Nonlinear Shell Finite Elements for Ultimate Strength and Collapse Analysis of Ship Structures
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The present thesis deals with ultimate strength and collapse analysis of ship structures. Within this are, the attention is directed towards simple and efficient nonlinear finite element models for stiffened plate panels in ship structures. Several types of Morley elements are investigated and two are selected for further development. These triangular elements assume constant stress distribution over the element area. The first element considered is a nonlinear facet shell element which is valid within moderate rotations. Its elastic formulation has been proposed earlier. In this work, the element matrices are extended to account for material plasticity. The second element, is a displacement-based curved element which undergoes arbitrary large displacements and rotations. The discrete equilibrium equations for this element are re-derived so as to make them more efficient with standard Newton-Raphson solution procedures. Material plasticity formulation using through-the thickness integration as well as resultants plasticity is presented. The evolution laws are derived from the natural laws of thermodynamics, and a return mapping algorithm with a backward Euler difference scheme is used for a solution of the evolution equations. The plasticity computations involve a solution of a single scalar yield surface for the plasticity multiplier. By performing the matrix algebra analytically, simple and explicit expressions are derived. These equations reduce the computational costs remarkably. Numerical examples, mostly selected from well-know benchmark problems, are presented to demonstrate the performance of the proposed formulations. Very good agreement is obtained when compared with published results. In addition, typical problems for ultimate strength and collapse analysis of ship hull-girder are analyzed. These include plate girders, stiffened plate panels, as well as a cruciform element. The results show good agreement not only with those obtained from commercial finite element programs, but also from the experimental observations. For stiffened plate panels, comparison is made with DNV design rules, which is found to give non-conservative estimates for some load conditions. Finally, a study on multi-span stiffened panels is performed so as to compare the estimates provided by the conventional single span model. It is observed that the conventional model provides conservative estimates, and the effect of transverse frames is especially significant on the finite element model of stiffened panels.