Showing papers by "Lehigh University published in 1969"

The use of eigenfunction expansions in the general solution of three-dimensional crack problems

Abstract: Eigenfunction expansion technique to analyze three dimensional crack and wedge problems, emphasizing stress field near straight edged crack

Cylindrical and spherical shells with cracks

Abstract: Meridional crack problem for cylindrical and spherical shells solved for uniform membrane load and bending moment, obtaining stress intensity components

Localized Orbitals in Polyatomic Systems

Abstract: Adams und Gilbert have derived a rigorous extension to the Hartree-Fock equation which allows one to obtain localized orbitals in some polyatomic systems. This extension is valid for all closed shell systems and all systems which may be represented by a single Slater determinant and is approximately valid for any system which one may approximate by a single Slater determinant. In this paper these results are put in a more convenient form and are analysed in powers of the interatomic overlap, where only first order terms in overlap are retained. A perturbative form of the equation is also developed. Wave functions are obtained for the LiH crystal. Adams und Gilbert haben eine strenge Erweiterung der Hartree-Fock-Gleichung abgeleitet, die es erlaubt, lokalisierte Bahnen in einigen mehratomigen Systemen zu erhalten. Diese Erweiterung ist gultig fur alle Systeme mit abgeschlossenen Schalen und alle Systeme, die durch eine einzige Slaterdeterminante dargestellt werden, und ist naherungsweise gultig fur alle Systeme, die durch eine einzige Slaterdeterminante approximiert werden konnen. In der vorliegenden Arbeit werden diese Ergebnisse in eine leichter zugangliche Form gebracht und in Potenzen der interatomaren Uberlappung analysiert, wobei nur die Uberlappungsterme erster Ordnung berucksichtigt werden. Eine Storungsform der Gleichung wird ebenfalls entwickelt. Fur LiH-Kristalle werden Wellenfunktionen erhalten.

Double punch test for tensile strength of concrete, Sept. 1969 (70-18) PB224770/AS (NTIS)

Abstract: This paper describes a new test technique for determining the tensile strength of concrete. In this test, a concrete cylinder (or cube) specimen is placed vertically between the loading platens of_a testing machine and compressed by two steel punches located concentrically on the top and bottom surfaces of the cylinder (or cube) . The relevant formula for computing the tensil,e strength in the new test is herein developed using the theory of perfect plasticity. It is shown that the necessary test arrangement, as well as the formula for computing the tensile strength of concrete, are very simple. The new test appears promising for practical use. * Assistant Professor, Fritz Engineering Laboratory, Department of Civil Engineering, Lehigh University, Bethlehem, Pennsylvania.

Adsorption of carbon monoxide-nitrogen, carbon monoxide-oxygen, and oxygen-nitrogen mixtures on synthetic zeolites

Abstract: Experimental results for the adsorption of the binary gas mixtures oxygen-nitrogen, oxygen-carbon monoxide and nitrogen-carbon monoxide on two synthetic zeolites are reported. In all of these experiments the temperature was −200°F. and the total pressure was 1 atm. Also reported are the isotherms for the three pure gases on the two zeolites at −200°F. The results indicate that these zeolites have a surface selectivity which is independent of any sieving effect based on the size of the adsorbed molecules. It does not appear that the strong separations obtained can be explained in terms of the van der Waals forces which are generally believed to be dominant in physical adsorption. The available methods of predicting binary adsorption data from the pure gas isotherms have been examined.

Combined Plane-Wave Tight-Binding Method for Energy-Band Calculations with Application to Sodium Iodide and Lithium Iodide

Abstract: A method of calculating energy bands, which we name the mixed-basis method, is developed. This method uses a wave-function expansion which includes free-atom or ion wave functions and plane waves, and it may incorporate relativistic effects. It is, in general, not equivalent to the orthogonalized-plane-wave (OPW) method, although the cases for which the two methods are equivalent are developed. A sample calculation is made for LiI and NaI, for which x-ray, valence, and conduction states are calculated. The agreement between theory and x-ray and optical-absorption data is excellent. The importance of relativistic effects is explored, and comparisons are made with conventional OPW results, which include relativity by first-order perturbation theory.

