  The focus of this paper is on topology optimization of continuum structures
subject to thermally induced buckling. Popular strategies for solving such
problems include Solid Isotropic Material with Penalization (SIMP) and Rational
Approximation of Material Properties (RAMP). Both methods rely on material
parameterization, and can sometimes exhibit pseudo buckling modes in regions
with low pseudo-densities. Here we consider a level-set approach that relies on
the concept of topological sensitivity. Topological sensitivity analysis for
thermo-elastic buckling is carried out via direct and adjoint formulations.
Then, an augmented Lagrangian formulation is presented that exploits these
sensitivities to solve a buckling constrained problem. Numerical experiments in
3D illustrate the robustness and efficiency of the proposed method.
