Large Deflection Analysis Of Membranes
Containing Rigid Inclusions
Author(s)
M. S. Nerantzaki & C. B. Kandilas
Abstract
In this paper the deformation of membranes containing rigid inclusions is
analyzed. These rigid inclusions can significantly change the entire stress
distribution in the membrane and therefore create major difficulties for the
design. The initially flat membrane, which may be prestretched by boundary
in-plane tractions or displacements, is subjected to externally applied loads and
to the weight of the rigid inclusions. The composite system is examined in cases
where it’s deformation reaches a state for which the undeformed and deformed
shapes are substantially different. In such cases large deflections of membranes
are considered, which result from nonlinear kinematic relations. The three
coupled nonlinear equations in terms of the displacements governing the
response of the membrane are solved using the Analog Equation Method (AEM),
which reduces the problem to the solution of three uncoupled Poisson’s
equations with fictitious domain source densities. The problem is strongly
nonlinear. In addition to the geometrical nonlinearity, the problem is itself
nonlinear, because the membrane’s reactions on the boundary of the rigid
inclusions are not a priori known as they depend on the produced deflection
surface. Iterative schemes are developed for the calculation of deformed
membrane’s configuration which converges to the final equilibrium state of the
membrane with the given external applied loads. Several example problems are
presented, which illustrate the method and demonstrate its accuracy and
efficiency. The method has all the advantages of the pure BEM.
Keywords: rigid inclusion, elastic membranes, large deflections, nonlinear,
boundary elements, analog equation method.
Keywords
rigid inclusion, elastic membranes, large deflections, nonlinear,
boundary elements, analog equation method.
Related Book
Other papers in this volume
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