Effect Of Shear Strain Research Articles

Structural characteristics of cylindrical pressure vessels of medium thickness

The cylindrical pressure vessel with a flat head is analysed for the redundant forces and stresses at the junction using a Reissner type theory. The flexibility coefficients and other functions required in the structural analysis of the vessel have been tabulated for different ratios of thickness to radius, and general formulae have been given for the determination of forces and displacements. The theory used in the paper resembles that proposed by Reissner [1, 2] and Nagdhi [3] but differs in details. The complete set of the constituent equations for the general case of a shell of arbitrary shape have been listed in the Appendix. It is hoped that the analysis presented in this paper, which is based on a shell theory corrected to include the effects of the transverse shear and normal strain, is an expedient to estimate the corrections to be applied in the analysis of prestressed concrete pressure vessels when using the thin-walled shell theory.

Theory of elastic plates in the reference state

A non-linear plate theory is developed on the basis of three-dimensional theory of elasticity in terms of a reference state. This includes the effects of transverse shear and normal strains, acceleration, material heterogeneity and anisotropy, and a temperature field. The results are valid for plates of constant thickness and contain those of certain earlier non-linear plate theories as special cases.

Bending of plates made of oriented glass-reinforced plastics

A plate made of oriented glass-reinforced plastic (GRP) is treated as a regular medium with numerous anisotropic layers. The problem of bending is solved in the elastic formulation of the problem without the use of the hypothesis of undeformed normals and a preliminary specification of the law of distribution of shearing stresses in transverse planes. The important effect of shear strains on the deflections and stresses in plates of oriented GRP is illustrated in the example of a simply supported square plate with transverse isotropy. An estimate is given of the errors introduced by arbitrary specification of the law of distribution of shearing stresses.

Coupled Vibrations of Thin-Walled Elastic Bars

A study of the coupled torsional and bending vibrations of thin-walled beams of asymmetric open section is made. The validity of existing theories has been examined both analytically and experimentally. Analytically, a higher order theory that includes effects of shear strains induced by bending and warping was constructed and compared with the existing elementary theory for five different boundary conditions. Experimentally, tests were conducted on beams of two different cross sections of various lengths. The resonant frequencies were found and compared with the values predicted from theoretical calculations. It is concluded that when the beam is long, the elementary theory is adequate to predict the natural frequencies for the first few torsion predominant modes, but is inadequate for bending predominant modes. For bending predominant modes, the higher order theory should be used. Also, the higher order theory serves as a guide for the range of validity of the elementary theory.

The role of surface shear strains in the adhesion of metals. Part I

The effect of surface shear strains on the adhesion of copper, aluminum, and gold surfaces is examined. In particular, the effect of shear strains on the structure of metal surfaces and substrata subsequent to adhesion is elucidated. It is shown that shear strains are necessary for adhesion to occur under most circumstances when unlubricated metals are in contact. Shear strains are very effective in removing surface oxides, and these oxides are buried at below the common interface. Shear strains roughen the surface, increase the amount of atomic contact, and produce a work-hardened zone near the common interface, all of which tend to make the adhesion more effective. In general, the concept of friction and adhesion advocated by the Cambridge school is confirmed.

On the plastic theory of plates

This paper presents a theory of the small deformations of a thin uniform plate under transverse load. The plate is made of non-hardening rigid-plastic material obeying the Tresca yield condition and associated flow rule. The basic assumptions are similar to those made in the conventional engineering theory of thin elastic plates, and the effects of transverse shear strain and rotatory inertia are neglected. Hitherto, the theory has been developed only under conditions of circular symmetry, and the object of the present paper is to remove this restriction. Attention is confined here to the derivation and classification of the field equations. The field equations involve the stress moments and the middle-surface curvature rates as the associated generalized stresses and strain rates. These equations are first referred to Cartesian co-ordinates. The condition of isotropy requires the coincidence of the directions of principal stress moment and curvature rate. One of these two families of directions is characteristic for the equations appropriate to certain plastic régimes. The field equations are therefore referred to curvilinear co-ordinates taken along these directions. A detailed study is made of discontinuities in the field quantities. The field equations are either parabolic or elliptic for the principal plastic régimes.