Abstract
Based upon the theorems of structural variations this paper derives a set of expressions for calculating partial derivatives of internal forces, stresses and joint displacements with respect to bar areas for truss structures. Compared with the known formulas for finding the gradients of structural behaviours the calculation effort with the proposed expressions in this paper is usually smaller because the additional virtual loadings needed are relatively fewer. It is of practical significance to various optimization methods in which the calculation of gradients of behaviours is widely used. Moreover, applying the derived formulas to the fully stressed design (FSD), we obtain an improved iterative method for FSD. The numerical examples show that the new method considerably reduces the reanalysis number required to converge to an FSD in comparison with the simple stress ratio method.
Similar content being viewed by others
References
Fox, R. L., Constraint surface normals for structural synthesis techniques,AIAA J. 3 (1965), 1517–1518.
Sander, G., and C. Fleury, A mixed method in structural optimization,Int. J. Num. Mech. Engng.,13, 2 (1978), 385–404.
Majid, K. I. and D. W. C. Elliott, Forces and deflections in changing structures,The Structural Engineer,31, 3 (1973), 93–101.
Fleury, C., A unified approach to structural weight minimization,Computer Methods in Applied Mechanics and Engineering,20 (1979), 17–38.
Razani, R., Behaviour of fully stressed design of structures and its relationship to minimum-weight design,AIAA J.,3, 12, 2262–2268.
Gallagher, R. H. and O. C. Zienkiewicz, eds.,Optimum Structural Design, Theory and Applications, John Wiley & Sons (1973), 33–49.
Tang, X., A new method of fully stressed design,Optimization Methods in Structural Design, edited by H. Eschenauer and N. Olhoff, Bibliographisches Institut (1982), 415–423.
Author information
Authors and Affiliations
Additional information
Communicated by Yeh Kai-yuan
Rights and permissions
About this article
Cite this article
Tang, X., Xiu-juan, Z. Sensitivity analysis of truss structures and its application to the fully stressed design. Appl Math Mech 9, 489–496 (1988). https://doi.org/10.1007/BF02465687
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02465687