# Showing papers in "Journal of Applied Mechanics in 1972"

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TL;DR: The numerical solution of problems of elastic stability through the use of the iteration method of Newton is examined in this paper, where it is found that if the equations of equilibrium are completed by a simple auxiliary equation, problems governed by a snapping condition can, in principle, always be calculated as long as the problem at hand is properly formulated.
Abstract: The numerical solution of problems of elastic stability through the use of the iteration method of Newton is examined. It is found that if the equations of equilibrium are completed by a simple auxiliary equation, problems governed by a snapping condition can, in principle, always be calculated as long as the problem at hand is properly formulated. The effectiveness of the proposed procedure is demonstrated by means of an elementary example.

672 citations

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556 citations

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, N. Levy1
TL;DR: In this paper, an elastic plate with part-through surface crack, determining stress intensity factor for remote tensile and bending loads was used to calculate the stress intensity for bending loads.
Abstract: Elastic plate with part-through surface crack, determining stress intensity factor for remote tensile and bending loads

472 citations

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TL;DR: In this paper, the uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids was studied under plane-strain conditions.
Abstract: The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.

293 citations

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TL;DR: In this article, a simple differential equation is derived to describe constrained-layer damping in nonsymmetric sandwich plates and beams composed of isotropic and homogeneous layers, and the natural boundary conditions related to this equation are determined.
Abstract: A simple differential equation is derived to describe constrained-layer damping in nonsymmetric sandwich plates and beams composed of isotropic and homogeneous layers. The natural boundary conditions related to this equation are determined and some typical numerical results obtained by this equation are given. The equation is valid within the linear theories of elasticity and viscoelasticity in the absence of any constraints on thicknesses, positions, symmetries, and densities of the layers.

202 citations

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195 citations

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188 citations

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173 citations

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139 citations

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TL;DR: In this article, the analysis of the free vibrations of an arbitrary structure in terms of component modes is presented based upon the use of the normal, free-free modes of the components in a Rayleigh-Ritz analysis with the constraint or continuity conditions.
Abstract: A method for the analysis of the free vibrations of an arbitrary structure in terms of component modes is presented based upon the use of the normal, free-free modes of the components in a Rayleigh-Ritz analysis with the constraint or continuity conditions

136 citations

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TL;DR: In this paper, a large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading, and does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading.
Abstract: : A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of dislocation dynamics A numerical scheme for calculating deformations is developed and applied to a thick walled spherical shell under internal pressure Various numerical examples are presented (Author)

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TL;DR: Axisymmetric plastic deformation of imperfection sensitive spherical shell after elastic buckling, considering load carrying capacity as mentioned in this paper, considering load-carrying capacity of spherical shell, is considered.
Abstract: Axisymmetric plastic deformation of imperfection sensitive spherical shell after elastic buckling, considering load carrying capacity

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TL;DR: In this article, the critical load for flutter was found independent of the foundation modulus, which characterizes the Winkler-type elastic imbedding, and the frequency of vibration of the beam increases with increasing base modulus but the magnitude of critical load is not affected.
Abstract: Discussion of a new aspect in the behavior of a cantilevered beam on an elastic foundation subjected to a follower force at its free end. The critical load for flutter is found to be independent of the foundation modulus which characterizes the Winkler-type elastic imbedding. The frequency of vibration of the beam increases with increasing foundation modulus, but the magnitude of the critical load is not affected. This result is valid for any 'tangency coefficient' value.

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, J. Duffy1
TL;DR: In this article, a modification of the torsional split Hopkinson bar is described, which superimposes a high rate of shear strain on a slower'static' rate.
Abstract: : A modification of the torsional split Hopkinson bar is described which superimposes a high rate of shear strain on a slower 'static' rate. The 'static' rate of 0.00005/sec is increased to 850/sec at a predetermined value of plastic strain by the detonation of small explosive charges; the rise time of the strain rate increment is about 10 microseconds. During deformation at the dynamic rate, direct measurement is made of the excess stress above the maximum static stress attained. Results for 1100-0 aluminum show that the initial response to the strain rate increment is elastic, followed by yielding behavior reminiscent in appearance to an upper yield point. The magnitude of the stress measured at this yield point is always less than the stress obtained at the same strain in a wholly dynamic test; as the stress-strain curve asymptotically. It is concluded that the material behavior is a function of strain, strain rate and strain rate history. (Author)

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TL;DR: Buckling of axially compressed circular cylindrical shells with localized or random axisymmetric imperfections, deriving asymptotic approximation formulas for stress calculation.
Abstract: Buckling of axially compressed circular cylindrical shells with localized or random axisymmetric imperfections, deriving asymptotic approximation formulas for stress calculation

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TL;DR: In this paper, the laminar boundary-layer equations were solved for incompressible flow past a parabola at angle of attack, and it was concluded that a singularity is always present at separation independent of the mildness of the pressure gradient at that point.
Abstract: : The laminar boundary-layer equations were solved for incompressible flow past a parabola at angle of attack. Such flow experiences a region of adverse pressure gradient and thus can be employed to study the boundary-layer separation process. The present solutions were obtained numerically using both implicit and Crank Nicholson type difference schemes. It was found that in all cases the point of vanishing shear stress (the separation point) displayed a Goldstein type singularity. Based on this evidence, it is concluded that a singularity is always present at separation independent of the mildness of the pressure gradient at that point. (Author)

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, Y. Chen1

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TL;DR: In this article, the authors considered the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory.
Abstract: The paper considers the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory. The technically most significant aspect of the work has to do with the analysis of the effect of anisotropy of the material, which is associated with previously not determined modes of coupling between stretching, bending, and twisting. Use of the general formulas of the theory is illustrated for a class of shells consisting of an 'ordinary' material (unable to support stress moments with axes normal to the middle surface of the shell, and unable to undergo transverse shear deformation). Here explicit formulas are obtained for certain types of open as well as of closed-cross-section beams.