Variational method of crack-contour location for three-dimensional problem with unilateral constraints

1980 ◽  
Vol 38 (5) ◽  
pp. 573-580
Author(s):  
V. I. Kerchman
Keyword(s):  
Variational Method ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Unilateral Constraints ◽  
Crack Contour

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

Some Remarks on the Behaviour of Surface Source Distributions near the Edge of a Body

1973 ◽  
Vol 24 (1) ◽  
pp. 25-33
Author(s):  
J W Craggs ◽  
K W Mangler ◽  
M Zamir
Keyword(s):  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Symmetric Case ◽  
The Body ◽  
Dimensional Problem ◽  
Surface Source ◽  
Asymmetric Case ◽  
Main Flow Direction ◽  
Flow Plane

SummaryWhen the incompressible potential flow past a three-dimensional body is represented by source distributions on the body surface, these source distributions have singularities near an edge or corner, for example á trailing edge of a wing or the (unfaired) intersection of a body and a wing. The nature of these singularities is discussed. When assuming slow variations of the geometry in the main flow direction we can consider a two-dimensional problem in the cross-flow plane. Here the tangential velocities and source distributions are proportional to certain powers of the distance from the corner. For example at a convex right-angled corner these powers are − ⅓ in the asymmetric case (the bisector is a potential line) and ⅓ in the symmetric case (the bisector is a streamline) for both sources and tangential velocities. At a concave right-angled corner the corresponding values for the source distributions are ⅓ (asymmetric case) and − ⅓ (symmetric case) whereas they are 1 and 3 respectively for the tangential velocities.

Dynamics of a Vibratory Feeder

1997 ◽  
Author(s):  
Peter Wolfsteiner ◽  
Friedrich Pfeiffer
Keyword(s):  
Coulomb Friction ◽  
Three Dimensional ◽  
Automatic Assembly ◽  
Trial And Error ◽  
Unilateral Constraints ◽  
Multiple Impacts ◽  
Three Dimensional Model ◽  
Transportation Process ◽  
Feeding Process ◽  
Small Parts

Abstract The most common devices used to feed small parts in an automatic assembly framework are vibratory feeders. They are used to store, feed, orientate and isolate the parts. Due to the complex mechanics of the feeding process the design of the feeders is still depending on trial and error. This paper presents a complete dynamical model of the transportation process including unilateral constraints and multiple impacts, both with coulomb friction. Some simulation results, computed with a three dimensional model, explain the practical benefit of the proposed tool.

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