scholarly journals Combining set propagation with finite element methods for time integration in transient solid mechanics problems

2022 ◽  
Vol 259 ◽  
pp. 106699
Author(s):  
Marcelo Forets ◽  
Daniel Freire Caporale ◽  
Jorge M. Pérez Zerpa
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Solid Mechanics ◽  
Time Integration

Time Integration of Impact Phenomena in Solid Mechanics: A One-Dimensional Model Problem

1996 ◽  
Author(s):  
V. Chawla ◽  
T. A. Laursen
Keyword(s):  
Finite Element ◽  
Solid Mechanics ◽  
Exact Analytical Solution ◽  
Time Integration ◽  
Dynamic Contact ◽  
Momentum Conservation ◽  
Integration Scheme ◽  
Mass System ◽  
Element Discretization ◽  
Time Integration Scheme

Abstract 1D impact between two identical bars is modeled as a simple spring-mass system as would be generated by a finite element discretization. Some commonly used time integrators are applied to the system to demonstrate defects in the numerical solution as compared to the exact analytical solution. Using energy conservation as the criterion for stability, a new time integration scheme is proposed that imposes a persistency condition for dynamic contact. Finite element simulation with Lagrange multipliers for enforcing the contact constraints shows exact energy and momentum conservation.

Particle Finite Element Methods in Solid Mechanics Problems

2007 ◽  
pp. 87-103 ◽  
Author(s):  
J. Oliver ◽  
J. C. Cante ◽  
R. Weyler ◽  
C. González ◽  
J. Hernandez
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Solid Mechanics

Practical Aspects of Finite Element Computations in Solid Mechanics

1986 ◽  
Vol 39 (11) ◽  
pp. 1678-1681 ◽  
Author(s):  
H. D. Hibbitt
Keyword(s):  
Finite Element ◽  
Numerical Method ◽  
Finite Element Methods ◽  
Solid Mechanics ◽  
Computer Language ◽  
Temporal Discretization ◽  
Material Behaviors ◽  
Algorithmic Problems ◽  
Computational Aspects ◽  
Language Environment

The paper focuses on practical aspects of the prospective use of finite element methods in problems in solid mechanics. It looks briefly at the computer and computer language environment in which the methods are used, and at the computational aspects of the numerical method itself. The fundamental algorithmic problems (spatial and temporal discretization, and the modeling of realistic material behaviors) are reviewed from an applications viewpoint, and some areas where further work is needed are mentioned.

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