Development of a program with finite element post-processing techniques for interpolating data

• Grant number: 13/21031-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2014
• End date: June 30, 2014
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Dimas Betioli Ribeiro
• Grantee: William Brascher
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project aims to develop a computer program for interpolating discrete data, using post-processing techniques commonly employed in programs that make use of the finite element method. These techniques consist in using the shape functions of the elements to obtain values at points of its domain from its nodal values. Values of a different nature from those obtained by solving the system of equations can also be calculated. For example, one may obtain the strain field of a domain from its displacement field. Several techniques may be found in the literature for interpolating discrete data, among them stand out formulations that employ machine learning. Such formulations use a set of examples for which the result is known, called training set, to train the algorithm and later predict the result for a new and unknown example. A very simple machine learning technique "k nearest neighbors" and consists of detecting k examples in the training set considered closer to the new example and calculate the average of their results . Such proximity is often based on Euclidean distance between points in n-dimensional space, where n is the number of input data for the example and the data values is the coordinates of the point. The formulation to be developed in this undergraduate research project can be considered an improved version of the technique "k nearest neighbors", because the average provides a unique value for the k neighbors while interpolation using shape functions allows introducing a continuous variation of the results. For one-dimensional elements, if k is 2 linear shape functions must be used, if k is 3 quadratic shape functions are used, and so on. Other machine learning techniques are also able to obtain continuous variations, however have the disadvantage of employing complex formulations that are not usually known for civil engineering professionals. The technique here proposed, on the other hand, is simple and uses techniques commonly used and therefore must become much more attractive to engineers. In future work, the formulation to be here developed may be extended to more dimensions, becoming a general tool for data mining.