The Refined Analysis of Axisymmetric Transversely Isotropic Cylinder under Radial Direction Surface Loading

Abstract

In this paper, the axisymmetric deformation of one cylinder with transversely isotropic is researched. According to the general solution of deformation body with transversely isotropic and the Lur’e method, the exact deformation field and exact stress field are represented by unknown functions with single independent variables. Based on boundary conditions of radial direction surface loading, the unknown functions can be ascertained. By dropping terms of high order, the approximate solution is derived, and the department field and the stress field for a circular cylinder under radial direction surface loading can be obtained. After simplifying, the states with isotropic can be obtained.

A refined theory of axisymmetric thermoporoelastic circular cylinder

“…The equation (40) is consistent with the results gained by Zhao and Wu (2012) which shows that the analysis in the refined theory of this paper is credible again. Moreover, the refined theory of the thermoporoelastic circular cylinder can be degenerated into other distinguished theories of elasticity, which can also be applied to the wider area based upon.…”

“…Cheng (1979) presented a method for the solution of 3D elasticity equations, and established a refined theory of plates by using the Lur'e method (Lur'e, 1964). Thereafter, the refined theory is extended to the transversely isotropic plates (Wang, 1990(Wang, , 1991, beam (Gao et al, 2007;Gao and Shang, 2010;Lu et al, 2013) and circular cylinder (Zhao et al, 2011;Zhao and Wu, 2012). The true importance of using the refined theory is in the fact that the high-dimensional theory can be transformed into low-dimensional theory to study by making use of elastic general solution and symbolic operation, and the problem can be simplified further.…”

The exact theory of axisymmetric electro-magneto-thermo-elastic circular cylinder

“…Equation ( 36) is the same with the displacement field and the stress state of axisymmetric deformation of a transversely isotropic circular cylinder under radial direction surface loading presented in Zhao and Wu (2012).…”

“…Cheng (1979) presented a method for the solution of 3D elasticity equations. With this method, refined theories of elastic circular cylinders were explicitly established (Zhao et al, 2011, Zhao andWu, 2012). The significance of the refined theory is that it opens a systematic way of developing the exact and approximate lower dimensional theory from a higher dimensional theory with the aid of the general solution of elasticity and symbolic computation.…”

The Refined Equations of Special Orthotropic Piezoelectric Plate-I: Anti-Symmetrical Transverse Surface Loadings

“…Base on the refined theory of an isotropic plate, an axisymmetric circular cylinder [3], plane problems for one-dimensional quasicrystalline bodies [4] and thick plate structures in onedimensional quasicrystals [5] was studied. In 2012, Zhao and Zhao [6] studied the refined theory of an axisymmetric circular cylinder with transversely isotropic under homogeneous boundary conditions.…”