Stiffness, definition

Note that if the system is linear, J = A. For a nonlinear system the stiffness definition is applied to its Jacobian and its eigenvalues. For the previous example the corresponding Jacobian is... 

O Rourke ME, Staessen J A, Vlachopoulos C, Duprez D, Plante GE. Clinical applications of arterial stiffness definitions and reference values. Am J Hypertens 2002 15 426 44. 

Note that the definite integrals in the members of the elemental stiffness matrix in Equation (2.77) are given, uniformly, between the limits of -1 and +1. This provides an important facility for the evaluation of the members of the elemental matrices in finite element computations by a systematic numerical integration procedure (see Section 1.8). 

There is a definite trend in the suppHer industry to develop multifimctional materials with value-added properties. One suppHer has introduced a modified hydrocarbon resin that softens, improves filler incorporation, improves mill banding, and increases tack in the green compound while imparting increased low strain (<100%) stiffness, significantly improving tear resistance in the vulcanized compound. 

What has been accomplished in preceding sections on stiffness relationships serves as the basis for determination of the actual stress field what remains is the definition of the allowable stress field. The first step in such a definition is the establishment of allowable stresses or strengths in the principal material directions. Such information is basic to the study of strength of an orthotropic lamina. 

The stress-strain relations in arbitrary in-plane coordinates, namely Equation (4.5), are useful in the definition of the laminate stiffnesses because of the arbitrary orientation of the constituent laminae. Both Equations (4.4) and (4.5) can be thought of as stress-strain relations for the k layer of a multilayered laminate. Thus, Equation (4.5) can be written as... 

Knowledge of the variation of stress and strain through the laminate thickness is essential to the definition of the extensional and bending stiffnesses of a laminate. The laminate is presumed to consist of per-... 

The Ajj are the sum of the product of the individual laminae Qy and the laminae thjcknesses. Thus, the only ways to obtain a zero individual Ay are for all Qy to be zero or for some Qy to be negative and some positive so that their products with their respective thicknesses sum torero. From the expressions for Uie transformed larnina stiffnesses, Qy, in Equation (2.80), apparently Qii, Q- 2, Q22 66 positive-definite... 

The term quasi-isotropic iaminate is used to describe laminates that have isotropic extensionai stiffnesses (the same in all directions in the plane of the laminate). As background to the definition, recall that the term isotropy is a material property whereas laminate stiffnesses are a function of both material properties and geometry. Note also that the prefix quasi means in a sense or manner. Thus, a quasi-isotropic laminate must mean a laminate that, in some sense, appears isotropic, but is not actually isotropic in all senses. In this case, a quasi-isotropic... 

The effect of the specific values of the B j can be readily calculated for some simple laminates and can be calculated without significant difficulty for many more complex laminates. The influence of bending-extension coupling can be evaluated by use of the reduced bending stiffness approximation suggested by Ashton [7-20]. If you examine the matrix manipulations for the inversion of the force-strain-curvature and moment-strain-curvature relations (see Section 4.4), you will find a definition that relates to the reduced bending stiffness approximation. You will find that you could use as the bending stiffness of the entire structure,... 

The definitions and relationships of mass, stiffness, and damping in the preceding section assumed a single-degree of freedom. In other words, movement was limited to a single plane. Therefore, the formulas are applicable for all single degree of freedom mechanical systems. 

As an initial step, the product designer must anticipate the conditions of use and the performance requirements of the product, considering such factors as life expectancy, size, condition of use, shape, color, strength, and stiffness. These end use requirements can be ascertained through market analysis, surveys, examinations of similar products, testing, and general experience. A clear definition of product requirements will often lead directly to choice of the material of construction. At times incomplete or improper product requirement analysis is the cause for a product to fail. 

Here E is Young modulus. Comparison with Equation (3.95) clearly shows that the parameter k, usually called spring stiffness, is inversely proportional to its length. Sometimes k is also called the elastic constant but it may easily cause confusion because of its dependence on length. By definition, Hooke s law is valid when there is a linear relationship between the stress and the strain. Equation (3.97). For instance, if /q = 0.1 m then an extension (/ — /q) cannot usually exceed 1 mm. After this introduction let us write down the condition when all elements of the system mass-spring are at the rest (equilibrium) ... 

The critical gel equation is expected to predict material functions in any small-strain viscoelastic experiment. The definition of small varies from material to material. Venkataraman and Winter [71] explored the strain limit for crosslinking polydimethylsiloxanes and found an upper shear strain of about 2, beyond which the gel started to rupture. For percolating suspensions and physical gels which form a stiff skeleton structure, this strain limit would be orders of magnitude smaller. 

Hardness is a somewhat ambiguous property. A dictionary definition is that it is a property of something that is not easily penetrated, spread, or scratched. These behaviors involve very different physical mechanisms. The first relates to elastic stiffness, the second to plastic deformation, and the third to fracturing. But, for many substances, the mechanisms of these are closely related because they all involve the strength of chemical bonding (cohesion). Thus discussion of the mechanism for one case may provide some understanding of all three. 

CDC Case Definition Arboviral infections may be asymptomatic or may result in illnesses of variable severity sometimes associated with central nervous system (CNS) involvement. When the CNS is affected, clinical syndromes ranging from febrile headache to aseptic meningitis to encephalitis may occur, and these are usually indistinguishable from similar syndromes caused by other viruses. Arboviral meningitis is characterized by fever, headache, stiff neck, and pleocytosis. Arboviral encephalitis is characterized by fever, headache, and altered mental status ranging... 

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