Large Deflection Analysis Of Membranes Containing Rigid Inclusions
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M. S. Nerantzaki & C. B. Kandilas
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.
rigid inclusion, elastic membranes, large deflections, nonlinear, boundary elements, analog equation method.