Isogeometric analysis of 2D gradient elasticity

Fischer, Paul; Klassen, Markus; Mergheim, Julia; Steinmann, Paul; Müller, Ralf
March 2011
Computational Mechanics;Mar2011, Vol. 47 Issue 3, p325
Academic Journal
In the present contribution the concept of isogeometric analysis is extended towards the numerical solution of the problem of gradient elasticity in two dimensions. In gradient elasticity the strain energy becomes a function of the strain and its derivative. This assumption results in a governing differential equation which contains fourth order derivatives of the displacements. The numerical solution of this equation with a displacement-based finite element method requires the use of C-continuous elements, which are mostly limited to two dimensions and simple geometries. This motivates the implementation of the concept of isogeometric analysis for gradient elasticity. This NURBS based interpolation scheme naturally includes C and higher order continuity of the approximation of the displacements and the geometry. The numerical approach is implemented for two-dimensional problems of linear gradient elasticity and its convergence behavior is studied.


Related Articles

  • An a-posteriori error estimator for linear elastic fracture mechanics using the stable generalized/extended finite element method. Lins, R.; Ferreira, M.; Proença, S.; Duarte, C. // Computational Mechanics;Dec2015, Vol. 56 Issue 6, p947 

    In this study, a recovery-based a-posteriori error estimator originally proposed for the Corrected XFEM is investigated in the framework of the stable generalized FEM (SGFEM). Both Heaviside and branch functions are adopted to enrich the approximations in the SGFEM. Some necessary adjustments to...

  • Nonconforming finite elements for the equation of planar elasticity. Yang, Yong-qin; Xiao, Liu-chao; Chen, Shao-chun // Applied Mathematics & Mechanics;Dec2010, Vol. 31 Issue 12, p1537 

    Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem are presented. Convergence rates of the elements are uniformly optimal with respect to λ. The energy norm and L norm errors are proved to be O( h) and O( h), respectively. Numerical tests...

  • A MIXED FINITE ELEMENT METHOD FOR THE CONTACT PROBLEM IN ELASTICITY. Dong-ying Hua; Lie-heng Wang // Journal of Computational Mathematics;Jul2005, Vol. 23 Issue 4, p441 

    Based on the analysis of [7] and [10], we present the mixed finite element approximation of the variational inequality resulting from the contact problem in elasticity. The convergence rate of the stress and displacement field are both improved from O(h¾) to quasi-optimal O(h|logh|¼). If...

  • Convergence rates for the coupling of FEM and collocation BEM. BRINK, ULRICH; STEPHAN, ERNST P. // IMA Journal of Numerical Analysis;1996, Vol. 16 Issue 1, p93 

    We prove convergence of the coupling of finite and boundary elements where Galerkin's methd is used for finite elements and collocation for boundary elements. We consider linear elliptic boundary value problems in two dimensions, in particular problems in elasticity. The mesh width k of the...

  • Local enrichment of the finite cell method for problems with material interfaces. Joulaian, Meysam; Düster, Alexander // Computational Mechanics;Oct2013, Vol. 52 Issue 4, p741 

    This paper proposes an efficient, hierarchical high-order enrichment approach for the finite cell method applied to problems of solid mechanics involving discontinuities and singularities. In contrast to the standard extended finite element method, where new degrees of freedom are introduced for...

  • Stress amplification in three-dimensional narrow zones created by cavities. Syngellakis, Stavros // Theoretical & Applied Mechanics; 

    The paper is concerned with a particular case of stress amplification arising from the proximity of a spherical cavity to the boundary of a loaded elastic solid. The performed approximate analysis yields distributions of stresses and displacements in the narrow region formed between a spherical...

  • Mixed finite element method for linear elasticity in a cracked domain. Bennania, M. A.; El Akkadb, Abdeslam; Elkhalfia, Ahmed // WSEAS Transactions on Applied & Theoretical Mechanics;2014, Vol. 9, p167 

    A mixed finite element procedure for plane elasticity system in a cracked domains is introduced and analyzed. There is a member of the family for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and each is stable and affords optimal order...

  • Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations. Jingjun Zhao; Jingyu Xiao; Yang Xu // Abstract & Applied Analysis;2013, p1 

    A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem....

  • A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations. Mauricio Santillana; Clint Dawson // Computational Geosciences;Jan2010, Vol. 14 Issue 1, p31 

    Abstract  In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based on the Galerkin...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics