Theory of Elasticity
The theory of elasticity means, when the property of solid materials to deform under the application of an external force and getting back to their original shape after the external force is removed .The external force which is applied on the external force is said to be stress, the amount of deformation is called the strain.
When the material has a force applied to it, let say, the compressive force is acting at each end of a bar; there will be an internal reaction to that force. This leads to the Newton’s third law, for every action there is an equal and opposite reaction. The internal reaction of the bar has the magnitude which is equal to the applied force. This will be very useful for engineers for considering the reactive force which is equally distributed over the cross sectional area of the bar.
When the material has applied force on it, that material will be deformed neither plastically (permanently) nor elastically. In elastic structures such as buildings and bridges, if the force is removed the change in shape will disappear. Strain is nothing but, the degree of deformation extension, compression, shear or torsion as a proportion of the original size of a material. Strain is a proportion, or ratio, so it is dimensionless, i.e. it does not have units. Depending on the amount of deformation, the strain can be expressed in percentage. The use of stress and strain in place of load and deformation will make the calculation easier for engineers.
The Linearized Theory of Elasticity
The linearized theory of elasticity has played the vital role in the analysis of engineering. The engineers have used the linearized theory of elasticity from the cast iron and steel truss bridges of the eighteenth century till the international space station. They are using them in making design decisions effecting the strength, stiffness, weight, and cost of structures and components.
The linearized theory of elasticity includes a comprehensive introduction to tenor analysis, specification of boundary conditions, and a survey of solution methods for important class of problems. It covers two and three dimensional problems, torsion of noncircular cylinders, variational methods and complex variable method. An widespread treatment of important solutions and solution methods, including the use of potentials, variational methods, and complex variable methods, follows the development of the linearized theory.