Stress-Constrained Size Optimization of an Underwater Walking Robot Frame Using Finite Element Analysis and Sequential Quadratic Programming

Structural design under severe handling loads can be formulated as a constrained optimization problem in which structural mass is minimized while prescribed safety requirements are satisfied. In this study, a mathematical size-optimization model was developed for the frame of an underwater walking robot subjected to extreme launch and recovery loads. The frame geometry was parameterized using cross-sectional lengths and regional thicknesses as design variables. The optimization problem was formulated by minimizing the frame mass subject to an inequality constraint on the maximum equivalent stress and prescribed bounds on the design variables. Finite element analysis (FEA) was employed to evaluate the structural response associated with each design, and sequential quadratic programming (SQP) was used to iteratively solve the resulting nonlinear constrained optimization problem. The computational behavior of optimization was examined through the evolution of the design variables, objective function, and stress constraint. The optimization converged to a feasible design that satisfied the prescribed stress requirement while reducing the structural mass. The design evolution also showed that the geometric variables changed differently according to their locations in the frame, resulting in a redistribution of the structural response during the optimization process. These results demonstrate that the coupled FEA–SQP framework provides a systematic numerical approach for solving stress-constrained structural size-optimization problems and illustrates the application of mathematical optimization to the design of engineering structures subjected to severe loading conditions.