Modified finite element analysis for exterior boundary problems in infinite medium

Abstract

Abstract. Modified algorithm of the 3d finite element analysis developed for solution of external boundary problem is considered. The method in question is based on incorporating the FEM and Somigliana's integral formula. Efficiency of software implementations of the algorithm has been tested. A stress-strain analysis of inhomogeneous medium with a cavity has been carried out to display the approach.

Rational Method of Experiment Planning for Modeling Stress-Strain States of Rock Arrays and Underground Structure Supports

“…However, due to the presence of layers of different composition and properties in the enclosing soil mass, complex shape of workings and various fastening characteristics significantly complicate the analytical calculations of the SSS of the rock mass and the support. Therefore, designers mainly use numerical methods, which are currently the most common tool for solving complex geo-mechanical problems [11][12].…”

Combining finite and infinite elements: Why do we use infinite idealizations in engineering?

“…The flow potential at 𝑅 = 𝑏 should include the contribution of the flow potential from these two regions. For a comparison of FEM and other techniques used for the external boundary problems, seeChernysheva and Rozin (2016).20 This is due to the fact that the Dirichelet condition at the truncated boundary 𝑅 = 𝑏 only ensures C 0continuity of the flow potential at this point. The fact that the point 𝑅 = 𝑏 is a physically internal boundary within the entire physical domain implies that both the flow potential and its first spatial derivative in the normal direction should be continuous across the point which leads to the set of C 1 -continuous conditions.21 No infinite loop is generated in computation because even if the series is taken to be as infinite, still one does not count it.…”