Designing for stiffness

E is Young s modulus. An incorrect interference can result on the one hand in cracking of the part, and on the other in loosening of the joint. Stress relaxation in the polymer and differences in thermal expansion coefficient must both be taken into account. Knurled metal surfaces enable the polymer to creep into depressions and increase joint strength. 

The maximuni stress occurs at the midspan, in the outer fibres, and is given 

The maximum shear stress occurs in the neutral plane at the centre of the ban 

These equations hold for small deflections, when the polymer is linearly viscoelastic. 

14 Creep data for PES at 150 C replotted (a) as isochronous curves and (b) as isometric curves (after ICI pic). 

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Equation (8.22) for a(0) is also special because, due to symmetry, there is only one adjacent point, a(l). The overall set may be solved by any desired method. Euler s method is discussed below and is illustrated in Example 8.5. There are a great variety of commercial and freeware packages available for solving simultaneous ODEs. Most of them even work. Packages designed for stiff equations are best. The stiffness arises from the fact that VJJ) becomes very small near the tube waU. There are also software packages that will handle the discretization automatically. 

The approximating scheme converts the system of partial differential equations to a set of ordinary differential equations in the axial spatial coordinate. The detailed equations are contained in Yu et al. (2). The advantage of reduction in this manner is that the transient location of the combustion zone does not have to be known a priori, but can be found in the course of the integrations. Gear integration, which is designed for stiff systems, is used to solve the two point boundary value problem in the axial direction. 

This material is a cyclic methylated high solids resin, designed for stiffness on Nylon and synthetics. This material is viscous in nature, and has extremely good storage stability. Catalysts are required. 

A very important gain in volume can be achieved if one uses tuned mass dampers. An example, with parametric analysis, shows clearly that one needs to consider a design for stiffness approach when dynamic loads are important. 

The numerical solution of the equation was achieved by using a library routine which selected the order and step size automatically and was designed for stiff differential equations (IMSL-DGEAR). The routine was applied in the following iterative scheme ... 

There are examples where control of deflection or deformation during service may be required. Such structural elements are designed for stiffness to control deflection but must be checked to assure that strength criteria are reached. A product can be viewed as a collection of individual elements interconnected to achieve an overall systems... 

The question of optimal design for stiffness and friction of seismic isolation systems has been addressed previously in the literature (e.g., Constantinou and Tadjbakhsh (1983), lemura et al. (2007), Jangid (2005)). The method of equivalent linearization in conjunction with a random process model for the earthquake excitation tuned to the El Centro record was used in Jangid (1996). Here, a full nonlinear dynamic analysis will be used as a basis for the computation of the structural response. The ground motion is modeled as a nonstationary (i.e., evolutionary) random process hence, the response should to be characterized in suitable probabilistic terms. 

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