Reliability-based topology optimization considering corrosion

Abstract

Mechanical engineers always expect to design a structure which could work properly in its whole lifetime. But there exist many random factors, such as dimension, material property and applied forces. Hence structures based on determinate design could fail with high probability. Reliability-based Topology Optimization (RBTO) is a computer-automated design method which combines reliability analysis and topology optimization method. Machines and equipments always have high reliabilities when they are new. But the structure working in corrosive environment will be gradually corroded, then the corroded structure may fail long before its expected lifetime in usual environment. If corrosive rate is also considered as a random factor in RBTO, the reliability constraint should be satisfied not at the beginning but at the end of the structure's expected lifetime. Unfortunately, most research about RBTO concern about the reliability of structure when it is new. In this paper, corrosion model fitting for RBTO is built. Since the structure's surfaces are corroded through the whole lifetime, new corrosion surfaces should be continuously updated. An algorithm is presented to find the finite elements on the surface of structure. Corrosion rate describes the corrosion depth in unit time, and it cannot be directly used to control the corrosion in a finite element. Hence corrosion coefficient α(t) is introduced to describe the fade of material volume density in finite element. The final corroded structure can be generated after simulating the corrosion phenomenon. Its reliability index is checked to see whether the corroded structure is safe enough during its whole lifetime. If it is not safe, then a stronger structure will be generated. If the reliability of the corroded structure is higher than the requirement, our method will generate a lighter optimal structure, which is our initial design goal. In this paper, first order reliability method (FORM) is used to find the Most Probable Point (MPP) on the curve of limited state function. Sequential Optimization and Reliability Assessment (SORA) is used to solve the RBTO problem. Three different cases of cantilever beam RBTO design considering different corrosion rate are presented, and the reliability analysis results based on Monte Carlo Method successfully prove the consistence between the reliability of optimum structure and the preset minimum reliability requirement.