A parametric knot adaptation approach to isogeometric analysis of contact problems
- PDF / 3,479,303 Bytes
- 22 Pages / 595.276 x 790.866 pts Page_size
- 92 Downloads / 176 Views
ORIGINAL ARTICLE
A parametric knot adaptation approach to isogeometric analysis of contact problems Emad Bidkhori1 · Behrooz Hassani1 Received: 5 January 2020 / Accepted: 23 May 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In this paper, an adaptive approach is presented to deal with isogeometric analysis of contact problems. Suggestion of an isogeometric adaptive refinement strategy for contact problems is the subject of this paper. Refinements are performed near the boundaries of the contact zone with insertion of new knots in the parametric domain. The performance and efficiency of the method are demonstrated via four examples, i.e., the Hertz problem and three hyperelastic contact problems. The obtained results are compared with solutions of very fine computational models. The proposed approach shows good convergence not only for the contact pressure but also for the contact zone limits. Another advantage of the method is eliminating the need for a priori guess of the contact zone limits. Keywords Contact analysis · Isogeometric analysis · Adaptivity
1 Introduction Nonlinearity in mechanical problems has four major sources: geometric nonlinearity, material nonlinearity, kinematic nonlinearity and force nonlinearity. Contact problems have kinematic and force nonlinearity due to the unknown contact zone limits and the unknown contact forces. These problems can become more complicated, especially when large deformations are involved. If the contact zone limits were known a priori and the problem did not have geometric and material nonlinearities, it would be changed to a linear boundary value problem. Hence, extraction of the contact zone limits has major importance in numerical analysis of contact problems. High oscillation of stress near the end of the contact zone is reported in the literature due to the change of boundary condition from contact to no contact. Therefore, in addition to the usual adaptive procedures that concentrate on the points of domain having high stress gradients, some adaptive
* Behrooz Hassani [email protected] Emad Bidkhori [email protected] 1
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
procedures have been suggested to refine the domain near the contact zone limits [1]. The use of functions employed to define geometry in computer aided design (CAD) as approximation in the finite element method (FEM) has recently been considered as a remedy to the problem of remodeling in some computational problems. In addition, the convergence problems that arise from the non-smooth C0 continuity of the traditional Lagrange finite element interpolation polynomials can easily be alleviated by using CAD functions with the higher order of continuity. In order to circumvent these problems, some researchers considered the use of basis functions like B-splines and non-uniform rational B-splines (NURBS) in finite element analysis [2–4]. Isogeometric analysis (IGA) introduces a technique to use basis functions originating from C
Data Loading...
