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Research Papers: Design Automation

# Multifunctional Topology Design of Cellular Material Structures

[+] Author and Article Information

Mechanical Engineering Department, The University of Texas at Austin, Austin, TX 78712ccseepersad@mail.utexas.edu

Janet K. Allen, Farrokh Mistree

G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 and Georgia Tech Savannah, Savannah, GA 31407

David L. McDowell

G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

Frame finite elements are a superposition of 1D beam and bar finite elements, subject to two displacement and one rotational degree of freedom per node.

In Ref. 40, nonperiodic variations in topology are considered.

A constant temperature is assigned during the structural analysis.

The vector of design variables changes for each experiment because a different node is removed in each experiment along with the elements connected to it. Topological robustness $σc$ reflects the sensitivity of performance to the removal of entire joints (and attached structural elements) as a result of a manufacturing imperfection or intentional removal by a designer for improved performance in a secondary functional domain. In contrast, topological derivatives (20,23-24) measure the sensitivity of performance to insertion of an infinitesimally small hole, and they are more appropriate for continuum topology optimization approaches rather than the discrete approaches adopted in this paper.

J. Mech. Des 130(3), 031404 (Feb 14, 2008) (13 pages) doi:10.1115/1.2829876 History: Received May 30, 2006; Revised July 03, 2007; Published February 14, 2008

## Abstract

Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultralight load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermoelastic properties, and limitations of classic topology optimization methods prevent a direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, a practical, two-stage topology design approach is introduced for applications that require customized multifunctional properties. In the first stage, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. In the second design stage, the flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions without degrading structural performance. The method is applied to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.

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Topics: Design , Topology

## Figures

Figure 7

Finite element analysis of a thermal ground structure

Figure 1

Examples of ordered, prismatic cellular materials

Figure 2

Outline of a two-stage multifunctional topology design method

Figure 3

A two-stage multifunctional topology design process

Figure 4

Schematic of a cellular combustor liner

Figure 5

Initial ground structure and boundary conditions for structural topology design

Figure 6

Set of acceptable structural topologies, ΦA, derived from the robust structural topology

## Errata

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