  
Vol 17 (9) ◽  
pp. 597-611 ◽  
Author(s):  
Yang Haitian ◽  
Gao Qiang ◽  
Guo Xinglin ◽  
Wu Chengwei
Keyword(s):  
Dynamic Analysis ◽  
Time Stepping ◽  
Linear Dynamic ◽  
Non Linear

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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