Otimização de topologia sob restrição de tensão para aplicação em subestruturas de submarino

Abstract

Due to the progress in the development of the first Brazilian Conventionally Armed Nuclear Submarine, the demand for knowledge in specific and increasingly critical areas has grown, particularly in the design of submarine structures. In this context, topology optimization under stress constraints, with applications in substructures, stands out due to the importance and challenging nature of the associated design problems. The purpose of this work was to develop a computational code for finite element analysis and topology optimization aimed at structural mass reduction without compromising strength, evaluated through maximum stress limits. The developed methodology is based on minimizing a mass objective function while incorporating von Mises stress constraints across all finite elements representing the structure, using the numerical method of the Augmented Lagrangian. These analyses were performed using optimization routines from MATLAB's fmincon package. Relaxation strategies for stress constraints were applied to enable solutions in degenerated regions of the design domain. The results demonstrated a significant reduction in structural mass while adhering to the imposed stress limits. Furthermore, the results exhibited sensitivity to the applied load magnitudes and material stress thresholds. Comparisons between optimized topologies considering stress constraints and those aimed at average flexibility in classical problems further validated the effectiveness of the developed methodology in meeting the specified stress limits. In conclusion, the integration of finite element analysis and topology optimization shows significant potential for the development of lighter and more efficient structures, contributing to the feasibility and competitiveness of the submarine project on the global stage.