Efficient Structural Dynamic Analysis Using Condensed Finite Element Matrices and Its Application to a Stiffened Plate

Abstract

In this study, we propose effective formulations for modal, frequency response, and transient analyses using condensed matrices of the finite element (FE) model. Employing the iterated improved reduced system (IIRS) method, a transformation matrix is defined that condenses the stiffness and inertial effects of nodes to be neglected into nodes of interest. Using this, the condensed mass and stiffness matrices are derived. With these two condensed matrices, a condensed damping matrix is derived using the Rayleigh damping. By considering the condensed matrices in the original structural dynamic formulation based on the global FE matrices, the condensed structural dynamic formulation is derived, and the approximated solutions are calculated from this condensed formulation. To verify the performance of the proposed formulation, we perform a structural dynamic analysis on a stiffened plate, and by comparison with the solutions calculated from the global FE matrices, the proposed formulations have been found to provide highly accurate solutions with an excellent computational efficiency.

Free and Forced Vibration Characteristics of a Composite Stiffened Plate Based on Energy Method

“…Liu et al [20] introduced a dynamic analysis method for stiffened plates under moving loads utilizing the FSDT along with Chebyshev polynomials for spatial discretization and penalty functions for various boundary conditions. Ko and Boo [21] proposed a condensed finite element matrix using the iterated improved reduced system (IIRS) method to address modal, frequency, and transient responses of stiffened plates. Guo et al [22] investigated the concentric stiffened plate free vibration using a two-dimensional spectral Chebyshev technique.…”