Simulation of Mechanical Behaviour of Materials Using Constant Boundary Elements - A Discussion on the Accuracy of Results for Beams

Abstract

The Boundary Element Method (BEM) is one among the most popular simulation techniques employed to simulate mechanical behaviour of materials, including smart engineering materials. Although BEM is a quite well-established numerical technique, literature tells that the method may not be well suited to simulate structures where one or two of the dimensions is much smaller than the remaining dimension/s (for a 3D problem). Hence in this work, deflection of a cantilever beam is simulated using constant boundary elements to get a feel of the accuracy of the BEM when used to simulate such type of structures. Although the concept is not new, the study assumes significance because studies which list the results in detail are not readily found in the literature. In this study, the results are obtained for different mesh resolutions also. The results indicate that - as expected - constant boundary elements are not a good choice for simulating the mechanical behaviour of smart materials when the structural member to be simulated is thin. Although it is a known fact that constant boundary elements converge very slowly, the present study helps to get a clearer picture on the accuracy and the convergence rate that one can expect from constant boundary elements. This paper heavily borrows content from this author’s PhD thesis [1]. The geometry considered in this paper is a beam. One may also note that the author is publishing another paper [2] (“Simulation of Mechanical Behaviour of Materials using Constant Boundary Elements - A Discussion on the Accuracy of Results for Bars”) that is very similar to this paper except that the geometry considered in that paper is a bar.