Meshfree generalized finite difference methods in soil mechanics—part I: theory

• Published in: GEM international journal on geomathematics Vol. 4; no. 2; pp. 167 - 184
• Main Authors: Ostermann, I., Kuhnert, J., Kolymbas, D., Chen, C.-H., Polymerou, I., Šmilauer, V., Vrettos, C., Chen, D.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2013
• Subjects: Applications of Mathematics; Computational Science and Engineering; Earth Sciences; Mathematics; Mathematics and Statistics; Original Paper; Weighted moving least squares (WMLS) method; 35D35; 65D05; 35Q74; Barodesy model; 65M99; Soft PARticle code (SPARC); Strong solution of coupled PDEs; Finite pointset method (FPM)
• ISSN: 1869-2672; 1869-2680
• DOI: 10.1007/s13137-013-0048-7

In soil mechanics, laboratory tests are typically used to classify soils or to test new material laws such as the barodesy model. The results of these tests provide the theoretical basis for subsequent simulations and analysis in geotechnical engineering (e.g., cuts, embankments, foundations). Simulation tools which are reliable as well as economical concerning the computing time are indispensable for applications. In this contribution we introduce two novel meshfree generalized finite difference methods—Finite Pointset Method and Soft PARticle Code—to simulate the standard benchmark problems “oedometric test” and “triaxial test”. One of the most important ingredients of both meshfree approaches is the weighted moving least squares method used to approximate the required spatial partial derivatives of arbitrary order on a finite pointset.