Showing papers in "Transactions of The Canadian Society for Mechanical Engineering in 1987"

Vorticity and Vortex Dynamics in Complex Turbulent Flows

Abstract: Some of the basic principles of vortex dynamics arc reviewed in this paper and applied to calculating and understanding various kinds of turbulent flows. After setting out the basic equations and b...

Interlayer Slip and Delamination Effect: A Hemivariational Inequality Approach*

Abstract: In the present paper we formulate hemivariational inequalities describing the interlayer slip and delamination effect in elastic structures. After the formulation of the interface conditions which are of a nonmonotone multivalued nature, we derive hemivariational inequalities for the static and dynamic problems. Further some methods for the numerical treatment of the problems are given (regularisation method and substationarity-point method). Two numerical examples concerning simple adhesively connected elastic structures are given to illustrate the theory.

Advanced Experimental Mechanics in Modern Engineering Science and Technology

Abstract: The explosive development of modern technology and the increasing societal awareness of technological risks are enforcing a more rigorous approach to the development of engineering theories, experiments, and design procedures. The recent progress in the theories and techniques of measurements has exposed various deficiencies of procedures of experimental and analytical mechanics. Major patterns of the rapidly emerging system of theories and experimental and analytical procedures based on scientific methodology -- which is called “advanced experimental mechanics” -- are outlined. The strong interdependence of advanced experimental mechanics, contemporary analytical mechanics and modern trends in applied materials science is illustrated by examples. Major issues are discussed within the framework of the modern scientific methodology formulated by Karl Popper, of Thomas Kuhn’s notion of paradigm in science, of Niels Bohr’s correspondence principle, and of the requirement of reliability of engineering procedu...

Discussion of Two Theories on the Penetration of Multilayer Metallic Targets

Abstract: A short survey of possible penetration theory approaches and possible penetration situations is given in order to show why a large number of different penetration theories can be found in the literature. Of this variety of theories, an empirical or quasianalytical theory and an approximate analytical one, used for estimating residual velocities and other parameters of the penetration of monolithic targets, are compared and applied to double layer and multilayer targets. The results are qualitatively in accordance, but differ quantitatively. The difference and some peculiarities are discussed.

On the Efficiency of Different Head Shapes to Perforate Thin Targets

Abstract: Thomson’s approach to the perforation of thin metal targets is used to compare the efficiency of conical, parabolic, tangent ogival and secant-ogival heads, Thompson’s approximation of an ogival head and Kucher’s optimal head. Well-established empirical evidence suggests that for this type of target the tangent-ogival head is the most efficient one for the usual ratios of head length to radius of projectile. This is theoretically confirmed and explained by this paper.

On Stability Equations of Spatial Rods - A Technical Theory*

Abstract: General nonlinear stability equations of naturally curved and pretwisted slender elastic rods are derived by means of a technically heuristic approach. The derived equations take account of such ef...

Effects of Mechanical and Thermal Relaxations on the Stresses in a Heated Viscoelastic Continuum with a Cylindrical Hole

Abstract: The paper deals with a problem of stress analysis in a heated viscoelastic medium containing a cylindrical hole. The medium is taken to be viscoelastic in shear but elastic in bulk deformation; the linear standard model is used to characterize the viscoelastic behaviour of the material. The analysis is carried out for two different sets of conditions for the bounding surface. The applicability of the analysis put forward in the paper has been illustrated through an attempt to compute the desired expressions by using suitable numerical techniques. The computed results are found to be in good agreement with those of related previous studies.

Computer Analysis of Continuously Variable Transmissions Using Non-Circular Gears*

Abstract: A mathematical model of theoretical continuously variable transmissions (CVT’s) using non-circular gears (NCG’s) was analyzed. Based on torque, efficiency and speed characteristics, generalized conclusions were drawn.

Analytical Trajectory Optimization of Seven Degrees of Freedom Redundant Robots

Abstract: The basic characteristic of kinematically redundant robots is that non-unique joint solutions may exist for a specified end effector location. Thus, trajectory planning for a kinematically redundant robot requires an optimization procedure to determine the joint displacements when solving the inverse kinematics relations. In this paper an analytical solution is developed for the trajectory optimization problem of redundant robots based on the classical Lagrange’s method. A detailed formulation is provided for seven degrees of freedom robots, which minimizes the Euclidean norm of joint dislacements for point-to-point motion trajectory planning.

Asymptotic Analysis of a Uniform Area Radiating Fin

Abstract: The present study considers in detail the problem of a uniform area radiating fin for large values of the radiation conduction interaction parameter N. A method is developed for improving the previously known asymptotic solution to make it applicable for relatively smaller values of N. While the method yields the exact solution in the case of linearized radiation, it leads to a close form solution, valid for all N, in the case of a fin radiating to a sink at zero temperature. The general case of a fin radiating to a sink at a non-zero temperature needs a numerical solution of equations that do not involve N. The results show an excellent agreement between the present calculations and the exact solutions available in the literature.

On the Stability of Motion of Several Types of Heavy Symmetric Gyroscopes with Damping Torques

Abstract: The sufficient conditions for the stability of a “temporarily” sleeping top with damping torque in three cases and the stability of regular precession and permanent rotation of a heavy symmetric gyroscope with damping torque and motor torque in four cases arc obtained by Liapunov’s direct method.

Further Results on the Stability of Viscoelastic Columns

Abstract: Recent results published by the authors on the stability behaviour of columns made of time-dependent materials are extended in a number of ways. Firstly, the closed-form expression obtained for the safe load limit of a simply supported column made of a linear three-element model material, is generalized for an arbitrary linearly viscoelastic constitutive law. The result, obtained by means of the static stability approach, is confirmed by an asymptotic solution of the dynamic stability equations. The same solution technique is used to generalize this expression for columns with arbitrary boundary conditions. Even though columns as structural members exhibit stable post-buckling behaviour, there are structural configurations, involving compression members, the overall load deflection behaviour of which indicate unstable post-buckling characteristics. A simple example is used to alert the designer to the possibility of encountering such configurations and the danger associated with such post-buckling behavio...

Flow Pattern of Solid Particles in a Double Vortex Chamber

Abstract: An experimentally determined air flow pattern in a double vortex chamber is utilized to predict the flow pattern of inserted solid particles. The minimum (critical) particle size retained in the vo...