# Showing papers in "Journal of Applied Mechanics in 1962"

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872 citations

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658 citations

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TL;DR: By repeating this process in small steps, a control variable program that minimizes one quantity and yields specified values of other terminal quantities can be approached as closely as desired.

Abstract: SYSTEMATIC and rapid steepest-ascent numerical procedure is described for determining optimum programs for nonlinear systems with terminal constraints. The procedure uses the concept of local linearization around a nominal (nonoptimum) path. The effect on the terminal conditions of a small change in the control variable program is determined by numerical integration of the adjoint differential equations for small perturbations about the nominal path. Having these adjoint (or influence) functions, it is then possible to determine the change in the control variable program that gives maximum increase in the pay-off function for a given mean-square perturbation of the control variable program while simultaneously changing the terminal quantities by desired amounts. By repeating this process in small steps, a control variable program that minimizes one quantity and yields specified values of other terminal quantities can be approached as closely as desired. Three numerical examples are presented: (a) The angle-of-attack program for a typical supersonic interceptor to climb to altitude in minimum time is determined with and without specified terminal velocity and heading. (6) The angle-of-attack program for the same interceptor to climb to maximum altitude is determined, (c) The angle-of-attack program is determined for a hypersonic orbital glider to obtain maximum surface range starting from satellite speed at 300,000 ft altitude.

446 citations

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Brown University

^{1}TL;DR: The second edition of the second edition as discussed by the authors provides a comprehensive overview of the structural stability and dynamics of rigid and flexible structures, including structural buckling, bending, and torsion.

Abstract: Chaos in Structural MechanicsUniversity of Michigan Official PublicationTheory and Analysis of Elastic Plates and Shells, Second EditionFoundations of the Nonlinear Theory of ElasticityHistory of Strength of MaterialsFlexural-Torsional Buckling of StructuresTheory of elasticityStability of Elastic StructuresMechanics of SolidsOn the Stability of Elastic EquilibriumTheory of Elastic StabilityThe Nonlinear Theory of Elastic ShellsMaterials Selection in Mechanical DesignStability Problems in Applied MechanicsProbabilistic Methods in the Theory of StructuresTheory of Elastic StabilityPlate Stability by Boundary Element MethodSemiconductor Nanowires II: Properties and ApplicationsApplied Plasticity, Second EditionFundamentals of Structural StabilityGeneral RegisterA Translation of the Stability of Elastic EquilibriumMechanics of Composite MaterialsA Treatise on the Mathematical Theory of ElasticityElementary Continuum Mechanics for EveryoneAnnouncementStability, Bifurcation and Postcritical Behaviour of Elastic StructuresStability of StructuresApplied Mechanics ReviewsNon-Classical Problems in the Theory of Elastic StabilityNonlinear Theory of Elastic StabilityBuckling of Laminated Composite Plates and Shell PanelsTheory Of Plates & Shells 2EAn Analytical Procedure for Predicting the Two-dimensional Impact Dynamics of a Spacecraft Landing GearTheory Of Elastic Stability 2EWave Motion in Elastic SolidsA General Theory of Elastic StabilityTheory of Elastic StabilityMechanics of StructuresProceedings of the Second International Conference on Structural Stability and Dynamics Resoundingly popular in its first edition, the second edition of Mechanics of Structures: Variational and Computational Methods promises to be even more so, with broader coverage, expanded discussions, and a streamlined presentation. The authors begin by describing the behavior of deformable solids through the differential equations for the strength of materials and the theory of elasticity. They next introduce variational principles, including mixed or generalized principles, and derive integral forms of the governing equations. Discussions then move to computational methods, including the finite element method, and these are developed to solve the differential and integral equations. New in the second edition: A one-dimensional introduction to the finite element method, complete with illustrations of numerical mesh refinement Expansion of the use of Galerkin's method. Discussion of recent developments in the theory of bending and torsion of thin-walled beams. An appendix summarizing the fundamental equations in differential and variational form Completely new treatment of stability, including detailed examples Discussion of the principal values of geometric properties and stresses Additional exercises As a textbook or as a reference, Mechanics of Structures builds a unified, variational foundation for structure mechanics, which in turn forms the basis for the computational solid mechanics so essential to modern engineering.Stability Problems in Applied Mechanics starts with the stability problems in statics. The example of buckling of columns is studied through Euler method followed by the energy method, based on Lagrange-Dirichlet theorem. Snap buckling, instability of shape, buckling due to follower load are also discussed. Insufficiency of static analysis for instability is clearly brought out and buckling problems are revisited from the point of view of dynamics. The next chapter provides the theory of Dynamical System and the foundations of bifurcation theory and explains the problems discussed in the previous chapter in the light of these unified mathematical concepts. This mathematical basis is then applied in the next chapter to investigate the stability problems encountered in dynamics of particle, rigid and flexible bodies. The last chapter explains the emergence of length scale and pattern formation as a consequence of instability in fluid, thermal and diffusion systems. Different notions of stability and the analysis of nonlinear states are briefly included in two appendices.A crucial element of structural and continuum mechanics, stability theory has

