Abstract
During the last decade, many hysteresis models have been developed and applied to practical problems. Wavelet analysis has begun to play a serious role in a broad range of applications, including modeling multiscale phenomena. It calls for a new approach to the use of mathematics in engineering that employs an approach to problems where mathematical process models. Hysteresis phenomena are common forms of nonlinearities that reflect the memory of a system and are associated with many physical phenomena such as ferromagnetism, ferroelectricity, plasticity, superconduction, etc. Currently available predictive algorithms for such nonlinearities are limited in scope. A new approach based on wavelet analysis and Preisach models is to develop a generalized formulation to predicting hysteretic efforts for smart material systems. We will address basic research issues relating to the feasibility, methodology and numerical implementation of this new approach.
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