共查询到20条相似文献,搜索用时 15 毫秒
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The classical brachistochrone problem was originally proposed by Johann Bernoulli more than 300 years ago, and is still one of the most elegant problems in modern mathematics. This paper examines a generalisation of the original brachistochrone problem by the inclusion of a non-conservative force in the form of Coulomb friction. Solutions to this problem are found using an evolutionary computational technique based on Darwinian natural selection and survival of the fittest. These evolutionary solutions tend to indicate that as friction is introduced the optimum curves develop from cycloidal (the analytical solution for the conservative problem) toward straight lines. The flexibility of the evolutionary method to optimise for other objectives is then discussed. 相似文献
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I. I. Argatov 《Journal of Applied Mechanics and Technical Physics》2001,42(6):1064-1072
The paper considers the problem of onesided frictionless compression of plane elastic bodies that are initially in contact with each other at a point. The first terms of an asymptotic solution of the problem are constructed by the method of joined asymptotic expansions. Determination of the approach of the bodies as a function of the pressing force reduces to calculating socalled of local compliance. The problems of contact of an elastic ring and elastic circular disks with punches and an elastic disk compressed between two elastic strips are considered. An asymptotic model for the quasistatic collision of plane elastic bodies is proposed. 相似文献
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We examine experimentally and theoretically the effect of frictional shakedown of a three-dimensional elastic rolling contact. Small oscillations of the local normal forces lead to incremental sliding processes within the area of contact. Consequently, this causes a macroscopic slip motion of the two contacting bodies. If the oscillation amplitude is sufficiently small, the frictional slip ceases after the first few loading periods and a safe shakedown occurs. Otherwise the slip motion is continued and the contact fails. 相似文献
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The efficiency of a geometric multigrid method for solving the tire rolling problem is studied. The optimal components of
this method are chosen. A good convergence of the method is shown for the systems that are large from the practical point
of view. Its distinctive feature is a grid refinement in the circumferential direction only. 相似文献
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The problem of finding the plane supporting curve (brachistochrone) along which a heavy particle released from rest at the given starting point slides with dry (Coulomb) friction and reaches the given destination point in least time, is stated as a variational isoperimetrical problem. The finite parametric equations of the extremal curve are obtained. This curve is the sought-for brachistochrone if the solution of the problem exists. Several numerical examples are given. 相似文献
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T. A. ANGELOV 《应用数学和力学(英文版)》2013,34(11):1361-1372
A steady-state, rigid-plastic rolling problem for temperature and strain-rate dependent materials with nonlocal friction is considered. A variational formulation is derived, coupling a nonlinear variational inequality for the velocity and a nonlinear vari- ational equation for the temperature. The existence and uniqueness results are obtained by a proposed fixed point method. 相似文献
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V. P. Legeza 《International Applied Mechanics》2008,44(12):1430-1436
The motion of a heavy homogeneous cylinder is considered as rolling without slipping along an unknown curve. A functional
in the form of the total time of rolling is found and minimized by solving a variational problem. The algebraic equation of
the quickest-descent directrix is derived in parametric form
Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 131–138, December 2008. 相似文献
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We use three complex potentials to solve the compression problem for a thin circular plate loaded along the external contour. We present the solution in series form and compare the obtained solution with the classical solution. 相似文献
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M. V. Gavrilkina V. V. Glagolev A. A. Markin 《Journal of Applied Mechanics and Technical Physics》2007,48(4):571-576
This paper considers a model for the opening-mode fracture separation process based on the introduction of an interaction
layer. This layer is defined as the region of localization of the fracture process. The stress-strain state of the layer material
is uniform in the cross section of the layer. A study is made of the deformation of a double-cantilever beam weakened by a
notch whose width is equal to the thickness of the interaction layer. The problem is solved in a linearly geometrical approximation.
The thickness of the interaction layer is estimated, and a method for solving the formulated problem is proposed.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 121–127, July–August, 2007. 相似文献
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