Torsional oscillations of a rigid disc bonded to multilayered poroelastic medium

This paper deals mainly with the dynamic response of a rigid disc bonded to the surface of a layered poroelastic half-space. The disc is subjected to time-harmonic torsional moment loadings. The half space under consideration consists of a number of layers with different thickness and material properties. Hankel transform techniques and transferring matrix method are used to solve the governing equations. The continuity of the displacement and stress fields between different layers enabled derivation of closed-form solutions in the transform domain. On the assumption that the contact between the disc and the half space is perfectly bonded, this dynamic mixed boundary-value problem can be reduced to dual integral equations, which are further reduced to Fredholm integral equations of the second kind and solved by numerical procedures. Selected numerical results for the dynamic impedance and displacement amplitude of the disc resting on different saturated models are presented to show the influence of the material and geometrical properties of both the saturated soil-foundation system and the nature of the load acting on it. The conclusions obtained can serve as guidelines for practical engineering.

STRESS INTENSITY FACTORS OF THE ECCENTRIC AND EDGE CRACKED CYLINDERS

By using the single crack solution and the regular solution of harmonic function, the torsion problem of a cracked cylinder was reduced to solving a set of mixed-type integral equations which can be solved by combining the numerical method of singular integral equation with the boundary element method. Several numerical examples were calculated and the stress intensity factors were obtained.

Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the crosssection(i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio Independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design Insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.

METHOD OF STRONGLY SINGULAR INTEGRAL EQUATION FOR THE TORSION OF CYLINDER WITH EDGE CRACK

From the dislocation type solution of the torsion of single crack, by using the concept of finite part integrals. The torsion problem of cylinder with a single crack was reduced into an integral equation with strong singularity. The numerical method was also obtained and several numerical examples were calculated successfully at the end of this paper.,

APPLICATION OF AN IMPROVED BOUNDARY ELEMENT METHOD ON THE PROBLEM OF ELASTIC TORSION

An improved boundary element method has been used in analyzing and calculating the problems of the torsion of a prismatic bar with elliptical cross-section. In this paper the calculated results correspond with the values of boundary element method. However, the quantity of data required by the improved boundary element method is much less than that required by boundary element method, and the calculating time will be greatly reduced. Therefore, the procedure of this paper is an economical and efficient numerical computational way for solving Poisson equation problem.

LAMINAR FLUID FLOW IN HELICAL ELLIPTICAL PIPE

By means of an orthogonal curvilinear coordinate system and the solution of complete N-S equations, the flow in a helical elliptical duct was analyzed by the perturbation method. The first-order solutions of the stream function, the axial velocity and the velocity of secondary flow were obtained. The effects of torsion, curvature and axial pressure gradient on the secondary flow were discussed. The torsion has first-order effect on the secondary flow in a helical elliptical pipe, and the secondary flow is dominated by torsion when the axial pressure gradient is small. For increasing gradient the secondary flow is eventually dominated by the effect due to curvature. The fact that the torsion has no effect on fluid flow in a helical pipe with a circular cross section was also confirmed. The most important conclusion is that the flow in a helical elliptical pipe to the first order can be obtained as a combination of the flow in a toroidal pipe and the flow in a twisted pipe.