Level Set Topology Optimization of Load Carrying Heat Dissipation Devices

In this paper, we introduce a level set topology optimization method subjected to coupled mechanical and thermal loads. Examples considering compliance minimization and stress minimization under temperature and volume constraints, and mass minimization under stress and temperature constraints, are presented. The p-norm of the stress field and temperature field is used to approximate the maximum stress and temperature, respectively. The developed method is applied in the design of an L-bracket and a battery package. The results show that designs obtained by ignoring the thermal or structural constraints can result in high values of temperature or stress, respectively. I. Nomenclature B, Bs = gradients of shape function matrices C = compliance d = displacement fm = mechanical force ft = thermal force E = elasticity modulus H = thermal force generating matrix Ks = structural stiffness matrix Kt = thermal stiffness matrix N , Ns = shape functions q = heat generation rate s = sensitivity t = temperature x = volume fraction α = coefficient of thermal expansion φ = level set function Ω = domain κ = conductivity coefficient = strain σ = stress (·)i = of an element i (·)e = at the elemental level ∗Postdoctoral Research Associate, Department of Structural Engineering, sakambampati@ucsd.edu †Research Engineer, AIAA Member, justin.s.gray@nasa.gov ‡Jacobs Scholars Chair Professor, Department of Structural Engineering, Associate Fellow, AIAA, alicia@ucsd.edu I