You are here

Design Analysis Methodology for Topology Optimization of Thermally Loaded Structures



OBJECTIVE: Develop and demonstrate a methodology to optimize topologies of structures exposed to high thermal loads and other important loads for the design of novel lightweight aircraft embedded nozzles and engine aft decks. 

DESCRIPTION: There is demand to reduce aircraft structural weight while safely responding to a more complex array of loads, and in the context of a more integrated aircraft system. Structures for supersonic and lower speed aircraft may be exposed to high thermal loads while supporting embedded nozzles within the aircraft outer mold line or when exposed to engine exhaust downstream of the nozzle. Traditional design methods have relied on superposition of loads in a linear analysis framework. As a result, important nonlinear responses and couplings are neglected. In particular, the typical practice of increasing stiffness by increasing structural size can exacerbate problems of structural response under thermal loads due to thermal expansion [1]. As an example of the costly failure of traditional design methods, the original aft-decks of some recent inventory aircraft have experienced cracks approximately 10 to 30 times faster than planned. Stress-based topology optimization and nonlinear thermoelastic analysis has been found to be an effective strategy for mitigating thermal loads in two dimensions for structures relevant to engine decks and embedded nozzles [1, 2]. With this general approach, structure is placed where beneficial to meeting lifetime-based design constraints and detrimental injection of structure is avoided. Minimum compliance methods have been shown to provide poor designs [1, 2]. This topic will focus on development of a topology optimization method meeting needs not addressed in previous studies: topology optimization of lightweight structures in three space dimensions; inclusion of a broad range of heat transfer mechanisms; inclusion of a broad range of load sources; definition and inclusion of multiple load cases; and optimization of structures fabricated with metals, composites, or both. To be practical, the topology optimization capability needs to compute feasible optima on a high-performance workstation or modestly sized cluster in no more than a day of wall-clock time, with faster speeds expected in building block steps testing incremental functionality. The capability should also: be applicable to domain boundaries of arbitrary shape; output configurations ready to analyze with ABAQUS for verification; and compute stresses and meet stress constraints in an accurate fashion. This topic will initially focus on demonstration of methodology in three dimensions for steady, nonlinear, thermoelastic analysis of metallic structure and the conceptualization of feasible approaches for addressing radiation heat transfer as a heat transfer mechanism coupled with the design analysis. The intent of Phase I is to identify a viable topology optimization strategy in three dimensions meeting Phase II objectives. Different topology optimization strategies have recently been surveyed [3]. Many of these methods benefit from the ability to compute analytical sensitivities as part of a gradient-based optimization strategy. In Phase II the methodology is extended and further demonstrated. Various load cases should be considered, including non-thermal mechanical and inertial load sources, provided they are thermally dominated. Radiation and convective cooling of substructure are additional heat transfer mechanisms of interest to include in the topology optimization process. Inclusion of composite materials should expand the range of design variables and potentially alter favorable topologies. 

PHASE I: Develop and demonstrate a practical topology optimization method for stress-based, thermoelastic, design of low mass fraction, metallic structures in three dimensions subjected to a prescribed, steady, heat flux. Demonstrate the feasibility for including radiation heat transfer in two dimensions. 

PHASE II: Extend the topology optimization methodology to include: radiation heat transfer; composite materials; and the definition and satisfaction of multiple load cases reflecting different notional use scenarios. Develop prototype designs of representative, lightweight structures demonstrating method functionality and practicality. Implement the methodology in scalable software; verify key analysis results with ABAQUS. 

PHASE III: Transition to support the preliminary design of next generation air platforms (e.g., next generation tactical air). Applicability to spacecraft (lightweight structures subjected to diurnal temperature variations or re-usable launch) and lattice design of pressure vessels (e.g., nuclear). 


1. Haney, M.A., Topology Optimization of Engine Exhaust-Washed Structures, Ph.D. Dissertation, Wright State University, 2006.

2. Deaton, J.D., Design of Thermal Structures Using Topology Optimization, Ph.D. Dissertation, Wright State University, 2014.

3. Deaton, J.D., and Grandhi, R., A Survey of Structural and Multidisciplinary Continuum Topology Optimization: Past 2000, SMO, 49(1), Jan. 2014, pp. 1-38.


KEYWORDS: Topology Optimization, Thermal Structure, Air Platform, Lightweight Structure, Complex Geometry, Design 

US Flag An Official Website of the United States Government