Plate-Shell Structural Optimization Based On Response Surface Methodology And Secondly Development On Strand7 Software

Plate and shell structures are broad using in engineering. Sectional optimization and program development of them are very necessary. Sensitivity analysis is often needed in conventional structural optimization. And it is well known that sensitivity analysis is difficult for complex problems. Even for some problems, the sensitivity can not be solved. The present paper introduces Response Surface Methodology (RSM), and applies it to construct the explicit expression of displacement and stress constraints, which avoids the difficulties of solving sensitivity. The way to do structural optimization without sensitivity analysis is advanced. At the same time, secondly development on Strand7 software has also been done. RSM is expounded in details, and improved some aspects of it for the features of structural optimization. In order to reduce the re-analysis times of structures, a new method of experiment design, the central extended design, has been developed, which is very suitable for structural optimization. When solving the response surface (RS), a different approach is adopted, which makes the center-point's response value equals to analysis value exactly. The results of numerical examples demonstrate that this method is very efficient. Evaluation on displacement RS has been done by examples. The displacement RS is compared with the explicit expression that constructed by structure mechanics, material mechanics (includes Mohr integration). It shows that the displacement RS constructed can approach the real displacement response. In this paper, RSM is used to construct the explicit expression of displacement and stress constraints instead of sensitivity analysis in conventional optimization. An optimization model take weight as objective function, subjects to the constraints of displacement and stress is set. Its design variables are the thickness of plate and shell structures. The optimization model is solved by quadratic programming method. Different modes are betaken to deal with the displacement and stress constraints. For two constraints above, the linear mode without and with constant terms are adopted respectively. For different loading cases, the forms of design variables are dealt differently. Numerical examples show that the dealing is very reasonable and effective. The performance of RS and effect of some optimization parameters on optimal results are studied by several numerical examples, and some valuable conclusions are obtained, which are useful for further study. At last, several classic numerical examples and engineering problems are optimized by the program. The results show that the present program is correct, steady, practicable and convenient.