Application of the Recursive Finite Element Approach on 2D Periodic Structures under Harmonic Vibrations
AbstractThe frequency response function is a quantitative measure used in structural analysis and engineering design; hence, it is targeted for accuracy. For a large structure, a high number of substructures, also called cells, must be considered, which will lead to a high amount of computational time. In this paper, the recursive method, a finite element method, is used for computing the frequency response function, independent of the number of cells with much lesser time costs. The fundamental principle is eliminating the internal degrees of freedom that are at the interface between a cell and its succeeding one. The method is applied solely for free (no load) nodes. Based on the boundary and interior degrees of freedom, the global dynamic stiffness matrix is computed by means of products and inverses resulting with a dimension the same as that for one cell. The recursive method is demonstrated on periodic structures (cranes and buildings) under harmonic vibrations. The method yielded a satisfying time decrease with a maximum time ratio of
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Yassine, R.; Salman, F.; Al Shaer, A.; Hammoud, M.; Duhamel, D. Application of the Recursive Finite Element Approach on 2D Periodic Structures under Harmonic Vibrations. Computation 2017, 5, 1.
Yassine R, Salman F, Al Shaer A, Hammoud M, Duhamel D. Application of the Recursive Finite Element Approach on 2D Periodic Structures under Harmonic Vibrations. Computation. 2017; 5(1):1.Chicago/Turabian Style
Yassine, Reem; Salman, Faten; Al Shaer, Ali; Hammoud, Mohammad; Duhamel, Denis. 2017. "Application of the Recursive Finite Element Approach on 2D Periodic Structures under Harmonic Vibrations." Computation 5, no. 1: 1.
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