Stiffening of Thermally Restrained Structures via Thermoelastic Topology Optimization

Abstract

In the past, the majority of work in the thermal structures field has focused on design problems whereby thermal expansion can be accommodated as a means to reduce or eliminate thermal stresses. In the modern day, several new applications, including engine exhaust-washed structures for embedded engine aircraft, are posing new design scenarios where this prescription is not possible. Thus it becomes necessary to utilize new design techniques to solve the problem of stiffening and stress reduction in thermal structures with restrained expansion. In this work, a design scenario is presented to demonstrate the challenges associated with design of thin shell structures in a thermal environment and the breakdown of common design methodologies. These challenges include a fundamental nonintuitiveness in the design space and the design dependency that occurs with thermal loading. Three different topology optimization formulations are presented and applied to solve this problem. The effectiveness of these methods are benchmarked against one another and general recommendations are made regarding effective design solutions for restrained thermal structures. NomenclatureA = cross section area c = compliance e = element index for topology optimization E = elastic modulus E e = elemental elastic modulus E o = base elastic modulus F = reaction force F o = reaction force at reference thickness F L = limit on reaction force in optimization F me = mechanical load vector in FEA F th = thermal load vector in FEA k = stiffness ratio parameter K s = spring stiffness K = stiffness matrix in FEA L = length M = reaction moment M o = reaction moment at reference thickness N = total number of topology design elements p = penalization factor ρ e = pseudo-density design variable ρ min = minimum allowable pseudo-density t = thickness t o = nominal baseline thickness ΔT = elevated temperature change U = displacement vector in FEA v e = element volume V f = allowable volume fraction for optimization w = width

Stress constrained thermo-elastic topology optimization with varying temperature fields via augmented topological sensitivity based level-set

“…Although the thermal load is small compared to the structural load, as noted in the fourth column of Table 3, this has a significant effect on the final topology. Next we consider engine exhaust-washed structure, used in a low observable supersonic aircraft; this was first studied by J. Deaton [17]. Due to low radar observability requirement, engine and exhaust system are buried inside the aircraft.…”

“…In [16], structural strain energy was minimized after considering thermo-mechanical coupling where the sensitivity was calculated via an adjoint approach and the optimization was solved using the method of moving asymptotes. Deaton and Grandhi [17] presented a design scenario for restrained thin shell structure in a homogeneous thermal environment where the traditional design approach by accommodating thermal expansion to eliminate thermal stress was impossible. SIMP was set up and it was shown a typical compliance minimization in the presence of thermal loading did not guarantee favorable designs.…”