Convergence analysis of Laplacian-based gradient elasticity in an isogeometric framework
暂无分享,去创建一个
[1] Antti H. Niemi,et al. Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems , 2016 .
[2] P. Skalka,et al. Novel approach to FE solution of crack problems in the Laplacian-based gradient elasticity , 2016 .
[3] Markus Kästner,et al. Isogeometric analysis of the Cahn-Hilliard equation - a convergence study , 2016, J. Comput. Phys..
[4] H. Askes,et al. Unified finite element methodology for gradient elasticity , 2015 .
[5] Carlos Armando Duarte,et al. One-dimensional nonlocal and gradient elasticity: Assessment of high order approximation schemes , 2014 .
[6] Bijan Boroomand,et al. Nonlocal elasticity defined by Eringen’s integral model: Introduction of a boundary layer method , 2014 .
[7] Krishna Garikipati,et al. Three-dimensional isogeometric solutions to general boundary value problems of Toupin’s gradient elasticity theory at finite strains , 2014, 1404.0094.
[8] M. Lazar,et al. On non-singular crack fields in Helmholtz type enriched elasticity theories , 2014, 1401.3158.
[9] Ju Liu,et al. Isogeometric analysis of the advective Cahn-Hilliard equation: Spinodal decomposition under shear flow , 2013, J. Comput. Phys..
[10] Angelo Simone,et al. One-dimensional nonlocal and gradient elasticity: Closed-form solution and size effect , 2013 .
[11] T. Hughes,et al. Local refinement of analysis-suitable T-splines , 2012 .
[12] John A. Evans,et al. Isogeometric finite element data structures based on Bézier extraction of NURBS , 2011 .
[13] E. Aifantis,et al. Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results , 2011 .
[14] Thomas J. R. Hughes,et al. An isogeometric analysis approach to gradient damage models , 2011 .
[15] Paul Steinmann,et al. Isogeometric analysis of 2D gradient elasticity , 2011 .
[16] I. Vardoulakis,et al. A three‐dimensional C1 finite element for gradient elasticity , 2009 .
[17] Ioannis Vardoulakis,et al. Two finite element discretizations for gradient elasticity , 2009 .
[18] T. Hughes,et al. Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .
[19] C. Wang,et al. The small length scale effect for a non-local cantilever beam: a paradox solved , 2008, Nanotechnology.
[20] E. Aifantis,et al. Finite element analysis with staggered gradient elasticity , 2008 .
[21] A. Zervos. Finite elements for elasticity with microstructure and gradient elasticity , 2008 .
[22] S. K. Park,et al. Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem , 2007 .
[23] Harm Askes,et al. Implicit gradient elasticity , 2006 .
[24] T. Hughes,et al. Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .
[25] Jia Lu,et al. NURBS-based Galerkin method and application to skeletal muscle modeling , 2005, SPM '05.
[26] O. C. Zienkiewicz,et al. The Finite Element Method: Its Basis and Fundamentals , 2005 .
[27] Fan Yang,et al. Experiments and theory in strain gradient elasticity , 2003 .
[28] Ahmad H. Nasri,et al. T-splines and T-NURCCs , 2003, ACM Trans. Graph..
[29] John Peddieson,et al. Application of nonlocal continuum models to nanotechnology , 2003 .
[30] N. Takeda,et al. Size effect on tensile strength of unidirectional CFRP composites— experiment and simulation , 2002 .
[31] E. Aifantis,et al. Numerical modeling of size effects with gradient elasticity - Formulation, meshless discretization and examples , 2002 .
[32] René Chambon,et al. Large strain finite element analysis of a local second gradient model: application to localization , 2002 .
[33] N. Aravas,et al. Mixed finite element formulations of strain-gradient elasticity problems , 2002 .
[34] M. Ortiz,et al. Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis , 2000 .
[35] N. Fleck,et al. FINITE ELEMENTS FOR MATERIALS WITH STRAIN GRADIENT EFFECTS , 1999 .
[36] Z. Bažant,et al. Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .
[37] E. Aifantis,et al. On Some Aspects in the Special Theory of Gradient Elasticity , 1997 .
[38] I. Vardoulakis,et al. Bifurcation Analysis in Geomechanics , 1995 .
[39] E. Aifantis,et al. A simple approach to solve boundary-value problems in gradient elasticity , 1993 .
[40] E. Aifantis. On the role of gradients in the localization of deformation and fracture , 1992 .
[41] I. Vardoulakis,et al. The thickness of shear bands in granular materials , 1987 .
[42] J. Strudel,et al. Influence of grain size on the mechanical behaviour of some high strength materials , 1986 .
[43] A. Eringen. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves , 1983 .
[44] A. C. Eringen,et al. Crack-tip problem in non-local elasticity , 1977 .
[45] A. Cemal Eringen,et al. NONLINEAR THEORY OF SIMPLE MICRO-ELASTIC SOLIDS-I , 1964 .
[46] Michael J. Borden,et al. Isogeometric finite element data structures based on Bézier extraction of T‐splines , 2010 .
[47] K. Höllig. Finite element methods with B-splines , 1987 .
[48] P. Gould. Introduction to Linear Elasticity , 1983 .
[49] A. Cemal Eringen,et al. Stress concentration at the tip of crack , 1974 .
[50] R. D. Mindlin,et al. On first strain-gradient theories in linear elasticity , 1968 .
[51] R. D. Mindlin. Micro-structure in linear elasticity , 1964 .
[52] R. Toupin. Elastic materials with couple-stresses , 1962 .
[53] R. Toupin. ELASTIC MATERIALS WITH COUPLE STRESSES, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS , 1962 .
[54] L. Richardson. The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, with an Application to the Stresses in a Masonry Dam , 1911 .
[55] E. Cosserat,et al. Théorie des Corps déformables , 1909, Nature.