Design and Performance Evaluation using Analytical Approximations

Empirical Similitude Method (ESM) is a technique developed to address the concerns of non – linear similitude. The process disconnects the scaling of material and shape response by assuming them to be independent to form a system transformation. Such a transformation requires modeling using three representative models instead of just one as is used in the Buckingham π theorem. In an effort to generalize this non – linear analysis, conformal mapping is employed, Schwarz – Christoffel Transformation in particular. Complex variables are used to define the system transformation over a continuous domain to obtain the scaling laws.