Large deformation and mechanics of flexible isotropic membrane ballooning in three dimensions by differential quadrature method

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Abstract: This paper presents a computationally efficient and accurate new methodology in the differential quadrature analysis of structural mechanics for flexible membranes ballooning in three dimensions under a negative air pressure differential. The differential quadrature method is employed to discretize the resulting equations in the axial direction as well as for the solution procedure. The weighting coefficients employed are not exclusive, and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients. A second-order paraboloid of revolution is assumed to describe the ballooning shape. This study asserts the accuracy, convergency, and efficiency of the methodology by solving some typical stability, straining analysis membrane problems, and comparing the results with those of the exact solutions and/or those of physical tests.