Stiffness is the capacity of a mechanical system to sustain external loads without excessive changes of its geometry (deformations). It is one of the most important design criteria for mechanical components and systems. While strength is considered the most important design criterion, there are many cases when stresses in components and their connections are significantly below the allowable levels, and dimensions as well as performance characteristics of mechanical systems and their components are determined by stiffness requirements. Typical examples of such mechanical systems are aircraft wings and frames and beds of production machinery (machine tools, presses, etc.), in which stresses frequently do not exceed 3 MPa to 7 MPa (500 psi to 1,000 psi), a small fraction of the ultimate strength of the material. Another stiffness-critical group of mechanical components is power transmission components, especially shafts, whose excessive deformations may lead to failures of gears and belts, while stresses in the shafts caused by the payload are relatively low.
Recently, there were achieved great advances in improving strength of mechanical systems and components. These advances are based on development of high-strength structural metals, composites, other materials, better understanding of fracture/failure phenomena, and development of better techniques for stress analysis and computation, which resulted in reducing of stress concentrations and safety factors. But these advances often result in reduction of cross-sections of structural components. Since the payload-induced loads in the structures usually do not change, structural deformations in the systems using high-strength materials and/or designed with reduced safety factors are becoming more pronounced. It is important to note that while strength of structural metals can be greatly improved by selection of alloying materials and/or of heat treatment procedures (as much as five to seven times improvements for steel and aluminum), modulus of elasticity (Young's modulus) is not very sensitive to alloying and to heat treatment. For example, the Young's modulus of stainless steels is even 5% to 15% lower than that of carbon steels, e.g., see Table 1.1 below. As a result, stiffness can be modified (enhanced) only by proper selection of the component geometry (shape and size) and by optimizing interactions between components of the system.