Abstract
In this paper we present numerical simulations of soil plasticity using isogeometric analysis comparing the results to the solutions from conventional finite element method. Isogeometric analysis is a numerical method that uses nonuniform rational B-splines (NURBS) as basis functions instead of the Lagrangian polynomials often used in the finite element method. These functions have a higher-order of continuity, making it possible to represent complex geometries exactly. After a brief outline of the theory behind the isogeometric concept, we give a presentation of the constitutive equations, used to simulate the soil behavior in this work. The paper concludes with numerical examples in two- and three-dimensions, which assess the accuracy of isogeometric analysis for simulations of soil behavior. The numerical examples presented show, that for drained soils, the results from isogeometric analysis are overall in good agreement with the conventional finite element method in two- and three-dimensions. Thus isogeometric analysis is a good alternative to conventional finite element analysis for simulations of soil behavior.
Highlights
In the design of foundations and geotechnical structures it is essential to predict soil behavior under different loading conditions
In this paper we present numerical simulations of soil plasticity using isogeometric analysis comparing the results to the solutions from conventional finite element method
Isogeometric analysis is a numerical method that uses nonuniform rational B-splines (NURBS) as basis functions instead of the Lagrangian polynomials often used in the finite element method
Summary
In the design of foundations and geotechnical structures it is essential to predict soil behavior under different loading conditions. Much research has been carried out to improve the ability of simulating the behavior of different soils and a number of new constitutive models have been developed Another important aspect when modeling geotechnical problems is the interaction between soil and structure, which can have a large influence on the structural design [1]. The higherorder smoothness of the basis functions in IGA opens up the possibilities of using quadrature rules evaluated on element boundaries reducing the total number of quadrature points [2] [7] Another interesting possibility within the IGA framework is the use of isogeometric collocation methods, a one-point quadrature rule that reduces the computational cost of analysis [11]. In this work we have evaluated how isogeometric analysis performs compared to the conventional finite element method for soil plasticity in two and three dimensions. The paper is concluded with two- and three-dimensional numerical examples, comparing the results to conventional finite element analysis
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