Reduction methods based on eigenvectors and Ritz vectors for nonlinear transient analysis

Reduction methods using eigenvectors and Ritz vectors as basis vectors are empolyed to reduce the finite element nonlinear system of equations using a 48 D.O.F. doubly curved thin plate/shell element. With and without basis updating, the solutions obtained by reduction methods are compared with the direct solutions. It is observed that basis updating is essential to obtain accurate solutions. The present reduction methods need a large number of basis vectors (eigenvectors and Ritz vectors) to account for the impact load which has high frequency characteristics. Furthermore, for nonlinear analysis, the reduction achieved in the CPU time are only marginal since most of the CPU time was spent in the calculation of the internal nodal force vector. These considerations indicate that reduction methods may not be efficient for the impact response analysis.

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