Paper Information

Journal:   AMIRKABIR   FALL 2006- WINTER 2007 , Volume 17 , Number 65-C; Page(s) 43 To 51.
 
Paper: 

OPTIMUM TIME STEP FOR DYNAMIC RELAXATION METHOD

 
 
Author(s):  ALAMATIAN J., KADKHODAIAN M.
 
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Abstract: 

Dynamic Relaxation is an iterative technique, which is used as an equation solver. In this paper, a new time step will be formulated for Dynamic Relaxation method. The suggested technique is based on the minimization of residual force in each iteration. Mathematical theories and numerical examples are used to verify efficiency of the formulation. By using optimum time step, mathematical convergence rank of DR algorithm will be infinite and two in linear and nonlinear analyses, respectively. To investigate the capability of the proposed formulation, isotropic plates and frame structure by linear and geometrical nonlinear behaviors are analyzed. This study shows that optimum time step reduces number of convergence iterations.
Therefore, the cost and the computational time will be reduced. As a result, the suggested formulation for optimum time step has higher mathematical and numerical efficiency than other common methods, such as constant time step. Therefore, the convergence rate of DR iterations will considerably improve.

 
Keyword(s): DYNAMIC RELAXATION, TIME STEP, RESIDUAL FORCE, LINEAR AND GEOMETRICAL NON LINEAR ANALYSIS
 
References: 
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