Stiffness techniques

Carver MB, Hanlet DV, Chapin KR. MAKSIMA-CHEMIST, A program for mass action kinetic simulated manipulation and integration using stiff techniques, Chalk River Nuclear Laboratories Report, Atomic Energy Canada Ltd. 6413, 1979 1-28. 

This type of coil was prepared from copper cladded printed circuit board material by applying photolithographic techniques. The p.c. board material is available with difierent copper thicknesses and with either a stiff or a flexible carrier. The flexible material offers the opportunity to adapt the planar coil to a curved three dimensional test object. In our turbine blade application this is a major advantage. The thickness of the copper layer was chosen to be 17 pm The period of the coil was 100 pm The coils were patterned by wet etching, A major advantage of this approach is the parallel processing with narrow tolerances, resulting in many identical Eddy current probes. An example of such a probe is shown in fig. 10. 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

Ultem PEI resins are amber and amorphous, with heat-distortion temperatures similar to polyethersulfone resins. Ultem resins exhibit high modulus and ate stiff yet ductile. Light transmission is low. In spite of the high use temperature, they are processible by injection mol ding, stmctural foam mol ding, or extmsion techniques at moderate pressures between 340 and 425°C. They are inherently flame retardant and generate Httie smoke dimensional stabiUties are excellent. Large flat parts such as circuit boards or hard disks for computers can be injection-molded to maintain critical dimensions. 

Once the driver and driven equipment have been chosen and it is deter mined that none of the items will be subject to any lateral vibration problems, the system torsional analysis is performed. If a calculated torsional natural frequency coincides with any possible source of excitation (Table 9-21, the system must be de-tuned in order to assure reliable operation. A good technique to add to the torsional analysis was presented by Doughty [8 j, and provides a means of gauging the relative sensitivity of changes in each stiffness and inertia in the system at the resonance in question. 

TTie force-curve mapping technique is often referred to as force-volume mapping commercially, although sample volume is not probed unless stiff levers or compliant surfaces are used. 

We have recently been exploring this technique to evaluate the adhesive and mechanical properties of compliant polymers in the form of a nanoscale JKR test. The force and stiffness data from a force-displacement curve can be plotted simultaneously (Fig. 13). For these contacts, the stiffness response appears to follow the true contact stiffness, and the curve was fit (see [70]) to a JKR model. Both the surface energy and modulus can be determined from the curve. Using JKR analyses, the maximum pull off force, surface energy and tip radius are... 

Dispersion-strengthened lead (DSL), obtained by a uniform dispersion of lead oxide through the lead particle matrix, has the traditional corrosion resistance of lead but much greater stiffness. DSL is fabrieated as pipe and other extruded items, but has a limited applieation for proeess plant construction because the welding technique does not provide adequate strengths in joints. 

The mechanics of materials approach to the micromechanics of material stiffnesses is discussed in Section 3.2. There, simple approximations to the engineering constants E., E2, arid orthotropic material are introduced. In Section 3.3, the elasticity approach to the micromechanics of material stiffnesses is addressed. Bounding techniques, exact solutions, the concept of contiguity, and the Halpin-Tsai approximate equations are all examined. Next, the various approaches to prediction of stiffness are compared in Section 3.4 with experimental data for both particulate composite materials and fiber-reinforced composite materials. Parallel to the study of the micromechanics of material stiffnesses is the micromechanics of material strengths which is introduced in Section 3.5. There, mechanics of materials predictions of tensile and compressive strengths are described. 

The analytical tools to accomplish laminate design are at least twofold. First, the invariant laminate stiffness concepts developed by Tsai and Pagano [7-16 and 7-17] used to vary laminate stiffnesses. Second, structural optimization techniques as described by Schmit [7-12] can be used to provide a decision-making process for variation of iami-nate design parameters. This duo of techniques is particularly well suited to composite structures design because the simultaneous possibility and necessity to tailor the material to meet structural requirements exists to a degree not seen in isotropic materials. 

In the coating of continuous metal coils, reverse roller coating is often used. In this technique the web is moving counter to the application roller direction, so that the paint is partly wiped off by the moving coil. Shear leads to better flowout. Another type of reverse roller coating is used for the application of stiff paste fillers to chipboard. Application is by forward roller, but this is immediately followed by a reverse roller, which presses the filler into the board and doctors it smooth. 

There are different techniques that have been used for over a century to increase the modulus of elasticity of plastics. Orientation or the use of fillers and/or reinforcements such as RPs can modify the plastic. There is also the popular and extensively used approach of using geometrical design shapes that makes the best use of materials to improve stiffness even though it has a low modulus. Structural shapes that are applicable to all materials include shells, sandwich structures, and folded plate structures (Fig. 3-8). These widely used shapes employed include other shapes such as dimple sheet surfaces. They improve the flexural stiffness in one or more directions. 

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