期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 316, 期 -, 页码 328-348出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2016.07.008
关键词
Generalized continuum; Gradient elasticity; Kirchhoff plate; Isogeometric analysis; Convergence analysis; Error estimates
资金
- Academy of Finland [270007, 260302]
- European Research Council [259229 ISOBIO]
- Academy of Finland (AKA) [260302, 270007, 270007, 260302] Funding Source: Academy of Finland (AKA)
Sixth-order boundary value problems of a one-parameter gradient-elastic Kirchhoff plate model are formulated in a weak form within an H-3 Sobolev space setting with the corresponding equilibrium equations and general boundary conditions. The corresponding conforming Galerkin method is proposed with error estimates for discretizations satisfying C-2 continuity requirements. Continuity, coercivity and consistency of the corresponding bilinear form are utilized for proving the theoretical results. Numerical computations with conforming isogeometric discretizations of CP-1-continuous NURBS basis functions of order p >= 3 confirm the theoretical results and illustrate the features of the problem for both statics and free vibrations. In particular, the effects of the additional boundary conditions and parameter-dependent boundary layers corresponding to the gradient elasticity theory are addressed by the numerical examples. (C) 2016 Elsevier B.V. All rights reserved.
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