Static And Dynamic Sensitivity Analysis Method Of Structure Based On Epsilon Algorithm

With the development of structural optimization theory,structural optimization plays an increasingly important role in structural design.Structural modification is an inevitable problem to be considered in the process of structural optimization.With the increase of the number of modifications,a large number of repeated calculations are generated in the process of structural modification.Scholars have proposed reanalysis theory in order to improve computational efficiency.In recent years,reanalysis theory has been developed in many aspects such as structural sensitivity analysis and static or dynamic responses problems.Reanalysis methods based on reanalysis theory have been gradually applied in practice,which have received extensive attention from scholars.Reanalysis methods combined with multiple algorithms have emerged as the times require.In this paper,a structural static and dynamic sensitivity reanalysis method based on the Epsilon algorithm is proposed.?First of all,this paper introduces the development of the reanalysis method in detail,then introduces the origin of the Epsilon algorithm and illustrates its calculation format through numerical and vector examples.The algorithm is proposed based on the mature extrapolation method in the approximation theory.In theory,it has the characteristics of accelerating the rapid convergence of the operation result to the target value,and the algorithm is relatively easy to implement on the computer.Combined with the improved Neumann series,this paper deduces the analytical expression of the first-order static displacement sensitivity reanalysis,construct the basis vector group,and further derives the static second-order displacement sensitivity reanalysis analytical expression.Then,the convergent solution vector is obtained by applying the Epsilon algorithm.At the same time,the calculation operations of the complete reanalysis and the reanalysis method in this paper are sorted out and calculated,and the efficiency of the method is evaluated.On this basis,this paper studies the dynamic problems,uses the Neumann series to construct the basis vector,deduces the expression for the reanalysis of the first-order mode shape sensitivity of the dynamic problem,and uses the Epsilon algorithm again to calculate the convergent solution.At the same time,we introduce the cumulative calculation method when the Newman series basis vector fails in the Epsilon algorithm.In engineering examples,the Epsilon algorithm also has high computational accuracy.This paper uses Matlab to implement the algorithm.For both static and dynamic problems,three numerical examples are used for each.The relationship between the number of iterative steps of the Epsilon algorithm,the size of the modification and the accuracy is explored.The results show that the results of the sensitivity reanalysis method based on the Epsilon algorithm to calculate the static and dynamic response of the structure are reliable,and the method achieves a balance between efficiency and accuracy?...