405 citations

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402 citations

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TL;DR: In this article, a review of the literature on fatigue testing is presented, which is aimed at being helpful to investigators trying to select the testing machine most suitable to their purposes, whereas it may be of minor importance whether he is to use a mechanical or an electrical machine; the abovementioned sequence will therefore be used for the classification system.

Abstract: r (d) Mechanical propert, Defiexion method, brittle coating method, bonded wire technique, moist coating method, vibration methods involving frequency and damping or damping changes during fatigue test. (e) Penetrating radiation tests. (f) Ultrasonic testing Reflection or through transmission methods. (g) Magneto-inductive tests. (h) Electrical tests. Electrical resistance or tribo-electrical methods. Destructive Tests (a) Heat tinting method (b) Chemical etching method (c) Recrystallization method (d) Damage line method (e) Impact method (f) Tensile pulling (g) Slow-bend test (h) Sectioning techniques A review ofexperimental data on the initiation and propagation of fatigue cracks in test specimens is given in Part 2 of the reference cited. For more detailed description of the various methods reference is made to the bibliography of the report by Demer containing about 200 references, and to the bibliography below. Fatigue testing machines may be classified from different viewpoints such as: purpose of the test, type of stressing, means of producing the load, operation characteristics, type of load, etc. The most appropriate sequence of these alternatives for building up a classification system depends upon who is going to use it. One system may be preferred by the manufacturer of testing machines and another by the research worker. The attitude of the latter will be taken in this chapter, which is aimed at being helpful to investigators trying to select the testing machine most suitable to their purposes. For this same reason it was decided to avoid detailed descriptions of individual machines, but to provide an ample number of references. Comprehensive reviews of the whole field are to be found in the following The purpose of the investigation is the most important item for the investigator, and he generally knows, when starting his investigation, what type of stressing he is going to use, whereas it may be of minor importance whether he is to use a mechanical or an electrical machine; the above-mentioned sequence will therefore be used for the classification system. The purpose of the test will be chosen as the basis of the first-orderdivision, the type of stressing as that of the second-order division, and the design characteristic as that of the third-order division. Each of these classes may be subdivided according to the operating characteristic, i.e. the machines may be either of the resonant type, which operate at or close to the natural frequency ofthe mass-spring system, or ofthe non-resonant type which do not. A further basis …

367 citations

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TL;DR: In this article, a system of n masses, equal or not, interconnected by nonlinear "symmetric" springs, and having n degrees of freedom is examined, and the problem of finding normal modes is reduced to a geometrical maximum-minimum problem in an n-space of known metric.

Abstract: A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the coupled equations of motion to n uncoupled equations whose natural frequencies can always be found by a single quadrature. An infinite class of systems, of which the linear system is a member, has been isolated for which the frequency amplitude can be found in closed form.

337 citations

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TL;DR: In this paper, the authors considered the problem of determining what shape column has the largest critical buckling load of all columns of given length and volume, assuming that all cross sections of the column are similar and similarly oriented.

Abstract: We consider the problem of determining what shape column has the largest critical buckling load of all columns of given length and volume This problem was previously solved for a column hinged (pinned) at both ends We solve it for columns clamped at one end and clamped, hinged, or free at the other end, assuming that all cross sections of the column are similar and similarly oriented We also prove that the column previously obtained in the hinged-hinged case is actually strongest and not merely stationary Graphs of the areas of the strongest columns as functions of distance along the columns are given for the various cases The results are also expressed as isoperimetric inequalities for eigenvalues of second-order ordinary differential equations with various boundary conditions Certain additional inequalities of this type are also obtained

239 citations

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232 citations

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230 citations

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TL;DR: In this paper, the authors studied the propagation of mechanical and thermal disturbances in a half-space by means of the solution of some transient boundary-value problems according to the coupled thermoelastic theory.

