Free and forced vibration analysis using the strong-form zonal free element method
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In this paper, a novel strong-form numerical method, a zonal free element method (ZFREM) is presented for the calculation of free and forced vibration analysis of elastodynamic problems. Based on the free element collocation method, this method combines the advantages of FBM and SFEM, by using the sub-domain mapping technique to simplify the complex geometry and easy to create regular collocation elements. In this method, at each collocation nodes, the surrounding nodes can be freely chosen to form an isoparametric element. As the same time, the dynamic equilibrium equations are collocated only at the internal nodes of zones, while the flux equilibrium equations are collocated at the interface and boundary nodes. Thus, the proposed method can obtain the lumped mass matrix which is convenient for one-dimensional storage and symmetric decomposition. In addition, as the mass term exists only on the internal nodes of every zone, using the subspace iteration method can avoid transforming the system equations and greatly improve the solution efficiency for the free vibration problem. A number of numerical examples of the free and forced 2D and 3D dynamic problems are carried out to demonstrate the correctness and efficiency of the proposed method.
