Nonlinear finite element analysis and design optimization of thin-walled structures

In this study, an efficient, accurate and robust methodology for nonlinear finite element analysis and design optimization of thin-walled structures is presented. Main parts of this research are: formulation and development of an accurate and efficient shell element, a robust nonlinear finite element analysis technique, and an efficient optimization methodology. In the first part, a new three-node triangular shell element is developed by combining the optimal membrane element and discrete Kirchhoff triangle (DKT) plate bending element, and is then modified for laminated composite plates and shells so as to include the membrane-bending coupling effect. Also, a moderately thick shell element is developed in a similar manner by combining the discrete Kirchhoff-Mindlin triangular (DKMT) plate bending element and the optimal membrane element. Using appropriate shape functions for the bending and membrane modes of the element, the "inconsistent" stress stiffness matrix is formulated and the tangent stiffness matrix is determined. In the second part, a robust nonlinear finite element analysis program based on the corotational technique is developed to analyze thin-walled structures with geometric nonlinearity. The new element is thoroughly tested by solving few popular benchmark problems. The results of the analyses are compared with those obtained based on other membrane elements. In the third part, optimization algorithms based on the optimality criteria are developed and then combined with the nonlinear finite element analysis to optimize different types of thin-walled structures with geometric nonlinearity. The optimization problem considers the thickness or geometry design variables, and aims to maximize the critical load of the structure subject to constant total mass, or minimize the total mass subject to constant applied loads. The optimization results based on the developed design optimization algorithm are compared with those based on the gradient-based sequential quadratic programming method to demonstrate the efficiency and accuracy of the developed procedure. An application of the thickness optimization for locating the potential places to add the stiffeners in stiffened panels is also presented. Also a method is presented to efficiently incorporate the effects of local buckling and mode switching during optimization process for stiffened panels