ABSTRACT
In this paper, the elastic constitutive relation of polycrystals contains the effect of the mesostucture coefficients. We consider a general case and derive the average elastic constitutive relation pertaining to polycrystals of cubic crystals with any symmetry of crystalline orientation in their statistical distribution. Following Budiansky and Wu, we used self-consistent estimates of eigenstrain to obtain the effective elastic constitutive relation of polycrystals in an explicit form. For the Voigt assumption and the Reuss assumption, the effective elastic constitutive relation of polycrystals on cubic crystals contains the the mesostructure coefficients up to linear terms. In general, the linear term expression works well for materials such as aluminum, the single crystal of which has weak anisotropy. However the same expression (which allows the anisotropic part of the effective elastic constitutive relation to depend only linearly on the mesostructure coefficients) does not suffice for materials such as copper, in which the single crystal is strongly anisotropic. Per the Taylor theorem, we expand the expression based on the self-consistent estimates with respect to the mesostructure coefficients up to quadratic terms for anisotropic polycrystals of cubic crystals. While our numerical data are very close to those of Morris, our expression is much simpler.
ABSTRACT
The connection between the leg members and diagonal members of the urban transmission line tower is mostly in the form of single-limb connection. This paper puts forward a new connection form of pipe double-limb double-plate connection joint, which is based on the model of key joints in an urban narrow base tower structure. The traditional pipe single-limb single-plate and new pipe double-limb double-plate joint are analyzed and studied from three aspects of theory, numerical simulation and experimental study. Through finite element analysis, it is obtained that the section stress of angle steel under eccentric load is 2.05 times of that under axial load, which is basically consistent with the 2.5 times of the theoretical calculation. This shows that the stress of the angle steel in the pipe double-limb double-plate joint is greatly reduced as the axial stress component, which can ensure the safety of the angle steel. Based on the theoretical analysis of the tensile force of two kinds of joints, through the test research and corresponding numerical simulation of pipe single-limb single-plate and pipe double-limb double-plate joints, under the same load, compared with pipe single-limb single-plate joints, the pipe double-limb double-plate joints designed in this paper can greatly reduce the stress of connection plates and members, and compared with the existing joint forms, the bending stress of joint plates can be reduced by about four times, which greatly improves the bearing capacity of the joint. The research on the pipe double-limb double-plate connection joint will provide the basis for the design of new connection joints of narrow base towers in urban areas.
