The Earthquake Engineering Online Archive

Additional Results on the Modal Analysis of Finite Elements for Finite Deformation Problems: Classical and Stabilized Formulations

Armero, Francisco

UCB/SEMM-1997/15, Dept. of Civil and Environmental Engineering, University of California, Berkeley, 1997-09-01, 28 pages (500 C23 97-15)

Presents closed-form expressions for the eigenvalues and eigenvectors of several finite elements in finite strain conditions. An axial tension/compression plane state of strain is considered in combination with a general Ogden model. The analysis identifies the instability of the enhanced strain formulations associated with material instabilities of the underlying material model. A new stabilization procedure is presented to avoid these numerical instabilities for the problem at hand, while maintaining the optimal performance of the elements in the small strain range.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-96-03.pdf (1 MB)