Stresses around two equal circular elastic inclusions in a pressurised cylindrical shell

The stress problem of two equal circular elastic inclusions in a pressurised cylindrical shell has been solved by using single inclusion solutions together with Graf’s addition theorem. The effect of the inter-inclusion distance on the interface stresses in the shell as well as in the inclusion is studied. The results obtained for small values of curvature parameter fi @*=(a*/8Rt) [12(1-v*)]“*, a, R, t being inclusion radius and shell radius and thickness) when compared with the flat-plate results show good agreement. The results obtained in non-dimensional form are presented graphically.

Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Quasi-2D XY Magnetic Properties and Slow Relaxation in a Body Centered Metal Organic Network of [Co-4] Clusters

Octahedral Co2+ centers have been connected by mu(3)-OH and mu(2)-OH2 units forming [Co-4] clusters which are linked by pyrazine forming a two-dimensional network. The two-dimensional layers are bridged by oxybisbenzoate (OBA) ligands giving rise to a three-dimensional structure. The [Co-4] clusters bond with the pyrazine and the OBA results in a body-centered arrangement of the clusters, which has been observed for the first time. Magnetic studies reveal a noncollinear frustrated spin structure of the bitriangular cluster, resulting in a net magnetic moment of 1.4 mu B per cluster. For T > 32 K, the correlation length of the cluster moments shows a stretched-exponential temperature dependence typical of a Berezinskii-Kosterlitz-Thouless model, which points to a quasi-2D XY behavior. At lower temperature and down to 14 K, the compound behaves as a soft ferromagnet and a slow relaxation is observed, with an energy barrier of ca. 500 K. Then, on further cooling, a hysteretic behavior takes place with a coercive field that reaches 5 Tat 4 K. The slow relaxation is assigned to the creation/annihilation of vortex-antivortex pairs, which are the elementary excitations of a 2D XY spin system.

Thermal stresses around circular holes in spherical shells

The thermal stress problem of a circular hole in a spherical shell of uniform thickness is solved by using a continuum approach. The influence of the hole is assumed to be confined to a small region around the opening. The thermal stress problem is converted as usual to an equivalent boundary value problem with forces specified around the cutout. The stresses and displacement are obtained for a linear variation of temperature across the thickness of the shell and presented in graphical form for ready use.

Two-Impurity Kondo Problem

The two-impurity Kondo problem is studied by use of perturbative scaling techniques. The physics is determined by the interplay between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins and the Kondo effect. In particular, for a strong ferromagnetic RKKY interaction the susceptibility exhibits three structures as the temperature is lowered, corresponding to the ferromagnetic locking together of the two impurity spins followed by a two-stage freezing out of their local moments by the conduction electrons due to the Kondo effect.

Determination of the optically equivalent model in three-dimensional photoelasticity

Any stressed photoelastic medium can be reduced to an optically equivalent model consisting of a linear retarder, with retardation 1 and principal axis at azimuth 1, and a pure rotator of power 2. The paper describes two simple methods to determine these quantities experimentally. Further, a method is described to overcome the problem of rotational effects in scattered-light investigations. This new method makes use of the experimentally determined characteristic parameters

A problem in micropolar elasticity

In this paper a three-dimensional analysis for statics and dynamics of a class of simply supported rectangular plates made up of micropolar elastic material is presented. The solution is in the form of series, in which each term is explicitly determined. For free vibrations, the frequencies are obtained by the solution of a closed form characteristic equation.

A method for separation of stresses in Two- and three-dimensional photoelasticity

A method for separation of stresses in two and three-dimensional photo elasticity using the harmonisation ofjrst stress invariant along a straight section is deve- ,dped. For two-dimensions, the equations of equilibrium are reformulated in terms ojsum and difference of normal stresses and relations are obtained which can be used for harmonisation of the first invariant of stress along a straight section. A similar procedure is adopted for three-dimensions by making use of the Beltrmi-MicheN equations. The new relations are used in finite d~yerencefo rm to evaluate the sum of normal stresses along straight sections in a three-dimensional body. The method requires photoelastic data along the section as well ~rra djacent sections. This method could be used as an alternative to the shear d@erence method for separation of stresses in photoelasticity. 7he accuracy and reliability of the method is ver$ed by applying the method to problems whose solutions are known.

