Reanalysis of Elasto-Plastic Structural Problems using Sensitivities

Abstract

SummaryThis paper describes a procedure to predict the elasto-plastic responses of structures within the framework of the finite element method when design variables are changed. Reanalysis technique was used applying the Taylor Series ExpansionMethod with the results of sensitivity analysis.In the incremental finite element analysis, the load magnification factor is usually introduced to control the load increments so that yielding of individual elements takes place exactly. In sensitivity analysis, sensitivity of the load magnification factor with respect to the design variable was newly derived. In this connection, the sensitivity of elasto-plastic responses with respect to the yield stress of the material was also derived.Some sample calculations were performed on plane truss, plane frame and plane stress problems. The results proved the rationality of the proposed method. The reanalysis solution was much improved by considering the sensitivity of the load magnification factor although the computational time for sensitivity analysis increases. The limit of changes in design variables was also discussed to get rational reanalysis solutions. IntroductionIn the optimal design of structures, it is essential to know the change in objective and constraint functions with respect to design variables. For this purpose, sensitivity analysis and reanalysis are generally performed, which occupy a major part in optimization procedures.A number of research works on sensitivity analysis and reanalysis have been performed regarding the linear elastic problems. Contrary to this, those for the nonlinear problems are very few."' Regarding elasto-plastic plane stress problems, the authors developed the fundamental procedure of sensitivity analysis within the framework of the finite element method' In that paper, the coordinates of nodal points and the thickness were taken as the design variables, and the first and second-order sensitivities of stress components and nodal displacements were derived. A series of reanalyses was also performed applying the Taylor Series Expansion Method. The first and second-order sensitivities were evaluated with good accuracy. However, there existed large differences between the results of reanalysis and the exact solutions especially when the design variables were largely changed.

Optimal Elastoplastic Structural Design Using Sensitivities by Incremental Procedure

“…2( a ) analyzed in Ref. 9). The load-load point displacement relationship for this truss is indicated by a broken line in Figs.…”

“…9) that in elastoplastic reanalysis using sensitivities, the predicted yielding order of elements sometimes differs from that of actual behaviour when the change in design variable is large. (18), (19) and (20) are not accurate, especially for a large change in design variable.…”

“…Research on nonlinear sensitivity analysis is in the initial stage.6,7) The authors have developed a method for the elastoplastic sensitivity analysis and reanalysis based on the incremental finite element method applying the Plastic Flow Theory. 8,9) Optimal design of nonlinear structural systems is also in the initial stage, and only a few papers have been presented on this subject. [10][11][12][13][14] In the present paper, a new method for the optimal elastoplastic structural design is presented using the elastoplastic sensitivities formulated in Ref.…”

“…[10][11][12][13][14] In the present paper, a new method for the optimal elastoplastic structural design is presented using the elastoplastic sensitivities formulated in Ref. 9). According to Ref.…”