Optimization of shells modeled using NURBS subjected to a dynamic loading condition

Abstract

This study presents an optimization method for the thickness of shell elements subjected to dynamic loads. Structural analyses were carried out using the finite element method. The analyzed domains were modeled using NURBS, and meshes were generated using a transformation of the parametric domain into the geometric domain via a geometric function. The shell element considered is a combination of a CST membrane element and a DKT plate element, forming an element with 15 degrees of freedom. The Newmark method with constant acceleration was applied to solve the equation of motion. The optimization approach was considered in two different ways: with uniform and variable thickness throughout the shell element. Due to the nonlinear constraints of the problem, the Sequential Quadratic Programming (SQP) method was employed. SQP routines are available in MATLAB, in which this study was performed. Useful examples were detailed in this study to demonstrate the applicability of the optimization method to real structures, such as the Igrejinha da Pampulha, a church located in Belo Horizonte, Brazil, whose modeling was performed.