Abstract: : The propagation of mechanical and thermal disturbances in a half-space is studied by means of the solution of some transient boundary-value problems according to the coupled thermoelastic theory. The problems considered are those of a half-space under step time-variations of strain, temperature or stress uniformly distributed over the free surface. The coupled solution of Danilovskaya's problem is thus included. The solution is obtained by the use of Fourier sine transforms, and the behaviors at short and long times, as well as the propagation of discontinuities, are studied. The principal differences between the present results and analogous ones derived by neglecting thermoelastic coupling are found to be: (1) mechanical discontinuities are not propagated unchanged in magnitude, but decrease exponentially with time because of the effect of thermoelastic damping (though the speed of their propagation is unaltered), (2) mechanical responses occur instantaneously at all points of the body (but are very small at large distances from the free surface), and (3) the temperature distribution is still continuous but exhibits jumps either in its first or second derivative. (Author)

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TL;DR: In this paper, it is shown that the boundary tangential displacement distribution is not symmetric about the rolling cylinder and, in fact, the point under the cylinder axis is displaced in the opposite direction to the motion.

Abstract: boundary displacement by integrating the line load solution, which requires analysis similar to that of Equations (36)-(38). T o obtain quantitative values, a realistic viscoelastic model should be used throughout the solution—in contrast to the paper where a combination of the "standard linear sol id" and the "constant loss tangent mode l " were used to illustrate the method. I t is easily seen that the boundary tangential displacement distribution is not symmetric about the rolling cylinder, and, in fact, the point under the cylinder axis is displaced in the opposite direction to the motion, but this is chiefly due to the inelastic properties of the material, here a " m e m o r y , " and not to the lack of symmetry in the pressure distribution which the paper shows is very small. In contrast to plastic or viscoplastie materials, the displacements in the viscoelastic material recover completely after the cylinder has rolled on sufficiently far.

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TL;DR: In this article, the effects of an axial magnetic field on the flow and heat transfer about a rotating disk were analyzed, and it was found that the presence of the magnetic field significantly decreases the flow velocities; but increases the torque required to maintain steady rotation of the disk.

Abstract: The effects of an axial magnetic field on the flow and heat transfer about a rotating disk were analyzed. It was found that the presence of the magnetic field significantly decreases the flow velocities; but increases the torque required to maintain steady rotation of the disk. The heat transfer was also decreased by the magnetic field, with greater reductions occurring for low Prandtl number fluids. (auth)

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TL;DR: In this paper, the authors present a set of basic techniques and practical applications for the optimal design of mechanical elements in realistic design settings, including simple illustrative examples and practical exercises.

Abstract: Updated and expanded new edition of this unique book of basic techniques and practical applications (including important new developments) for the optimal design of mechanical elements in realistic design settings. Reviews necessary background information, explains the method of optimum design (MOD) and automated optimal design (AOD), and covers optimization problems both for simple and complex mechanical elements. Many simple illustrative examples and practical exercises.

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TL;DR: In this paper, the problem of dynamic stresses and displacements around a cavity and rigid inclusion of arbitrary density is examined for an elastic medium during the passage of a plane shear wave, and it is shown that the dynamic stresses are dependent upon the incident wave number and Poisson's ratio of the medium.

Abstract: : The problem of dynamic stresses and displacements around a cavity and rigid inclusion of arbitrary density is examined for an elastic medium during the passage of a plane shear wave. In the cavity case, the dynamic stresses and displacements are found to be dependent upon the incident wave number and Poisson's ratio of the medium. In the rigid inclusion case, it is found that dynamic stresses and the rigid body rotation and translation are dependent upon the incident wave numbers, the Poisson's ratio, and the density ratio of the medium and the insert. Close coupling is observed between the stresses and the rigid body motion of the insert.

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TL;DR: In this article, the mean square deflections, slopes, bending moments and shear forces were compared for four different dynamical models with three different damping mechanisms, subjected to a distributed transverse loading process which was uncorrelated space-wise and which was either ideally, white time-wise or band-limited with an upper cut-off frequency.

Abstract: : The mean square deflections, slopes, bending moments and shear forces were compared for 4 different dynamical models with 3 different damping mechanisms, subjected to a distributed transverse loading process which was uncorrelated space-wise and which was either ideally, white time-wise or band-limited with an upper cut-off frequency. The dynamic models were the Bernoulli-Euler beam, the Timoshenko beam and two intermediate models, the Rayleigh beam, and a beam which has the shear flexibility of the Timoshenko beam but not the rotatory inertia. The damping mechanisms were transverse viscous damping, rotatory viscous damping, and Voigt visco-elasticity. Many of the mean square response quantities were finite when the excitation was ideally white (i.e., when the input has infinite mean square), however some of the responses were unbounded. For these cases the rate of growth of the response was obtained as the cut-off frequency of the excitation was increased. (Author)

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