Reanalysis Method For Second-order Sensitivity Of Static And Dynamic Responses

With the development of science and technology,structural design is mainly inspired by structural optimization.And structural modification is often the basis of structural optimization,since most of structural optimization is obtained by iterative structural modification.Such an iterative process needs a lot of repeated calculations.In order to improve the calculation efficiency in this repeated calculation processes,many researches were focus on the reanalysis algorithm and obtained development in recent decades,which had used to solve static,dynamic and sensitivity responses.However,as an indispensable second-order sensitivity in many optimization theories,systematic research has not been studied.This thesis is aimed at the lack of reanalysis system and structural optimization theory,and the second-order sensitivity reanalysis for static and dynamic response of structures has been studied.In this thesis,the development of reanalysis algorithm is overviewed in detail.Then the classic combined approximate reanalysis algorithm is reviewed,and the solution steps using the combined approximate reanalysis algorithm are summarized.This method is used to derive the formula for the second-order sensitivity reanalysis of the structural static response,and the programmatic procedure of formulations construction is provided.In addition,the numbers of operation calculations in the process of complete reanalysis and combined approximate reanalysis are calculated,which is used to evaluate the efficiency of this method.The analytical relationships of the degrees of freedom,the number of design variables,and the number of basis vectors are obtained.Therefore,the criterion of whether to choose the reanalysis method for solving is provided in this thesis.What’s more,the second-order sensitivity reanalysis for the structural dynamic response(eigenvalues,eigenvectors)using the combination approximation method is further studied.The detailed formulations of the second-order sensitivity analysis to solve the eigenproblem are derived,including complete and reanalysis method.And the programmatic solving steps and matters are described in detail.Since the generalized eigenproblem solving methods are different,the number of calculation operations of this method are not easy to be counted,so that efficiency is evaluated by tracking the time spent in the solution process.To compare the time spent in complete analysis and combined approximate reanalysis,this method shows the high efficiency.In addition,the normalized error are difined to evaluate the accuracy of the proposed algorithm in this thesis.The algorithm in this thesis are implemented by MATLAB codes.For both static and dynamic cases,three numerical examples are used respectively.The relationship between the number of basis vectors,the range of modification and the accuracy is studied respectively.In dynamic problem,the relationship between the order of mode and the accuracy is also studied.The results show that the second-order sensitivity of the static and dynamic responses calculated by the combined approximate reanalysis algorithm are robustness,which achieves the purpose of sacrificing a little precision and improving significant efficiency.