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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 197
Transient Elastodynamic Analysis of Plane Structures Using Coons-Patch Macroelements and Modal Superposition C.G. Provatidis
Department of Mechanical Engineering, National Technical University of Athens, Greece Full Bibliographic Reference for this paper
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.
Summary
Early attempts to develop approximate methods by Ritz [1], Galerkin [2] and Trefftz [3]
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 [4] and Bathe [5]. 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 [6]) have been applied to the whole spectrum of
mechanics as well as meshless and mesh-free techniques (Atluri [7], Liu [8]) 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 [9] 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 [10]. 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 [13]. 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. References
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