Canonical representation of influence functions in elastic media (Q1096444)

In linear elasticity, the influence functions due to various concentrated forces are usually given as complicated algebraic expressions. Although these different functions are derived from a common basis, the precise interrelationships are hidden by the algebraic complexities. On the other hand, the expressions for these functions become particularly simple if the coordinate axes happen to be properly aligned with the load and field points. Even in an arbitrarily oriented coordinate system, it is possible to represent the influence functions by means of a compact matrix formulation, which recognizes the tensor characteristics of the functions. It is shown how the influence functions for point loads of single forces and double forces can be decomposed, and represented in a very simple matrix structure. The representation effectively isolates the functional dependence of the influence functions on the load point-to-field point distance from the coordinate axis orientation, and makes the interrelationships between the various influence functions more apparent. Furthermore, using the canonical representation, influence functions for the point displacement discontinuities are defined.