Showing papers by "Applied Science Private University published in 1971"

On Detecting Total or Partial Symmetry of Switching Functions

Abstract: This note presents a method for identifying total or partial symmetry of switching functions based on the application of the principle of residue test by numerical methods. The invariance of a switching function under a single interchange of two variables can be readily detected from the equality of some of the residues of expansion about these two variables. This procedure of detecting invariance is directly applied for the identification of total or partial symmetry of a switching function whose variables of symmetry may be either all unprimed (or all primed), mixed, or of multiform nature.

Determination of the Period of Nonlinear Oscillations by Means of Chebyshev Polynomials

Abstract: Mit Hilfe einer auf der Tschebyscheff-Approximation beruhenden schnell konvergierenden Reihe wird fur die Schwingungsdauer eines nichtlinearen, symmetrischen, konservativen Systems eine Naherungsformel aufgestellt. A new formula is proposed for the approximate computation of the period of a nonlinear symmetrical autonomous system with a single degree of freedom, in the form of a rapidly convergent series, based on the Chebyshev approximation.

Acoustic emission testing and microfracture processes

Abstract: IN RECENT YEARS KNOWLEDGE OF THE MECHANISMS OF MICROCRACK FORMATION AND PROPAGATION HAS INCREASED GREATLY. IT IS NOW UNDERSTOOD, AT LEAST QUALITATIVELY, HOW PLASTIC DEFORMATION IS ABLE TO INITIATE CRACKS, HOW CRACKS ARE ABLE TO GROW, AND HOW LARGE-SCALE GROWTH LEADS TO MACROFRACTURE. NONETHELESS, THERE ARE MANY QUANTITATIVE ASPECTS OF THE MICROFRACTURE PROCESS THAT STILL ARE NOT WELL UNDERSTOOD. SOME OF THESE ASPECTS MAY BE BETTER UNDERSTOOD WITH ACOUSTIC EMISSION TESTING. THOSE AREAS IN WHICH ACOUSTIC EMISSION TESTING HAS ASSISTED OR COULD ASSIST MATERIALS SCIENTIST WHO ARE INVESTIGATING MICROFRACTURE PROCESSES IN SOLIDS ARE DESCRIBED. /AUTHOR/

Motion of a rigid disc in an elastic solid

Abstract: A rigid circular disc embedded in an infinite, isotropic elastic solid is assumed to be excited by a normally-incident plane, harmonic compressional wave. The disc is assumed to be either in perfectly welded or perfectly smooth contact with the surrounding solid. In each case, the problem is reduced to the solution of Fredholm integral equations of the second kind. For the case of the welded contact, exact numeral solutions valid at any given frequency are given. Approximate solutions valid at low and high frequencies are obtained for both cases and are compared with the exact solution. The displacement and compliance of the disc as well as other quantities of interest are presented graphically as functions of frequency.

The influence of strain-hardening and grain size on early fatigue damage based on a micromechanics theory

Abstract: E arly fatigue damage is assumed to correspond to the build-up of local plastic shear strain. The influence of strain-hardening and grain size on the early stage of fatigue damage of a polycrystal subjected to fluctuating stress is considered. The calculations are based on a micromechanics theory proposed recently by the authors. It is shown that the increase of the strain-hardening rate and/or the decrease of the grain size decreases the rate of early fatigue damage. In order to produce 100 per cent local plastic shear strain for a given number of loading cycles, the range of the alternating stress decreases with increasing amounts of mean stress. This result is shown to be rather insensitive to the rate of strain-hardening and is found to lie between the values predicted by Gerber's parabolic law and by the modified Goodman linear law for fatigue failure.

Conditions for the onset of vaporization in superfluid liquid He II in the presence of heat flow

Abstract: Studies of the vaporization onset associated with heat flow are used as a tool to probe the superfluid thermohydrodynamics during entropy transport. Onset-flux-density data of the heat flow suggest that the normal fluid viscous force dominates during entropy transport from a single source (strip) to bulk He II over a layer of thickness 10−4 cm (upper bound) or less.

Conjugate Gradient and Decomposition—Analogy

Abstract: This note demonstrates that the [\ik]-orthogonal vectors in the conjugate gradient method as applied to structural analysis are shown to be proportional to the vectors identifying the new coordinates in matrix decomposition.

Plastic Buckling of Point-Loaded Spherical Shells

Abstract: The effects of inelastic strains on the deflection and stability of thin spherical domes with roller-supported edges under point loads at the apex are studied analytically and experimentally. The governing nonlinear differential equations are derived by applying Reissner's nonlinear shell theory and the total deformation theory of plasticity. These equations are solved by a finite difference scheme using Newton's method. Four domes, hydroformed from 6061-0 aluminum, are tested. It is concluded that the inelastic strains do account for most of the discrepancies existing between the analytically predicted (based on elastic analysis alone) and the experimentally observed shell responses. It is found that for certain geometric configurations (i.e., λ > 6) the local existence of finite strains and significant strain reversal indicates that closer correlation between theory and experiment is possible using an incremental plasticity theory.