Buckling-based topology optimization for underwater pressure hull with modified parameterized level-set method

Buckling is a common phenomenon in compression structures, and its occurrence will cause significant damage, especially in the application of underwater pressure hulls. In this paper, a new mathematical model based on an improved parameterized level-set method is developed to solve fundamental buckling load factor maximization and buckling-constraint topology optimization problems, and further the continuous descriptions of normal velocities are derived using the theory of the shape derivative and bifurcation analysis. In this model, a regularization term is introduced to ensure numerical stability, and an augmented Lagrange multiplier is presented to realize stable transitions of both optimization problems during the convergence process. Besides, Kreisslmeier–Steinhauser function is employed to aggregate multiple buckling load factors to a differentiable one. In this case, an easily implemented method is proposed to discretize normal velocities to every nodal point in the design area. By means of the developed method, the clear contours of the optimal structures are obtained, and the pseudo-buckling modes during optimization process is alleviated. To further prove the effectiveness, three-dimensional cases of underwater cylindrical pressure hull are extended, and corresponding buckling-based problems are solved, in which the optimal results with clearer contour and more details are approached. The current method can be used to deal with the similar buckling-based problems of underwater pressure hulls and the final structures are more easily manufactured in practical application.