On partial contact of a thin-walled circular cylinder and a rigid half-space

Abstract

We study the influence of the eccentricity of the load and the ratio R/t on the stress state of the cylinder using the theory of thin shells in bending. The elastic displacements are presented in the form of a Fourier expansion, the coefficients of which are found by the variational formulation of the problem combined with the penalty approach for a numerical implementation of contact conditions. Results are applied to certain problems of buckling of a circular bar and compared with previous approximate solutions.

Transient Thermoelastic Contact and Stability of Two Thin-Walled Cylinders

“…The corresponding material properties used are given in Table 1 of [6]. In the classification of reference [12], this is a type 2 material combination, for which instability can be obtained for sufficiently large heat flux in either direction, the stability boundaries being defined by Figure 3 of [12].…”

“…The range of parameters under which this approximation is legitimate is discussed in a similar isothermal problem by Azarkhin and Barber [12]. …”

“…Figure 4 shows the real part of the dimensionless growth rate for Q* = -200. This corresponds to a point below the line R in Figure 2 of [12], and we therefore find a range of wave lengths with real growth rates and a contiguous range with complex growth rates. The parameter values were chosen so as to make the first wave (i = 1) occur near the maximum growth rate in the real range.…”

“…(9). Furthermore, since the asymptotic behavior of the temperature field at large y is described by the linear terms Cn + Do, we conclude that T2(y, r) + 0 as y + m and therefore is conveniently represented in the Fourier integral form This expression satisfies the heat conduction equation (5) and the boundary condition (12) for all values of the arbitrary function Ao(n), which can therefore be used to satisfy the initial condition T2(y, 0).…”

“…The exponential growth rate b can be characterized by a relation between dimensionless growth rate B*, heat flux Q*, and spatial frequency R*, where and R' = aR/ap is the derivative of the contact resistance with respect to pressure at the steady-state pressure p,, at which the resistance is R,. For more details of the relations between these quantities, the reader is referred to [12]. Figure 2 shows the dimensionless growth rate for Q* = 100.…”