The ponding problem on elastic membranes: an analog equation solution |
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Authors: | J T Katsikadelis M S Nerantzaki |
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Affiliation: | (1) Department of Civil Engineering National Technical University, GR-15773, Athens, Greece, GR |
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Abstract: | In this paper, the nonlinear response of elastic membranes with arbitrary shape under partial and full ponding loads has
been analyzed. Large deflections are considered, which result from nonlinear kinematic relations. The problem is formulated
in terms of the displacements components and the three coupled nonlinear governing equations are solved using the analog equation
method (AEM). The membrane may be prestressed either by prescribed boundary displacements or tractions. Using the concept
of the analog equation the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with fictitious
sources under the same boundary conditions. Subsequently, the fictitious sources are established using a procedure based on
the BEM and the displacement components as well as the stress resultants at any point of the membrane are evaluated from their
integral representations. In addition to the geometrical nonlinearity, the ponding problem is itself nonlinear, because the
ponding load depends on the deflection surface that it produces. Iterative schemes are developed which converge to the equilibrium
state of the membrane under the ponding loads. Several membranes are analyzed which illustrate the method and demonstrate
its efficiency and accuracy. The method has all the advantages of the pure BEM, since the discretization and integration is
limited only to the boundary.
Received 28 July 2001 |
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Keywords: | Heat conduction Convection Radiation TVD scheme |
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