Theory of Elasticities and Materials

Strength of material refers to the structural engineering analysis of a part to determine its strength properties. There is also the important empirical approach that is based on experience and observations rather than theory. The basic optimization design theory can be related to the systematic activity necessary, from the identification of the market/user need, to the selling of the successful product to satisfy that need. It is an activity that encompasses product, process, people, and organization. 

An alternative problem formulation assumes a state of stress that satisfies equilibrium of forces and corresponds to the loading and boundary conditions. Compatibility of strains is not necessarily satisfied. The strength of materials approaeh solves problems that would be very unwieldy using elasticity methods. Because the stress distribution is assumed beforehand, it is apparent that the latter approach would be meaningless if one were required to find the stress concentration due to a hole in a tension 

Where the theory of elasticity results in a tractable formulation, the solution is accurate to the degree described in the loading and boundary conditions, and to the degree to which the material approaches the assumed ideal of an homogeneous, isotropic solid. Under these conditions, the elasticity solution would be expected to be superior to the strength of materials approach. However, the strength of materials method may be favorable when an assumed stress distribution accurately portrays the system due to factors such as local yielding. 

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