Element matrix formulation for bi-quadratic infinite element

Abstract

In reality, no physical domain extends to infinity but for the convenience of calculation in certain instances like unbounded domains it is better to develop mathematical models with the assumption that it extends to infinity. Unbounded domains are present in a wide variety of practical engineering problems. Specific examples can be found in fields like solid mechanics, fluid flow, acoustics, heat and mass transfer. The common engineering approach when it comes to defining an unbounded domain is to limit it to a very large finite area. This method of using finite element analysis over a very large domain is called truncation. The determination of the finite boundary requires a lot of experience and intuition. This method results in an approximated approach, which takes up a significant amount of computational effort and time due to the large number of elements required to mesh the region. In this research paper, the use of a bi-quadratic infinite element to solve infinite domain structural problems is studied. The effect of truncation to represent an infinite domain element is examined. The infinite solution is found using infinite element method.