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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Transient Elastodynamic Analysis of Plane Structures Using Coons-Patch Macroelements and Modal Superposition
Department of Mechanical Engineering, National Technical University of Athens, Greece
C.G. Provatidis, "Transient Elastodynamic Analysis of Plane Structures Using Coons-Patch Macroelements and Modal Superposition", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 197, 2006. doi:10.4203/ccp.83.197
Keywords: elastodynamics, plane structures, large finite elements, modal analysis.
Early attempts to develop approximate methods by Ritz , Galerkin  and Trefftz  were based on global approximation of the displacement within the whole structure. Later, finite element methods (FEM) suggested several local approximation schemes as overviewed by Zienkiewicz  and Bathe . However, due to high manual effort required for mesh generation as well as further needs for increased accuracy in calculations, a lot of attempts have been made in order to replace or improve conventional finite element methods. In this context, boundary element methods (e.g. Brebbia and Dominguez ) have been applied to the whole spectrum of mechanics as well as meshless and mesh-free techniques (Atluri , Liu ) have been applied for a over a decade. Concerning the particular area of dynamic analysis of structures, substructuring and dynamic condensation techniques aiming to reduce the order of the equations system have been applied by Guyan  and other researchers.
Within this context, the author has previously proposed a global approximation approach by constructing large finite elements with the nodal points mostly along the boundaries. The background of the relevant method is Coons' interpolation formula . This method has been successfully applied to static and eigenvalue elasticity problems [11,12]. Concerning transient analysis, a preliminary study under uniform tensile loading using a Poisson's ratio of zero value in conjunction with a central-difference time-integration scheme has led to promising results . Moreover, the proposed Coons-patch macroelements (CPM) have been successfully applied to potential time-dependent (hyperbolic and parabolic) problems [14,15].
This paper further investigates the applicability of two-dimensional Coons macroelements to solve transient dynamical problems using modal superposition and compare with conventional FEM for two typical test cases chosen from literature. The first example refers to a rectangular cantilever of dimensions (2x4 m2) under impulsive flexural load while the second to a dam-like structure subject to sinusoidal excitation. The proposed CPM methodology is successfully compared with conventional four-node FEM with the same boundary discretization. It was found that in the current formulation only consistent global mass matrices are applicable.
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