WIT Press

Optimization Of Linearly Distributed Pre-stress In Laminated Cylinders


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P. Procházka


Recently the author published several papers on optimal pre-stress of laminated composites with lamina-wise uniform distribution of pre-stresses. The result of such an approach leads to the uniform distribution of stresses through the thickness of the structure under consideration (laminar hollow cylinders, plates, etc.). It appears from practical application that in the case of hollow laminar cylinders the distribution of pre-stresses is rather linear and it is more appropriate to consider such a type of pre-stressing. In order to express the pre-stressing, eigenparameters are used. They were recently applied to different types of structures and they have been introduced as a generalization of Transformation Field Analysis, established by G. J. Dvorak from RPI, Troy, USA. The generalization was carried out by Dvorak and the author of this paper. 1 Introduction Recently, the author with coauthors have published several papers, e.g. [2], [4], on optimization of stresses controlled by an appropriate choice of eigenparameters in certain sense (plain optimization, the optimization of reinforcing pre-stresses, the lay-ups and pre-stressing). These optimizations were mostly connected with minimization of the variance of stresses acting in some directions, cf. a simple example in Appendix, when the tools of the Transformation field analysis, [1], were employed. Extended Hashin-Shtrikman variational principles were applied and enabled one to consider anisotropic and non-homogeneous bodies, [3]. The method from the numerical point of view leads to a linear system of equations for unconstrained problem and when restrictions are imposed on the stresses a nonlinear problem is to be solved. The solution of such systems is