Extreme crack shapes


Extreme crack shapes  [c.103]

In the following we analyse the behaviour of the solution as 5 —> 0. It will enable us in the sequel to prove the existence of extreme crack shapes. The formulation of this problem is given below. So, for every fixed 5 there exists a solution = iyV of the problem  [c.103]

Extreme crack shapes in a shallow shell  [c.284]

Existence of extreme crack shapes  [c.289]

Consider the problem of finding the extreme crack shapes. The setting of this problem is as follows. Let C be a convex, closed and  [c.289]

Asymmetrical shapes of unequal thickness should be avoided for galvanizing. Extremes in weight and cross sections of design members also should be avoided.  [c.43]

A contact problem for a plate having a vertical crack is considered. The solution satisfies two restrictions of the inequality type. The first restriction is imposed in the domain and represents the mutual nonpenetration condition in the plate-punch system the second one is put on the crack faces and corresponds to the nonpenetration of these faces. The corresponding variational inequality describing the equilibrium of the plate has its fourth order along the normal to the plate and its second order in the horizontal direction. The regularity of the solution is analysed. Boundary conditions having a natural physical interpretation are found on the crack faces. The existence of extreme crack shapes is also investigated. Specifically, the cost functional is defined on the feasible set of functions describing the crack shapes. The functional characterizes the deviation of the displacement vector from a given function. The problem consists in maximizing this functional. The existence of solutions of the formulated problem is proved. This section follows (Khludnev, 1995a).  [c.95]

At the beginning we study the (5-dependence of the solution and next we consider the problem of finding extreme crack shapes. First, let us note that the problem (4.168) has a solution owing to the coercivity and the weak lower semicontinuity of II5 on the space The solution is unique for  [c.286]

This section is concerned with an extreme crack shape problem for a shallow shell (see Khludnev, 1997a). The shell is assumed to have a vertical crack the shape of which may change. From all admissible crack shapes with fixed tips we have to find an extreme one. This means that the shell displacements should be as close to the given functions as possible. To be more precise, we consider a functional defined on the set describing crack shapes, which, in particular, depends on the solution of the equilibrium problem for the shell. The purpose is to minimize this functional. We assume that the  [c.284]

With modem high-speed computers, it is feasible to solve the coupled set of radial equations only for a restricted basis set of unperturbed states regarded as being closely and strongly coupled. For electron-atom (molecule) collisions at low energies E, the frill quantal close-coupling method is extremely successfiil in predicting the cross sections and shapes and widths of resonances which appear at energies just below the various tln-esholds for excitation of the various excited levels. As E increases past the tln-eshold for ionization, it becomes less successful, and is plagued by problems with convergence both in the number of the basis  [c.2050]


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Analysis of cracks in solids  -> Extreme crack shapes