Topic
Deflection (engineering)
About: Deflection (engineering) is a research topic. Over the lifetime, 30862 publications have been published within this topic receiving 298849 citations.
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TL;DR: In this paper, the authors assess the practical value of Euler's theory of elastic instability and show that the theory can be extended to take account of plastic distortion, and by reference to a mechanical example they indicate what kind of result is to be expected when inaccuracies in the specimen or in the experimental apparatus introduce displacements which increase continuously with the load.
Abstract: 1. In the concluding section of a paper published in 1913 I endeavoured to assess the practical value of a theory of elastic instability. Two factors operate to impair agreement with experimental results: (1) the finite strength of actual materials, and (2) unavoidable imperfections of workmanship, which prohibit the realisation of its concept of a “critical load.” I showed how in one problem (the centrally loaded strut) theory can be extended to take account of plastic distortion; and by reference to a mechanical example I indicated what kind of result is to be expected when inaccuracies in the specimen or in the experimental apparatus introduce displacements which increase continuously with the load. Thus (to take the simplest example as an illustration) the well-known theory of Euler indicates that an initially straight and centrally loaded strut will remain straight while the end thrust is increased from zero up to a certain value Pc, but that when this “critical load” is attained the strut may bend into the form of a single bow, since this form can be maintained by end thrust acting alone . There is an “exchange of stabilities”, whereby for end thrusts exceeding the critical value the equilibrium of the straight form becomes unstable and that of the bent form stable. If on the other hand the strut is initially bowed, so that the central deflection has a small but finite value when the end thrust P is zero, this central deflection will increase with P, and experiment may be expected to yield some curve of the type shown by full lines in fig. 1, where l denotes the length and EI the (uniform) “flexural rigidity” of the strut. The smaller the initial deflection, the more closely will the experimental curve approach the limiting form OAB, which is the curve given by Euler’s analysis.
309 citations
TL;DR: It has been found that although the component of the stiffness matrix differentiating the enhanced stiffness model from the conventional one is not always positive definite, the resulting stiffness matrix can still be positive definite.
Abstract: This paper presents the enhanced stiffness modeling and analysis of robot manipulators, and a methodology for their stiffness identification and characterization. Assuming that the manipulator links are infinitely stiff, the enhanced stiffness model contains: 1) the passive and active stiffness of the joints and 2) the active stiffness created by the change in the manipulator configuration, and by external force vector acting upon the manipulator end point. The stiffness formulation not accounting for the latter is known as conventional stiffness formulation, which is obviously not complete and is valid only when: 1) the manipulator is in an unloaded quasistatic configuration and 2) the manipulator Jacobian matrix is constant throughout the workspace. The experimental system considered in this study is a Motoman SK 120 robot manipulator with a closed-chain mechanism. While the deflection of the manipulator end point under a range of external forces is provided by a high precision laser measurement system, a wrist force/torque sensor measures the external forces. Based on the experimental data and the enhanced stiffness model, the joint stiffness values are first identified. These stiffness values are then used to prove that conventional stiffness modeling is incomplete. Finally, they are employed to characterize stiffness properties of the robot manipulator. It has been found that although the component of the stiffness matrix differentiating the enhanced stiffness model from the conventional one is not always positive definite, the resulting stiffness matrix can still be positive definite. This follows that stability of the stiffness matrix is not influenced by this stiffness component. This study contributes to the previously reported work from the point of view of using the enhanced stiffness model for stiffness identification, verification and characterization, and of new experimental results proving that the conventional stiffness matrix is not complete and is valid under certain assumptions.
307 citations
TL;DR: In this article, the dynamic response of initially stressed functionally graded rectangular thin plates subjected to partially distributed impulsive lateral loads and without or resting on an elastic foundation is investigated, and the formulations are based on classical small deflection plate theory, and account for the plate-foundation interaction effects by a two-parameter model.
304 citations
TL;DR: In this article, a logarithmic flow formula for open channels is valid for flow over a roughness cover made up of flexible plastic strips, and three regimes of boundary behavior are observed for flexible plastic roughness, leading to two resistance functions.
Abstract: The logarithmic flow formula for open channels is valid for flow over a roughness cover made up of flexible plastic strips. The deflection of such roughness is an important parameter as the deflection directly influences the relative roughness. Dimensionless parameters which relate the amount of bending to the stiffness of the roughness and the boundary shear are defined. Three regimes of boundary behavior are observed for flexible plastic roughness, leading to two resistance functions. The flexible plastic roughness is produced by affixing thin plastic strips of various thickness to the bed of a flume. The flow of water over flexible plastic strips simulates flow over a vegetative channel lining.
301 citations