Topic

# Deflection (engineering)

About: Deflection (engineering) is a(n) research topic. Over the lifetime, 30862 publication(s) have been published within this topic receiving 298849 citation(s).

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TL;DR: In this article, a modified version of the Newton-Raphson method is proposed to overcome limit points in the finite element method with a fixed load level and a constraint equation.

Abstract: Riks [1] has recently proposed a new solution procedure for overcoming limit points. To this end, he adds, to the standard equilibrium equations, a constraint equation fixing the length of the incremental load step in load/deflection space. The applied load level becomes an additional variable. The present paper describes a means of modifying Rik's approach so that it is suitable for use with the finite element method. The procedure is applied in conjunction with the modified Newton-Raphson method in both its original and accelerated forms. The resulting techniques not only allow limit points to be passed, but also, improve the convergence characteristics of the unconstrained iterative procedures. Illustrative examples include the large deflection analysis of shallow elastic shells and the collapse analysis of a stiffened steel diaphragm from a box-girder bridge.

1,491 citations

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TL;DR: In this paper, the authors calculated the thermal noise of a cantilever with a free end by considering all possible vibration modes of the cantilevers and showed that if the end is supported by a hard surface, no thermal fluctuations of the deflection are possible.

Abstract: Thermal fluctuations of the cantilever are a fundamental source of noise in atomic force microscopy. We calculated thermal noise using the equipartition theorem and considering all possible vibration modes of the cantilever. The measurable amplitude of thermal noise depends on the temperature, the spring constant K of the cantilever and on the method by which the cantilever deflection is detected. If the deflection is measured directly, e.g. with an interferometer or a scanning tunneling microscope, the thermal noise of a cantilever with a free end can be calculated from square root kT/K. If the end of the cantilever is supported by a hard surface no thermal fluctuations of the deflection are possible. If the optical lever technique is applied to measure the deflection, the thermal noise of a cantilever with a free end is square root 4kT/3K. When the cantilever is supported thermal noise decreases to square root kT/3K, but it does not vanish.

1,434 citations

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1,329 citations

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TL;DR: In this article, a fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles, based on a determination of the initial tilt and the maximum twist of the crack front between particles.

Abstract: A fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles. The analysis is based on a determination of the initial tilt and the maximum twist of the crack front between particles, which provides the basis for evaluating the deflection-induced reduction in crack driving force. Features found to be important in determining the toughness increase include the volume fraction of second phase, the particle morphology and aspect ratio, and the distribution of interparticle spacing. Predictions are compared with expected surface area increases.

1,212 citations

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TL;DR: In this paper, the authors examined the competition between deflection and penetration when the materials on either side of the interface are elastic and isotropic and determined the range of interface toughness relative to bulk material toughness which ensures that cracks will be deflected into the interface.

Abstract: A crack impinging an interface joining two dissimilar materials may arrest or may advance by either penetrating the interface or deflecting into the interface. The competition between deflection and penetration is examined in this paper when the materials on either side of the interface are elastic and isotropic. The energy release rate for the deflected crack is compared with the maximum energy release rate for a penetrating crack. The results can be used to determine the range of interface toughness relative to bulk material toughness which ensures that cracks will be deflected into the interface.

1,106 citations