Free Edge Conditions Research Articles

Thermal stresses in plates with circular holes

The temperature and membrane stress distribution in a finite rectangular plate with an insulated circular hole is investigated. The temperature varies along the coordinates within the plane. The temperature distribution is determined as the solution of the steady state heat conduction equation, then the membrane stresses due to the temperature are analyzed. For both steps the free edge conditions around the insulated circular hole are satisfied exactly while the boundary conditions at the outer edges of the plate are satisfied at selected points by the method of point matching. The numerical results are presented for temperature distribution and membrane stresses.

Thermal buckling of shallow shells

The large deflection equations for a thin shallow shell are modified to include thermal effects. The temperature is considered to be an arbitrary function of the space coordinates.The resulting equations are used to study thermal buckling and post-buckling behavior of a simply supported cylindrical shell panel, subjected to a parabolic temperature distribution along its axial direction. It is assumed that the temperature is constant across the thickness of the shell and along its circumferential direction. Buckling charts for various curvatures, Ky, and aspect ratios, λ, are presented for two cases of edge conditions. In one case the edges of the panel are free to displace, and in the second case the edges are restrained.The critical temperature is found to fall outside the practical temperature range of the material for Ky ≥ 200 in the free-edge condition and for Ky ≥ 50 in the restrained-edge condition.

Relation between the Onsager and Pfaffian Methods for Solving the Ising Problem. I. The Rectangular Lattice

An algebraic proof is given showing the equivalence of the Pfaffian and Onsager methods of solution of the Ising problem for the two-dimensional rectangular lattice with free edge conditions. With cyclic conditions on the rows and columns and with helical edge conditions it is shown how the two solutions differ. The relation between the appearance of crossed long-range bonds and the appearance of unwanted negative signs in the Pfaffian method is shown explicitly for this particular lattice.

Experiments on Stability on Spherical Caps

Series of experiments on shallow spherical shells (caps) were carried out to determine deformations and critical concentrated loads at the apex, and thus to provide additional design data and information on the mechanism of buckling of caps. A snap-through buckling was observed for simply supported and free edge conditions for all types of concentrated loads. The cut-off geometry parameter, λ, coincides with previously found values and different types of loadings. Clamped caps do not buckle under the constant load concentrated loads; this was observed previously for constant displacement concentrated loads.

On the Tension in an Orthogonally Aeolotropic Strip with a Circular Hole

In this paper, the tension in an orthotropic strip with a circular hole, which has practical importance, is treated. The solution of the same subject for isotropic material, has been presented by R.C.J. Howland and lately improved by M. Isida to study the stresses in a strip with an elliptic hole by the use of orthogonal co-ordinates. In this paper, the same methods are adopted to express the free edge conditions at the rim of the strip and of the circular hole and the stresses are given in the form of the power series of λ which is the ratio of the radius of the circular hole to the half breadth of the strip.