Protoelastic bodies with large deformation

Abstract: The ability to obtain exact solutions of the equations of equilibrium of isotropically elastic bodies with arbitrary strain energy functions can be largely credited with the interest and drive that nonlinear continuum theories have exhibited since the middle fifties. Since this ability stems largely from the fact that the stress tensor admits a potential that is a function of the strain tensor, it is reasonable to look for extensions of such potential-like representations. Now, a potential representation for the stress tensor in terms of the strain tensor may be looked upon as the Euler-Lagrange derivative* if we view the strain energy function as the Lagrangian function and the displacement gradients as the field variables. With this in mind, it is a simple extension to consider strain energy functions that contain functionals of the strain as arguments in addition to the usual arguments of a strain energy function. In this way we arrive at a theory for a class of materials that we term protoelastic. The essential aspects of such materials is that the stress tensor at a given point of the body will depend on the displacement gradients at all points within the body; the stress becomes a nonlocal quantity. The essential aspects of the calculus of variations for Lagrangian functions that have functionals as arguments is given in Section 2. After a development of the variational statements that are equivalent to the law of balance of linear momentum for a deformable body in Section 3, a protoelastic body is defined in Section 4 in terms of a protopotential function and the associated variational forms for such bodies are examined. The implications of the laws of balance of moment of momentum and of energy for protoelastic bodies are given in Section 5, where it is shown that the protopotential function can depend on the displacement gradients only through a dependence on the material Cauchy-Green deformation tensor. Section 6 briefly examines the types of structure that are included under the general heading of protoelastic bodies; elastic bodies, bodies with rate effects, bodies with dependence on gradients of the deformation tensor, and bodies that exhibit intrinsically nonlocal properties. Suitable extensions of RIVLIN'S inverse method of obtaining exact solutions are shown to be possible for protoelastic bodies. Exact solutions for the biaxial shear of a rectangular protoelastic body and for the torsion of a protoelastic cylinder are given; both problems giving rise to nonlocal effects.

Hydrothermal Ore Deposits in the Western United States: A NewConcept of Structural Control of Distribution.

Abstract: Empirical plotting of four sets of equidistantly spaced shear stress trajectories, based on regularities in distribution of actual faults and ore veins in the continental area and on the landward prolongation of the big fracture zones of the northeastern Pacific, givesrise to a prospecting net for the western United States. Preferential accumulation of big ore deposits (including such deposits as Bingham and Tintic) along landward prolongation of the main fracture zones of northeastern Pacific, in the vicinity of intersections of four systems of trajectories, and along boundaries of crustal blocks suggests several possibilities for prospecting for unknown hydrothermal deposits in the Cordilleran part of the United States.

Eigenstates of the (sp) 3P Multiplet for Two‐Electron Atoms and Phonon‐Induced Optical Transitions

Abstract: Eigenfunctions of L2, S2, J2, and Jz have been obtained for the (sp) 3P multiplet. Matrix elements of the linear electron-lattice interaction show how only Γ12 and Γ′25phonons relax selection rules to permit electric dipole transitions to 3P0 and 3P2 states. It is suggested that the 3P0 state may play a significant role in both absorption and emission processes for mercury-like impurities in alkali halides. Die Eigenfunktionen von L2, S2, J2 und Jz fur das (sp) 3P-Multiplett fur Zwei-Elektron-Atome werden berechnet. Die Matrixelemente der linearen Elektron–Gitter-Wechselwirkung zeigen, das nur Γ12- und Γ′25-Phononen zur Aufhebung von Auswahlregeln bei tragen, wodurch Dipolubergange zu 3P0- und 3P2-Zustanden ermoglicht werden. Es wird vorgeschlagen, das der 3P0-Zustand eine wichtige Rolle in Absorptions- und Emissionsprozessen fur Hg-ahnliche Storionen in Alkalihalogeniden spielen konnte.

Electronic Energy Bands, Excitons, and Plasmons in Lithium Fluoride Crystal

Abstract: The electronic band structure of lithium fluoride has been worked out using the mixed basis (MB) method recently proposed by one of the authors. Due to the effect of exchange, F− wave functions are rather compact, and mixing of plane waves in the valence band wave functions is unimportant. The minima of the conduction band occur at equivalent L-points in the Brillouin zone. Recent ultraviolet, soft X-ray, and electron energy loss spectra are analyzed in the light of the present calculation.

Soil Mechanics and Theorems of Limit Analysis

Abstract: An attempt is made to exhibit the plastic limit theorems in terms more familiar to the civil engineer. The interpretation of a continuous velocity region as the limiting case of infinitely many rigid blocks separated by surfaces of discontinuity provide an excellent technique for obtaining energy dissipation needed for upper bound calculations on plastic limit load. Similarly, the intuitive approach of imagining a pinconnected truss to support loads is shown to provide an excellent technique for obtaining lower bounds. Also a graphical procedure is introduced to eliminate much of the tedium associated with the construction of a stress field. The problems of the loaded truncated wedge and the wedge under unilateral pressure are treated as illustrative examples. Then the general strip foundation is solved. Upper and lower bounds are plotted and are seen to be rather close. Friction effects on the bearing capacity of foundations are also discussed.

