The Modified Semi-analytical Sensitivity Analysis Method And Its Implementation On SIPESC

Sensitivity analysis methods are the essential part of gradient based structural optimization problems.Sensitivity analysis techniques with high accuracy and efficiency are positively contribute to the implementation in a convenient and efficient way.Semi-analytical sensitivity analysis methods,compared to global finite difference method,possess higher efficiency and compared to analytical method,is more universal and easy to implement by programming.So the method is prevalently applied to variable structural optimization problems.However,traditional semi-analytical methods based on element level need matrices both from the initial and perturbation structures,which post a negative influence on computational efficiency.In addition,when the number of significant figures of element stiffness matrices are limited,the traditional method will suffer from errors.In order to solve the above problems.This paper presents a modified semi-analytical sensitivity analysis method under the guidance of Professor Gengdong Cheng.Firstly,a modified semi-analytical sensitivity analysis technique based on global structural equations is proposed for static displacement and stress problems,and its program implementations are provided.Consequently,the modified method is extended to other analysis tasks including natural frequency,linear buckling and transient analysis.Meanwhile,the modified method is verified by typical finite element models with beam and shell elements.The results highlight the applicability of the modified method to various analysis types mentioned above,and the accuracy as well as the efficiency is enhanced by the modified method.Especially,the method exhibits excellent stable features with respect to perturbation step length of design variables,which can make sure that meshes of initial and perturbation structures are consistent.So the method will be more suitable for shape optimization of complex engineering structures.Besides,when semi-analytical sensitivity analysis method is applied to beam-like structures with shape parameters as design variables,the method will suffer from errors.The causes of the errors are discussed and a modified error correction technique is presented where the error correction term can be separated from main flows of sensitivity analysis and added directly to the results of sensitivity analysis.So the existing sensitivity analysis programs can be made full use of.In addition,different from the form of matrices in traditional error correction methods,the form of error correction terms is vectors/numbers,which will exhibit higher efficiency when applied to unstructured mesh based shape optimization problems.Consequently,the error correction terms of both beam elements and shell elements are derived.Then,the specific deducing process of error correction terms concerning beam and shell elements is described.Next,the modified method is firstly verified by a typical finite element model built by beam and shell elements respectively.The results highlight the applicability of the modified method to various analysis types mentioned above,and the accuracy is not influenced by the number of elements and perturbation step length.Besides,the results illustrate that compared to shell elements,beam elements suffer from more serious errors.Besides,a larger scale model is established to show advantages of the error correction method which can maintain its accuracy when the element number is relative large.After that,efficiency test is conducted to demonstrated the modified error correction method possess higher efficiency.In addition,the application of modified semi-analytical sensitivity analysis method to stiffened shells is discussed.Firstly,influences posted by the eccentricity of stiffeners on finite element analysis as well as sensitivity analysis are illustrated and the importance of properly taking the eccentricities into consideration is highlighted.Then,the advantages of the application of modified method to stiffened shells is demonstrated.A simple stiffened shell model and an airfoil model are established to verify that under this situation semi-analytical method won't suffer from errors related to rotation rigid motion and semi-analytical method is more accurate with regard to this kind of problems compared to global finite differences.The research work is based on independently developed finite element software SiPESC of Dalian University of Technology.Thus,programming flows based on python scripts of SiPESC related to the finite element analysis and semi-analytical are illustrated.Then,a general sensitivity analysis algorithm framework is presented.The framework can contain various sensitivity analysis apart from semi-analytical methods which can make a connection between the finite element analysis module and the optimization algorithm module on SiPESC.To achieve a complete optimization flow on SiPESC will be facilitated.