The axial stiffness of the connection joints in a transmission tower will affect the stability bearing capacity of the tower. The axial stiffness of different forms of connection joints has different effects on the stability bearing capacities of triangular and quadrilateral lattice towers. This paper takes triangular and quadrilateral lattice towers as the comparative research objects and considers the influence of the stiffness of the single-limb, single-plate joint (SLSPJ) and double-limb, double-plate joint (DLDPJ) of the tower. Under vertical load, the vertical stability bearing capacities of triangular and quadrilateral transmission towers are studied from hte three aspects of theoretical analysis, numerical simulation and test result analysis. The influence rules of the SLSPJ and DLDPJ on the vertical stability bearing capacities of triangular and quadrilateral transmission towers are clarified. Through the energy method, considering the influence of the axial stiffness of connection joints, the calculation expressions of the vertical stability bearing capacities of triangular and quadrilateral lattice towers are derived. Through quantitative analysis, it is found that the axial stiffness of the connection joints has a more significant influence on the vertical stability bearing capacities of triangular lattice towers. The finite element models of the triangular and quadrilateral lattice towers including the SLSPJ and DLDPJ are further established. Through nonlinear finite element analysis, it is found that the DLDPJ can improve the vertical stability bearing capacity of the triangular lattice tower by 22.7% and the quadrilateral lattice tower by 14.9%. Through theoretical calculation, the expressions of the vertical stability bearing capacities of the triangular and quadrilateral lattice towers including the SLSPJ and DLDPJ are obtained. Combined with the test results of the SLSPJ and DLDPJ, it is found that the DLDPJ can improve the vertical stability bearing capacity of the triangular lattice tower by 23.4% and the quadrilateral lattice tower by 15.6%. The research results show that the DLDPJ can improve the vertical stability bearing capacities of triangular and quadrilateral lattice towers. The improvement effect of the vertical stability bearing capacity of the triangular lattice tower is 1.50∼1.52 times that of the quadrilateral lattice tower. The research results can provide a reference for the engineering popularization, application, and design of the DLDPJ in transmission towers.

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.

An orthogonal composite material $\mathsf{\Omega }$ with fibers consists of a matrix and orthothombic distribution fibers. In addition to the matrix properties, the fiber properties and the fiber volume fraction, the effective (macroscopic) elastic stress–strain constitutive relation of $\mathsf{\Omega }$ is related to the fiber direction distribution. Until now, there have been few papers that give an explicit formula of the macroscopic elastic stress–strain constitutive relation of $\mathsf{\Omega }$ with the effect of the fiber direction distribution. Taking the expanded coefficients of the Fourier series as the fiber direction distribution coefficients, we give a formula of the fiber direction distribution parallel to a plane computed through the fiber directions. By the self-consistent estimates, we derive an explicit formula of the macroscopic elastic stress–strain constitutive relation of $\mathsf{\Omega }$ with the fiber direction distribution coefficients. Since all tensors are represented in Kelvin notation, the macroscopic elastic stress–strain constitutive relation of $\mathsf{\Omega }$ can be derived and computed only by matrix manipulations. To check the explicit formula, we use the FEM computation to obtain the macroscopic elastic stress–strain relation of $\mathsf{\Omega }$ for three examples. The computational results of the explicit formula for the three examples are consistent with those of the FEM simulations.