Showing papers in "Journal of Applied Mechanics in 1970"
3,823 citations
TL;DR: In this article, a bending theory for anisotropic laminated plates developed by Yang, Norris, and Stavsky is investigated, which includes shear deformation and rotary inertia in the same manner as Mindlin's theory for isotropic homogeneous plates.
Abstract: : A bending theory for anisotropic laminated plates developed by Yang, Norris,and Stavsky is investigated. The theory includes shear deformation and rotary inertia in the same manner as Mindlin's theory for isotropic homogeneous plates. The governing equations reveal that unsymmetrically laminated plates display the same bending-extensional coupling phenomenon found in classical laminated plate theory based on the Kirchhoff assumptions. Solutions are presented for bending under transverse load and for flexural vibration frequencies of symmetrical and nonsymmetrical laminates. Good agreement is observed in numerical results for plate bending as compared to exact solutions obtained from classical elasticity theory. For certain fiber reinforced composite materials, radical departure from classical laminated plate theory is indicated. (Author-PL)
1,123 citations
TL;DR: In this paper, a general kinematical relation is developed between the macroscopic inelastic strain tensor and microstructural slip displacements, as modeled either by continuum shearing on crystallographic planes of individual grains or by the motion of discrete dislocation lines.
Abstract: The paper is concerned with the structure of multiaxial stress-strain relations in timedependent metal plasticity, as for transient creep and rate sensitive yielding. First. a general kinematical relation is developed between the macroscopic inelastic strain tensor and microstructural slip displacements, as modeled either by continuum shearing on crystallographic planes of individual grains or by the motion of discrete dislocation lines. It is assumed that at any given slipped state, the rate of slipping on a particular system is governed by the resolved shear stress on that system (or by the local \"forces\" on dislocation lines). 'This leads to the primary result of the paper: Components of the macroscopic inelastic strain rate tensor are deriz!able, at each instant in the course of deformation, from a potential function of stress, General features of the flow potential surfaces in stress space are discussed, and some specific functional forms are examined, Linear viscoelasticity and tirre-independent plasticity are developed as limiting cases of the flow potential formulatic!, and the appropriateness of a potential function for stationary creep is discussed,
307 citations
TL;DR: In this paper, a three-zone scheme is proposed to model the mean flow structure during drag reduction, which is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile at the limits of zero and maximum drag reductions.
Abstract: The maximum drag reduction in turbulent pipe flow of dilute polymer solutions is ultimately limited by a unique asymptote described by the experimental correlation: f−1/2=19.0 log10(NRef1/2)−32.4 The semilogarithmic mean velocity profile corresponding to and inferred from this ultimate asymptote has a mixing-length constant of 0.085 and shares a trisection (at y+ ∼ 12) with the Newtonian viscous sublayer and law of the wall. Experimental mean velocity profiles taken during drag reduction lie in the region bounded by the inferred ultimate profile and the Newtonian law of the wall. At low drag reductions the experimental profiles are well correlated by an “effective slip” model but this fails progressively with increasing drag reduction. Based on the foregoing a three-zone scheme is proposed to model the mean flow structure during drag reduction. In this the mean velocity profile segments are (a) a viscous sublayer, akin to Newtonian, (b) an interactive zone, characteristic of drag reduction, in which the ultimate profile is followed, and (c) a turbulent core in which the Newtonian mixing-length constant applies. The proposed model is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile, respectively, at the limits of zero and maximum drag reductions.
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TL;DR: In this paper, a straight beam with fixed ends, excited by the periodic motion of its supporting base in a direction normal to the beam span, was investigated analytically and experimentally.
Abstract: A straight beam with fixed ends, excited by the periodic motion of its supporting base in a direction normal to the beam span, was investigated analytically and experimentally. By using Galerkin’s method (one mode approximation) the governing partial differential equation reduces to the well-known Duffing equation. The harmonic balance method is applied to solve the Duffing equation. Besides the solution of simple harmonic motion (SHM), many other branch solutions, involving superharmonic motion (SPHM) and subharmonic motion (SBHM), are found experimentally and analytically. The stability problem is analyzed by solving a corresponding variational Hill-type equation. The results of the present analysis agree well with the experiments.
98 citations
TL;DR: In this article, the stability of simply supported conical shells under axial compression was investigated for four different sets of in-plane boundary conditions with a linear Donnell type theory, and the first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure.
Abstract: : The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expressions for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the 'classical' ones are obtained for all but the stiffest simple supports SS4 (v = u = o). The low buckling loads for 'classical' simple supports SS3 are confirmed by two different methods of analysis, a closed form solution in Hankel functions and a finite difference solution. Except for short shells, the effects do not depend on the length of the shell. Buckling under combined axial compression and external or internal pressure is studied and interaction curves were calculated for the 4 sets of in-plane boundary conditions. (Author)
TL;DR: In this paper, the governing system of differential equations for the linear problem of the transient interaction of plane acoustic waves and a submerged elastic cylindrical shell is transformed into a system of Volterra integral equations of the second kind.
Abstract: The governing system of differential equations for the linear problem of the transient interaction of plane acoustic waves and a submerged elastic cylindrical shell is transformed into a system of Volterra integral equations of the second kind. The integral equations are solved by a step-by-step integration scheme and numerical results to the problem are obtained exactly within the limit of series solution imposed by the Gibb’s phenomenon and within the limit of numerical truncation and roundoff errors. Detailed features of the transient response of the shell were revealed.
TL;DR: In this article, the authors extended the algorithm used by the author previously in the solution for the elastic quarter plane, and evaluated the stress components on the top and side surfaces of the quarter space for four values of Poisson's ratio mu = 1 2, 1 3, 1 4, 1 6 and 0.
Abstract: : The algorithmic procedure used by the author previously in the solution for the elastic quarter plane, is extended in this paper for the elastic quarter space. Values of the stress components were evaluated on the top and side surfaces of the quarter space for four values of Poisson's ratio mu = 1/2, 1/3, 1/6 and 0. (Author)
TL;DR: In this article, an analysis of stresses and deflections produced in a thin, complete spherical shell when it is compressed between two parallel rigid plates is presented, and the deformation state at which the contact region buckles is given.
Abstract: Abstract : The paper presents an analysis of stresses and deflections produced in a thin, complete spherical shell when it is compressed between two parallel rigid plates. The analysis accounts for finite deflections and rotations, but assumes that the material remains linearly elastic throughout the deformation. It is also assumed that the region of the shell which is in contact with the plate remains flat. The deformation state at which the contact region buckles is given. (Author)
TL;DR: In this article, low gravity fuel sloshing in axisymmetric rigid tank, calculating oscillations by modified Galerkin method, calculated oscillations using modified GCL method.
Abstract: Low gravity fuel sloshing in axisymmetric rigid tank, calculating oscillations by modified Galerkin method
TL;DR: Incompressible laminar flow in entrance region of rectangular duct allowing direct computation of eigenvalues as mentioned in this paper, allowing direct computations of the eigenvalue of a function.
Abstract: Incompressible laminar flow in entrance region of rectangular duct allowing direct computation of eigenvalues
TL;DR: Continuous structural systems stability under random load excitation from linear PDEs of motion was studied in this article, where the authors showed that the stability of structural systems was not affected by random load loads.
Abstract: Continuous structural systems stability under random load excitation from linear partial differential equations of motion