Modified one Dimension Sub-Spaces in Non Linear Dynamic Analysis

The usual finite element methods reduce the infinite number of degree of freedom (D.O.F.) of system to a model with a limited number of D.O.F. while capturing the significant physical behavior. Base relation methods reduce number of D.O.F. in new coordinate. One of the base relation methods is gained from Ritz-Wilson vectors which is much better than the conventional base relation methods and eigen value methods in a lot of cases because of simpler and dependence on dynamic load. Also to be costly in large system calculations and to ignore loading parameter can be mentioned as the disadvantages of eigen vectors. Fewer number of required Ritz vectors in comparison with eigen values and considering place distribution of external loading and dominant frequency content of loading has pushed the researchers into applying Ritz vectors. Base alteration methods in nonlinear problems are not usually much applicable due to frequent matrix change of system. Generalized one dimensional subspace method presents an appropriate solution for geometric nonlinearity problems by means of Ritz-Wilson technique. In this article generalized one dimensional subspace method is combined with mode-acceleration technique in order to analyze nonlinear dynamic problems. Based on inside error component and generalized one dimensional subspace method, a modified criterion using mode-acceleration technique in order to update required base vectors for stiffness changes in nonlinear dynamic analysis is proposed. The results indicate that the accuracy and speed of the modified method are appropriate.