Calculation And Analysis On Curved Beam With Different Moduli In Tension And Compression

Several studies show that many materials such as graphite, organic glass, alloyedmetals, ceramics and some composite etc. show the characteristics of different moduli intension and compression, which is the characteristics of different elastic propertiesemerged when these materials is under the conditions of tension and compression. Nowthe calculation methods used in practical projects are always based on the classicalsingle modulus theory, while for those materials whose tension modulus are muchdifferent from compression modulus, the results obtained have large differencecompared with the ones from the classical single modulus theory. So it’s necessary touse the theory of different moduli in tension and compression for further study andprovide the theoretical foundation for structural accurate analysis. As most of thescholars mainly focus on the problems of straight beam now, the work aimed at curvedbeam with different moduli in tension and compression in this paper has certain actualmeaning.This paper has made further calculation and analysis of curved beam with differentmoduli in tension and compression, which is based on the foundation of simplifiedmechanical model, then obtained the one-dimensional solution (namely the solution ofmechanics of materials) and two-dimensional solution (namely the solution of elasticmechanics). When inferring the one-dimensional solution, for different section shapes(including rectangle, T,工and box shape), the normal bending stress of curved beamwith different moduli in tension and compression is obtained by transforming theproblem of different moduli into the problem of single modulus with the method ofequivalent section, then using the method of classical single modulus to get it.Meanwhile, this paper also discusses the application of the method of equivalent sectionin the curved beam with metabolic curvature in-plate and other cases with differentboundary conditions and external forces. During the inferring of the two-dimensionalsolution of cured beam, the stress component expressions with unknown constants intension area and compression area are obtained based on the method of stress function.Then the elastic solutions of stress and displacement for the curved beam with differentmoduli in tension and compression are also obtained through integrating the boundaryconditions and the continuous stress condition at neutral layer. This paper then madenumerical analysis through FEM (finite element method) at last and made comparison among the one-dimensional solution, two-dimensional solution and numerical solution.The results show that the one-dimensional solution is close to the two-dimensionalsolution and it will change the mechanical response with the importing of the differentmoduli in tension and compression.This paper creatively made full use of the method of equivalent section to solve thecurved beam problems in many cases, which improved the efficiency and simplified theinferring process. And it creatively used the continuous stress condition at neutral layerto get the two-dimensional solution of the curved beam with different moduli in tensionand compression. The conclusion in this paper could provide necessary theoreticalsupport for analyzing and designing the structures with different moduli in tension andcompression. For the present researches are lack of prototype testing, we still need topromote a series of testing work in the future.