ies Linear and Nonlinear Finite Element Analysis of Large Deformation of Thin Shell Structures

Abstract

This thesis presents the linear and nonlinear analysis of thin shell structures. The linear formulation is based on three finite elements namely the: four nodes degenerated shell element (DE4), the four nodes flat shell element (FE4) and the nine nodes degenerated shell element (DE9). Each one of these elements has six degrees of freedom per node. Additional elements have been developed; these are: the four nodes element, employing the Mixed Interpolation of Tensorial Components approach (MITC) proposed by Bathe to avoid shear locking applied on DE4 and FE4 , the NonConforming Element (NCE) to improve the behavior in bending situations, and the nine nodes element with Selective Reduced Integration (SRI) and Weighted Modified Integration (WMI). These elements are used to overcome the shear and membrane lock in lieu of using reduced integration. The verification of linear formulation was based on using patch test. The DE4 element passes all patch tests except the pure bending test, while the other elements pass the tests partially. Further verification was done by using numerical examples; and the elements perform very well when the results are compared with exact ones as they are in good agreement. The problems of shear and membrane locks result in the divergence of the solution for these shells with increase in the number of elements. A solution is proposed to correct the convergence curve to be asymptotic to the exact solution curve by using extrapolation. This was done by selecting a Weibull model to correlate the displacement and mesh size through the number of joints. The model depends on parameters; the values of which depend on the values of displacements before the divergence occurs. Good results are obtained when applying the method in different numerical examples for the DE4 element.

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