Reduction of Numerical Model in Some Geotechnical Problems
Author:
Góral Artur1, Lefik Marek2, Wojciechowski Marek2
Affiliation:
1. Division of Geotechnics and Engineering Structures, Department of Concrete Structures , Lodz University of Technology , Al. Politechniki 6 , Łódź 2. Division of Geotechnics and Engineering Structures, Department of Concrete Structures Lodz , University of Technology , Al. Politechniki 6 , Łódź
Abstract
Abstract
The concept of equivalence of the realistic, initial reference model and the simplified, reduced model is proposed. In reduced models, the action of the soil on the structure is replaced by the action of a layer with prescribed properties, defined by a set of parameters. The main difficulty here is to find the parameter values required by the simplified theory. The subject of this work is to find the dependence of the parameters of the reduced model on the parameters of the full model, including realistic soil behavior, in order to ensure the equivalence of both models. We show the potential of the method by presenting two examples: Winkler and Pasternak's model of a plate on the ground. We assume that both models are equivalent if they give identical results (displacements) at a finite number of observation points. An artificial neural network (ANN) is built in order to approximate and record the dependence of the parameters of the reduced model (at the network output) from the parameters of the full model (given at the network input). The complex network acts as a formula that assigns the parameters of the reduced model to a realistic description of the soil structure that is used for finite element method (FEM) modeling. The formalism we propose is quite general and can be applied to many engineering problems. The presented procedure is entirely numerical; it allows to calculate the parameters of the reduced model without resorting to symbolic calculations or additional theoretical considerations.
Publisher
Walter de Gruyter GmbH
Subject
Computers in Earth Sciences,Mechanics of Materials,Geotechnical Engineering and Engineering Geology,Civil and Structural Engineering
Reference37 articles.
1. Ataman, M., Zbiciak A., Szcześniak, W.: Drgania własne płyty cienkiej na podłożu Kerra – Jemielity, https://www.researchgate.net/publication/263414439, 2009 2. Ataman, M.: Inercyjne, Sprężyste modele podłoża odkształcalnego w zadaniach z mechaniki konstrukcji, Logistyka-nauka, 6, s. 1515, 2014. 3. Boso, D.P., Lefik, M. and Schrefler B. A.: Generalised self consistent homogenisation as an inverse problem. Z. Angew. Math. Mech., 90(10–11), pp. 847 – 860, 2010. 4. Chen T., Chen H.: Universal Approximation to Non-linear Operators by Neural Networks with Arbitrary Activation Functions and Its Application to Dynamical Systems, IEEE Trans. on Neural Networks, Vol.6, No 4, 911–917, 1995. 5. Favre, H.: Sur une loi régissant la déformation d’un sol horizontal sous l’action d’une charge répartie à la surface. Comptes Rendus, Acad. Sci., 252, 1961, 2988–2990.
|
|