General Basis Functions for Parametric Representation of Energy Deposition Processes

Abstract

General basis functions for parametric representation of energy deposition processes are constructed according to the general physical characteristics of energy deposition within a volume of material from a beam energy source. These basis functions include previously constructed source functions as special cases. The construction of a general parameterization of energy deposition processes, e.g., welding and rapid prototyping, is necessary for inverse analysis of such processes. The structure of such a parameterization follows from the concepts of model and data spaces that imply the existence of an optimal parametric representation for a given class of inverse problems. Accordingly, the optimal parametric representation lying within the model space is determined by the characteristics of the available data, i.e., data space, which contain both experimental measurements and numerical simulation data. Experimental measurements include solidification cross-sections, thermocouple measurements, and microstructural changes. Numerical simulation data include general temperature field trend characteristics, response characteristics of materials to volumetric energy deposition, and the relative sensitivity of temperature field characteristics to phenomena occurring on different space and time scales. A general procedure is described for using basis functions with the available experimental and numerical data to construct a multidimensional field representation of a large class of energy deposition processes.