Enhancing buckling resistance in topology optimization under pressure loading using a mixed formulation

Abstract

Buckling resistance is a critical consideration in structural designs for ocean and aerospace engineering. This study proposes an algorithm for enhancing buckling resistance in topology optimization of structures subjected to pressure loading, using a mixed formulation approach. The proposed algorithm integrates incompressible fluid, elastic solid, and air phases into the mixed formulation by introducing a phase parameter field derived from design variables, enabling an effective distinction of the fluid phase from the other phases. Buckling analysis within the mixed formulation presents distinct challenges due to the design-dependent pressure loading and the integration of different phases in finite element analysis. This study establishes a comprehensive computational framework for buckling analysis within the mixed formulation. A stress relaxation function is employed to eliminate pseudo buckling modes, and the accuracy of the buckling analysis is verified through comparative studies. A linear material model is adopted to simplify the allocation of material properties across different phases. Since 0/1 designs cannot be directly obtained using a linear material model, the floating projection topology optimization method is used. This method applies implicit floating projection constraints to design variables to drive intermediate density elements toward binary states, thereby ensuring smooth 0/1 material distributions. The effectiveness of the proposed approach is validated through four numerical examples, demonstrating that the algorithm achieves compliance minimization while precisely satisfying buckling constraints with stable convergence.