## Shape Optimization of a Shell Structure Restricted to a Complex Design Space

This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

Shape optimization tools have been used for several decades to optimize the mechanical performance of shell structures. These tools assume that the shell structure is confined within a predefined design space with appropriate boundary conditions. They are particularly useful in the pre-conceptual design phase of a shell structure. In the literature, shape optimization problems of a shell structure are often simplified which can lead to an improper representation of the system under investigation. Manual modifications to the optimization results might then be required to complete the final design. For instance, optimization is often performed from a simple design space such as a rectangular cuboid. However, design spaces are generally more complex, seeking to avoid mechanical interference with other components. Another oversimplification concerns the boundary conditions of the shell structure. Usually, boundary conditions are assumed at connection points that can vary during the optimization process. However, in many instances, boundary conditions should be maintained at fixed points within the design space. The main objective of this paper is to propose a shape optimization formulation for a shell structure restricted to an arbitrary design space while ensuring that the shell passes as close as possible to a given set of connection nodes in the design space. In the proposed formulation, the inputs of the optimization problem are the design space defined by a computer-aided design file (e.g. STEP, STL, etc.) and a set of connecting nodes for the shell structure. The objective of the optimization problem is to minimize the elastic strain energy, and it is performed with a genetic algorithm. The geometry of the shell structure is defined by a parametrized surface using B-spline functions. The variables to be optimized are the coordinates of each point of the surface control net. The optimization problem is formulated in such a way so as to ensure that the result remains within the design space. To that end, a penalty is first included in the cost function to bring the shell as close as possible to the desired connecting nodes. Secondly, nonlinear optimization constraints are considered to maintain the shell structure within the design space and to prevent the shell from folding on itself. As a case study, a recreational vehicle component is designed using the proposed optimization formulation. A parametric study of this component is then presented to show the influence of the main optimization parameters (i.e. penalty factor, number of control points¬¬) on the final design. Finally, an optimization results analysis highlights the benefits of the proposed formulation.

### Document Details

Reference NWC_19_188 Paquin. S English Paper 18th June 2019 Laval Universite Global