Shear Boundary Conditions Research Articles

Buckling of thick layered composite plates under inplane moment loading

In this paper a first-order shear deformation laminate theory that accounts for the Green Lagrange strain vector is described and its finite element model is developed. The element is used to study the effects of anisotropy, transverse shear moduli, aspect ratio and boundary conditions on the buckling behaviour under in-plane triangular loading. It is observed that for an angle ply (± θ) thick plate, maximum load occurs at ±15°, whereas for thin plate it occurs at ±30°. It is found that the effects of aspect ratio, boundary conditions and transverse shear are significant on buckling load.

Analysis of plates using isoparametric quadratic element—Shear, reaction, patch loading and some convergence studies

The derivation of reactions at the supported edge of a plate using isoparametric quadratic element has been presented. Straight and curved plates have been analysed to study the influence of shear rigidity, boundary conditions and support geometry on the value of shears and reactions at the edges. It has been found that convergence is slower for shear than for moments. The explicit value of the element loading matrix due to a patch load has been indicated, and plates having different aspect ratios due to a central patch load have been studied.

Forced axisymmetric motion of circular, viscoelastic plates

Williams' method for forced motion of elastic systems is applied to circular, viscoelastic plates where the effects of rotatory inertia, transverse shear and time-dependent boundary conditions are included. The viscoelastic material is assumed to have a constant Poisson's ratio. A particular problem is solved for a symmetrically loaded, completely free plate. The material used is vulcanized rubber where the viscoelastic behavior in shear is used in specifying the material parameters of a three-element solid.

Twisting and Bending of Thin-Walled Prismatic Beams of Open Cross-Sectional Profile

Previous studies of the behaviour, in generalized co-ordinates, of thin-walled, prismatic beams of open cross-sectional profile have included, explicitly, only the effects of distributed transverse forces, q x and q y, distributed longitudinal forces, q z, and distributed torsional couples, m z. Using the principle of virtual displacements, the work of previous investigators is extended to include, quite generally, the effects of the hitherto neglected distributed couples, m x and m y. The derivation of the differential equation relating to the twisting of an open-section prismatic beam is presented fully whilst those relating to transverse and axial displacements of cross-sections are merely stated. The kinematic and static boundary conditions for a cantilever are also established from the virtual work equations. These show that the free-end shear boundary condition associated with transverse bending which is usually adopted in engineering calculations is inadequate for such a generalized loading system.

Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer

The two-dimensional flow of an incompressible viscous fluid past a circular cylinder, symmetrically placed in a uniform shear field, is considered both theoretically and experimentally for small values of the shear Reynolds number. A series of angular rotational speeds is covered, each giving rise to a fundamentally different flow pattern. It is shown first that the Stokes solution to this problem is not entirely consistent everywhere with the linear shear boundary condition which presumably exists far from the body. Using the method of inner and outer expansions, this solution is then improved by properly taking into account the first-order effects of the inertia terms, but, surprisingly, the streamline structure in the outer region is still found to depart from that of the uniform shear sufficiently far away from the object. In spite of the somewhat bizarre nature of the theoretical solution far from the cylinder, experimental studies clearly show, however, that it accurately represents the actual flow within the inner region over a wide range of cylinder rotation rates.