Topology optimization of continuum structures under buckling constraints

•Compliance minimization under volume and buckling constraints is considered.•A new approach is developed for dealing with pseudo eigenvalue modes.•The eigenvalue shift and pseudo mode identification techniques are employed.•Two-phase optimization algorithms are developed.•Numerical results are presented to illustrate the effectiveness of the algorithms. This paper presents a study on topology optimization of continuum structures under buckling constraints. New algorithms are developed for minimization of structural compliance considering constraints on volume and buckling load factors. The SIMP (Solid Isotropic Material with Penalization) material model is employed and nodal relative densities are used as topology design variables. A new approach based on the eigenvalue shift and pseudo mode identification is proposed for eliminating the effect of pseudo buckling modes. Two-phase optimization algorithms are also proposed for achieving better optimized designs. Numerical examples are presented to illustrate the effectiveness of the new methods.