On the Optimization of Shape Parameters in the Local Radial Point Interpolation Collocation Method for Modeling of Heterogeneous Materials

Jalušić, Boris and Jarak, Tomislav and Sorić, Jurica (2015) On the Optimization of Shape Parameters in the Local Radial Point Interpolation Collocation Method for Modeling of Heterogeneous Materials. = On the Optimization of Shape Parameters in the Local Radial Point Interpolation Collocation Method for Modeling of Heterogeneous Materials. In: 8th International Congress of Croatian Society of Mechanics, 29.9.-2.10.2015., Opatija, Hrvatska.

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Official URL: http://bib.irb.hr/prikazi-rad?rad=780971

Abstract

In this contribution, the collocation meshless method is applied for the modeling of deformation responses of heterogeneous materials. Heterogeneous structures consist of various homogeneous subdomains with linear elastic material properties. These subdomains are discretized by grid points, where equilibrium equations may be imposed. Independent variables are approximated using meshless interpolation functions in such a way that each subdomain is treated as a separate problem. The solution for the entire domain is then obtained by gluing the solutions for displacements and tractions along the interfaces of the subdomains by enforcing the corresponding continuity conditions. The linear elastic boundary value problem for each subdomain is discretized by using the independent interpolations of only displacements (primal approach) or of both displacements and stress components (mixed approach). In the mixed approach, the nodal stress values are expressed in terms of the displacement components using the kinematic and constitutive relations. For the approximation of the unknown field variables, the radial point interpolation method with polynomial reproduction (RPIM) is applied. It possesses the interpolation property at the nodes, which enables a simple enforcement of the essential boundary conditions. The natural boundary conditions are enforced via the direct collocation approach. In the RPIM, two different radial functions with dimensionless shape parameters, the Gaussian and the Multiquadric, are applied. To improve the accuracy of the LRPICM method, fine tuning of radial basis shape parameters is considered. The accuracy and numerical efficiency of both primal and mixed approaches are demonstrated by a set of suitable numerical examples.

Item Type: Conference or Workshop Item (Lecture)
Keywords (Croatian): RPICM collocation method, heterogeneous materials
Subjects: TECHNICAL SCIENCE > Mechanical Engineering
Divisions: 200 Department of Engineering Mechanics > 210 Chair of Mechanics and Strength of Materials
Indexed in Web of Science: No
Indexed in Current Contents: No
Date Deposited: 22 Apr 2016 11:02
Last Modified: 30 Nov 2016 13:59
URI: http://repozitorij.fsb.hr/id/eprint/5752

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