A Corrosion Correction for Minimal Weight Design of Truss Structures under Compliance Constraint

Corrosion-induced stiffness and strength reduction are often neglected in truss optimization. In the case of the uniform corrosion of truss members, the stiffness reduction is proportional to the corroded area, and it has a significant effect for the typically required lifespan of steel truss structures. The corroded area can be predicted via a simplified model that takes into account the face orientation of surfaces and the exposure time. The corrosion correction can be incorporated into minimal weight design under the global compliance constraint. The compliance constraint is formulated as a linear matrix inequality for a single load or multiple loads with an ellipsoidal uncertainty (a worst-case scenario problem). Herein, one continuous design variable is used to describe the area for rectangular cross-sections. The formulations with fixed width and with fixed aspect ratio yield convex and difference-of-convex programming problems, respectively. These problems are solved using interior-point methods with the CVX package for disciplined convex programming called from MATLAB. The procedure scales well up to 1900 degrees of freedom and 3660 members on a laptop (producing a design within 12 minutes). The relative correction of the total mass of the structure due to corrosion is documented for illustrative examples. It can be larger than the loss area of the effective cross-section under a specific condition.