| The pure bending problem of the composite combined tube is a generalized plane problem,which needs to be solved by the flexibility method with double stress functions.In this paper,finite element numerical simulation of the stress characteristics of composite tubes with 0° or 9° entangling layers and isotropic layers is carried out.It is pointed out that the internal stress and the external stress are present when there are other winding layers adjacent to each other.So even if the special winding layer and isotropic layer also need to use double stress function to solve.Then,Compliance method including two stress functions is analyzed and discussed in detail.(1)Lekhnitskii's single stress function method can only solve the problem of special entanglement and its combination.(2)The contact-parameter method between the traditional double stress function is based on the internal stress,and the external stress is obtained through the contact parameters.It is suitable for solving the other winding layers.However,since some contact parameters are singular in the special layers,it is difficult to solve the problem of the special winding.(3)The unified contact parameter method does not contain any singular contact parameter term,which can solve any situation where the multi-layer contains both the special winding layer and the ordinary winding layer.However,the unified-parameter is artificially constructed and lacks a rigorous theoretical basis.In addition,it is necessary to determine the parameter limit according to the derivative of the material parameter.Since isotropic material layers is no winding angle,it is difficult to solve the limits of its unified parameters.On this basis,this paper directly investigates the compatibility equations of the special entanglement layer and the isotropic material layer.It is found that the two compatible equations are independent of each other and can be solved separately.So it is no need to introduce the contact parameters between the two stress functions.The double stress functions are independent of each other,in other words,the in-plane stress and the out-of-plane stress calculated are independent or separate from each other.In this paper,the backward-contact-parameter method is proposed for the other tangent layers,and the forward and backward contact parameter method is combined without changing the content of the double stress function.The result of anastomosis provides a reliable theoretical basis for the unified parameter method.For the case of special entanglement,it is only necessary to use the results of the independent double stress function method without calculating the limit of the unified contact parameter,thus avoiding the difficulty of analyzing the limit of the unified contact parameter.In particular,it avoids the difficulty that the isotropic material can not analyze the limits of the contact parameter because it is no winding angle.According to the theory of this paper,eight simple composite combined tube including[Steel/90],[Steel/45],[Steel/25],[Steel/45/-45],[Steel/25/-25],[Steel/90/45/25],[Steel/45/90/25]and[Steel/25/45/90]are calculated.At the same time,compared with the results of finite element numerical simulation,the results are in good agreement.On the basis of this,the equivalent bending stiffness of the composite composite pipe with the change of the winding angle is compared and analyzed,which provides useful help for the design.Since the lack of effective and convenient man-machine interface,it is difficult for engineers to use the unified parameter method directly.Thus,the practical value of this method can not be used.In order to provide fast and convenient analysis tools,Man-machine interface(GUI)is created on the basis of the method for designers.It will help designers calculate and analyses different design schemes by Man-machine interface(GUI)which has very important practical engineering value. |
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