Punches

In the ancient times" the 1950s), data were transferred to computers by using punched cards. But already in 1959 Ascher Opier from Dow Chemical Company reported the use of a light pen for graphical entiy of chemical structures into a computer. Light pens were also used in the Chemical Abstracts Service in the 1970s. 

A year later, a novel method of encoding chemical structures via typewriter input (punched paper tape) was described by Feldmann [42]. The constructed typewriter had a special character set and recorded on the paper tape the character struck and the position (coordinates) of the character on the page. These input data made it possible to produce tabular representations of the structure. 

CTfilcs originated in the time of punched cards and therefore their format is quite restrictive. For example, blanks usually arc significant and several consecutive spaces cannot simply be replaced by a single one. Spaces may correspond to missing entries, empty character positions within entries, spaces between entries, or 2cros in the case of numerical entries. Thus, eveiy piece of data has a precise and fixed location within a line in a data file. Moreover, the line length of CTfilcs is restricted to 80 characters. 

Using PCMODEL, draw H2O. Minimize using the MM3 force field. Save to the filename water.inp (or some such) in the GAMESS format. Copy to your GAMESS directory. Copy to filename INPUT and be sure that PUNCH has been renamed to PUNCH.OLD or has been erased entirely. Run using GAMESS.EXE > FILENAME.OUT. The INPUT file... 

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. 

Let a punch shape be described by the equation z = ip(x), and xi,X2,z be the Descartes coordinate system, x = xi,X2). We assume that the mid-surface of a plate occupies the domain fl of the plane = 0 in its non-deformable state. Then the nonpenetration condition for the plate vertical displacements w is expressed by the inequalities... 

The meaning of the relation (1.37) is the following. The punch pressure p = — / is equal to zero if a contact is absent. If the punch pressure... 

Thus, the relations (1.36) or (1.37) describe the interaction between a plate and a punch. To derive the contact model for an elastic plate, one needs to use the constitutive law (1.25). Contact problems for inelastic plates are derived by the utilizing of corresponding inelastic constitutive laws given in Section 1.1.4. 

Variational inequality characterizing an interaction between the punch and the plate can be written in the form... 

Thus, we have obtained that the right-hand side of (1.40) is always nonnegative, which gives (1.39). To derive a complete system of relations describing the interaction between the punch and the plate we should add to (1.38), (1.39) the constitutive law equations of Sections 1.1.3 and 1.1.4. 

The model of the plate considered in this section actually corresponds to a shallow shell having zeroth curvatures. The gradient of the punch surface is assumed to be rather small, so that the nonpenetration condition imposed in the domain is the same as in the usual case for a plate. Meanwhile, the restriction imposed on the crack faces contains three components of the displacement vector. 

Assume that the equation 2 = x,y) describes a punch shape, x,y) G 0, G 6 (0). A nonpenetration condition for the plate-punch system can be written as... 

The equilibrium problem for the plate contacting with the punch z = x, y)... 

In what follows we prove the solution regularity in a neighbourhood of points belonging to the crack faces and not having contact with the punch. Let a ° G be any fixed point such that w x ) > moreover,... 

Our aim is to analyze the solution properties of the variational inequality describing the equilibrium state of the elastic plate. The plate is assumed to have a vertical crack and, simultaneously, to contact with a rigid punch. 

Considering the crack, we impose the nonpenetration condition of the inequality type at the crack faces. The nonpenetration condition for the plate-punch system also is the inequality type. It is well known that, in general, solutions of problems having restrictions of inequality type are not smooth. In this section, we establish existence and regularity results related to the problem considered. Namely, the following questions are under consideration ... 

The existence of punch shape which provides the minimal opening of the crack. 

We note that if the crack opening is zero on F,, i.e. [%] = 0, the value of the objective functional Js u) is zero. We also assume that near F, the punch does not interact with the shell. It turns out that in this case the solution X = (IF, w) of problem (2.188) is infinitely differentiable in a neighbourhood of points of the crack. This property is local, so that a zero opening of the crack near the fixed point guarantees infinite differentiability of the solution in some neighbourhood of this point. Here it is undoubtedly necessary to require appropriate regularity of the curvatures % and the external forces u. The aim of the following discussion is to justify this fact. At this point the external force u is taken to be fixed. 

The nonpenetration condition is imposed both in the domain and on T. Thus, let the equation 2 = (a ,y) describe the punch shape, (a , y) G fl, G C°°(fi). Then the nonpenetration condition for the plate-punch system in a linear approach takes the form... 

In so doing, the boundary value of on F is assumed to provide nonemptiness of the set K. The equilibrium problem for the plate contacting with the punch and having the crack can be formulated as a variational one ... 

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