Propagation of Sinusoidal Small‐Amplitude Waves in a Deformed Viscoelastic Solid. II

Abstract: The propagation of a sinusoidal wave of small amplitude in an initially isotropic viscoelastic solid, which is subjected to a static pure homogeneous deformation, is discussed The secular equation for a plane wave propagating an arbitrary direction with respect to the principal directions of the static deformation is derived The complex slownesses corresponding to propagation along the principal axes of the static strain are found Relations are obtained between these and the principal stresses associated with the static deformation, which generalize earlier formulas obtained by Ericksen for elastic materials

Residual stress and local buckling strength of steel columns

Abstract: This report presents the results of a study of the local buckling strength of steel columns. The effect of residual stress is given attention. The finite difference method was employed throughout the analysis and proved to be a suitable method for obtaining solutions for this type of problem. Numerical results are presented for plate buckling curves for plates with idealized residual stress distributions of various magnitudes. The boundary conditions of the plates are simply supported at the loading edges, and four combinations of free, simply supported and fixed at the unloaded edges. An illustrative result is also presented for the local buckling of a column cross section. The theoretical results were correlated with experimental results of eight pilot tests of square welded columns of ASTM A7 and A514 steels.

The LEADER retrieval system

Abstract: The LEADER system is a new service-oriented prototype designed to meet the retrieval needs of research scientists working within or in conjunction with the Center for the Information Sciences at Lehigh University. In the first part of this paper, we describe the major conceptual apparatus and principal design features of LEADER, while the second part contains a brief discussion of system implementation and user interaction.

The effect of D2O on fatigue-crack propagation in a high-strength aluminum alloy

Abstract: The rates of fatigue-crack propagation for a high-strength aluminum alloy (7075-T651) in an environment of D2O (99.98% purity) at room temperature were determined and compared with data obtained in high-purity argon and distilled water. The results showed that D2O caused a ten-fold increase in the rate of fatigue-crack propagation (up to 10−4 inch per cycle), which is equal to the increase caused by distilled water. These results lend further support to the previous observation that the rate controlling process for fatigue-crack propagation in this alloy (at rates below 10−4 inch per cycle) is the mechanical process of creating new crack surfaces, instead of either the transport of aggressive environment to the crack-tip or diffusion of hydrogen ions into the material ahead of the crack tip.

Curvature and the solution of eccentrically loaded columns

Abstract: THE ECCENTRICALLY LOADED COLUMN OF PERFECTLY PLASTIC MATERIAL HAS BEEN STUDIED ANALYTICALLY IN CONSIDERABLE DETAIL, BUT THE APPROACH TO DATE ALWAYS BEGINS BY SOLVING THE BASIC DIFFERENTIAL EQUATIONS FOR THE DEFLECTION CURVE. SIMPLE ILLUSTRATIONS DEMONSTRATE THAT THE CURVATURE CURVE OF THE COLUMN PLAYS EXACTLY THE SAME ROLE AS DEFLECTION DID, WHILE THE NECESSARY STEPS IN OBTAINING THE SOLUTIONS ARE REDUCED CONSIDERABLY. USING THIS CONCEPT, EXPRESSIONS FOR THE CURVATURE CURVE OF AN ECCENTRICALLY LOADED COLUMN OF RECTANGULAR CROSS-SECTION AT ALL STAGES OF PLASTICITY ARE DERIVED. IT IS SHOWN HOW SOLUTIONS FOR THE CRITICAL LOADS OF THE COLUMN MAY BE OBTAINED DIRECTLY FROM THIS APPROACH. THE ANALYTICALLY OBTAINED RESULTS OF COLUMN CURVES ARE COMPARED WITH THE EXISTING SOLUTIONS. /ASCE/

Transition temperatures and structural correlations for cellulose triesters

Abstract: Six homologs of the cellulose triester series were found to exhibit, in general, three second-order transitions as determined dilatometrically. A parallel study of torsional modulus versus temperature revealed one glass–rubber transition, which allowed molecular assignment of one of the above. The dependence of the remaining two transition temperatures on length of the ester group permits some speculation with regard to their origin. The glass–rubber and secondary transitions exhibit an inversion for cellulose trivalerate and higher homologs, the two secondary transitions occurring at temperatures higher than the glass–rubber transition. A possible explanation for this anomaly in terms of side-chain crystallization is discussed.