Two-scale Homogenization Analysis Of Tube-sheet

The tube-sheet structure is a kind of typical equipment widely used in heatexchangers. There are lots of tube bundles in it, and the span of the size between thetube and the bundle is very large. The number of the bundles and the span of the sizewill make it difficult and low efficient to analysis the model. So, it is necessary to use anequivalent model to make it simple.In this paper, the basic theoretical formulas of two-scale homogenization methodare achieved, based on the displacement expansion of small parameter epsilon, byapplying the constitutive relation and the control equations of linear elasticity, thecomposite with periodicity unit cell. And the eigenfunction and homogenizationcoefficient are introduced in the process.To verify the two-scale homogenization method, unidirectional fiber reinforcedcomposites is adopted. Because of that the composite can turn into tube-sheet when itselastic modulus is zero. The influences of the choice of the unit cell and the fibervolume fraction are investigated. The results of numerical computing of the two-scalehomogenization method are in good agreement with the mixed method and theexperiments, and prove the method applicability and effectiveness.Then, the effective elastic constants of the tube-sheet are discussed by usingtwo-scale homogenization method in this paper, and get a good result. The influences ofthe hole pattern, the ratio between the elastic modulus of the tube-sheet and the pipe,hole rate and the thickness of tube-sheet on macro effective elastic constants of thetube-sheet are studied.Finally, the strength of a double tube-sheet in one vessel is analyzed in the last partof this paper. The model of the double tube-sheet is simplified and equivalent. Thestrain field and stress field of the model are obtained, and the maximum stress and itsposition are determined.