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Meshfree generalized finite difference methods in soil mechanics. I: Theory. (English) Zbl 1277.74076

Summary: 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.

MSC:

74S20 Finite difference methods applied to problems in solid mechanics
74L10 Soil and rock mechanics
35D35 Strong solutions to PDEs
35Q74 PDEs in connection with mechanics of deformable solids
65D05 Numerical interpolation
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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