Análisis de las funciones de atenuación en la teoría integral de elasticidad no local usando elementos finitos (2020)
In this research implementation of the non-local elasticity theory using finite elements is presented. To do this, a theoretical analysis was carried out on one of the parameters of said model, the attenuation function. This analysis takes up most of the research. In the first place, the mathematical origin of this function was sought. Historically, it was given more importance and in turn, its meaning was modified. Therefore, we proposed 4 attenuation functions. The first 3 were based on previous research of Polizzotto (2001) and the last one, was a manual modification of the biexponencial function. For each of these functions, tests were carried out with comparable case studies. The objective of carrying out these tests is to check whether at the time of applying the method it is relevant to choose one or another attenuation function. Based on the results obtained, it was found that the attenuation functions have great importance in the solution of phenomena, especially, they affect the results obtained in the outer regions of the domain. This means that the attenuation functions should be used as a parameter of the model. In turn, it was shown that the shape of the attenuation function is relevant to the shape of the solution. It was observed that those that have the same origin cause their results to be grouped in specific areas.