Determination of the optically equivalent model in three-dimensional photoelasticity

Any stressed photoelastic medium can be reduced to an optically equivalent model consisting of a linear retarder, with retardation delta1 and principal axis at azimuth phgr1, and a pure rotator of power phgr2. The paper describes two simple methods to determine these quantities experimentally. Further, a method is described to overcome the problem of rotational effects in scattered-light investigations. This new method makes use of the experimentally determined characteristic parameters.

Effect of boundary condition description on convergence of solution in a boundary-value problem

It is well known that the numerical accuracy of a series solution to a boundary-value problem by the direct method depends on the technique of approximate satisfaction of the boundary conditions and on the stage of truncation of the series. On the other hand, it does not appear to be generally recognized that, when the boundary conditions can be described in alternative equivalent forms, the convergence of the solution is significantly affected by the actual form in which they are stated. The importance of the last aspect is studied for three different techniques of computing the deflections of simply supported regular polygonal plates under uniform pressure. It is also shown that it is sometimes possible to modify the technique of analysis to make the accuracy independent of the description of the boundary conditions.

Ring loading of a long, thin, circular cylindrical shell enclosing a soft, solid core: A recalculation by the love function method of elasticity.

The problem is solved using the Love function and Flügge shell theory. Numerical work has been done with a computer for various values of shell geometry parameters and elastic constants.

Comparison of elasticity and shell-theory solutions for finite circular cylindrical shells

A finite circular cylindrical shell subjected to a band of uniform pressure on its outer rim was investigated, using three-dimensional elasticity theory and the classical shell theories of Timoshenko (or Donnell) and Flügge. Detailed comparison of the resulting stresses and displacements was carried out for shells with ratios of inner to outer shell radii equal to 0.80, 0.85, 0.90 and 0.93 and for ratios of outer shell diameter to length of the shell equal to 0.5, 1 and 2. The ratio of band width to length of the shell was 0.2 and Poisson's ratio used was equal to 0.3. An Elliot 803 digital computer was used for numerical computations.

Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Circular elastic inclusions in cylindrical shells

The problem of a circular elastic inclusion in a cylindrical shell subjected to internal pressure or thermal loading is studied. The two shallow-shell equations governing the behaviour of a cylindrical shell are transformed into a single differential equation involving a curvature parameter and a complex potential function in a non-dimensional form. In the shell region, the solution is represented by Hankel functions of first kind, whereas in the inclusion region it is represented by Bessel functions of first kind. Boundary conditions at the shell-inclusion junction are expressed in a simple form involving in-plane strains and change in curvature. The effect of such inclusion parameters as extensional rigidity, bending rigidity, and thermal expansion coefficients on the stress concentrations has been determined. The results are presented in non-dimensional form for ready use.

Analysis of edge delaminations in laminates through combined use of quasi-three-dimensional, eight-noded, two-noded and transition elements

The use of appropriate finite elements in different regions of a stressed solid can be expected to be economical in computing its stress response. This concept is exploited here in studying stresses near free edges in laminated coupons. The well known free edge problem of [0/90], symmetric laminate is considered to illustrate the application of the concept. The laminate is modelled as a combination of three distinct regions. Quasi-three-dimensional eight-noded quadrilateral isoparametric elements (Q3D8) are used at and near the free edge of the laminate and two-noded line elements (Q3D2) are used in the region away from the free edge. A transition element (Q3DT) provides a smooth inter-phase zone between the two regions. Significant reduction in the problem size and hence in the computational time and cost have been achieved at almost no loss of accuracy.