Tensor Manipulations in Complex Coordinates with Application to the Mechanics of Materials

摘要

Research into the strength and failure of composite materials is benefited substantially by the development of tensor manipulation techniques in complex coordinates which insure a problem representation that is compact, simple, and invariant. Such techniques are developed through the introduction of several new notations and integer functions. The techniques are then applied to problems connected with analytic formulations in composite materials research, such as basic formulation of anisotropic plane-linear elasticity theory, the elastic constants of laminated composites, graphic representation of tensor transformations, and tensor-polynomial approximation functions to yield surfaces. The techniques are general and can be used whenever two-dimensional tensor formulations are desired. (Author)