Session: DAC-10-4: Design of Engineering Materials and Structures

Paper Number: 148302

148302 - Topology Optimization, Structural Frames, Structural Shapes, Geometry Projection 

Structural shapes are widely used in structural design. Their extensive use owes to the standardization of dimensions and mechanical properties, making them readily available, practical, reliable, and easy to economically assemble. Common applications of these structures include machinery frames; civil structures like  bridges and buildings; frames for aerospace applications like instruments and satellites; offshore platforms, to mention a few. Although prescribed solutions that are well-understood and easy to fabricate exist for particular applications (e.g., bridges), there are frame design problems for which it is not intuitive to determine optimal frame designs, therefore we must resort to structural design techniques such as topology optimization.

Conventional density-based and level-set methods for continuum topology optimization (cf.\ \cite{sigmund2013topology}) cannot in general be used to design this type of structures, as they render organic designs. An alternative using topology optimization for continua  are the feature-mapping techniques (\cite{Wein_2020}). In these methods, the structure is represented via the combination of geometric primitives such as bars and plates.  Feature-mapping methods have been used successfully to design structures made of solid bars and plates, however, they are yet to be used for design with structural shapes. This is because  these techniques require a finite element size small enough to accurately capture the structural behavior of each bar, and to ensure design sensitivities are well defined (\cite{Norato_2015}). Roughly speaking, at least two elements are required through the thickness of the primitive. In the case of structural shapes, having two elements through the thickness of, e.g., the webs and flange of an H-beam or the wall of a tube would result in a large number of elements making the finite element analysis expensive and impractical. For this reason,  feature-mapping techniques have been limited to model structural shapes such as rectangular tubes (\cite{bai2020hollow}) with  the dimensions of the design region are comparable to those of the structural shapes.

To address these shortcomings, this work formulates a topology optimization method based on the geometry projection technique for the design of frames made of structural shapes. An equivalent-section approach is formulated that represents the cross-section of the structural shapes as a homogeneous rectangular section. A novel geometric representation is introduced to represent the equivalent section as a cuboid. This representation is endowed with an explicit expression for the computation of the signed distance to the boundary of the primitive and of its sensitivities, allowing for an efficient implementation. An example is presented demonstrating that the proposed method renders optimal designs and exhibits good convergence.

Presenting Author: Nicolas Cuevas Carvajal School of Mechanical, Aerospace, and Manufacturing Engineering University of Connecticut

Presenting Author Biography: I am currently a Ph.D. candidate in the Department of Mechanical Engineering at the University of Connecticut (USA) and is advised by Professor. Julian Norato. I received a Bachelor’s degree in Mechanical Engineering from the Escuela Colombiana de Ingeniería Julio Garavito in Colombia. My research interests focus mainly in computational mechanics and Topology optimization methods.

Authors:

Nicolas Cuevas Carvajal School of Mechanical, Aerospace, and Manufacturing Engineering University of Connecticut
Miguel Fernando Montoya Vallejo Escuela colombiana de ingeniería julio garavito
Julian A. Norato School of Mechanical, Aerospace, and Manufacturing Engineering University of Connecticut