Solution of 1D finite element problems with explicit time integration

2012 ◽  
Vol 40 (1-2) ◽  
pp. 5-32
Author(s):  
Gergely Molnár ◽  
Imre Bojtár
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Explicit Time Integration

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

scholarly journals Adaptivity in Crashworthiness Calculations

1993 ◽  
Vol 1 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Ted Belytschko ◽  
Sang-Ho Lee ◽  
I-Sheng Yeh ◽  
Jerry I. Lin ◽  
Chen-Shyh Tsay ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Transient Analysis ◽  
Time Integration ◽  
Adaptive Finite Element ◽  
Data Preparation ◽  
Adaptive Finite Element Methods ◽  
Explicit Time Integration ◽  
Car Model ◽  
Nonlinear Transient

h-Adaptive finite element methods for nonlinear transient analysis by explicit time integration are described. Examples are given of adaptive calculations for simple components and prototype calculations for a full car model. h-Adaptivity offers substantial reductions in data preparation costs and improvements in accuracy.

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