Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6915969 | Computer Methods in Applied Mechanics and Engineering | 2016 | 30 Pages |
Abstract
The fourth-order boundary value problems of one parameter gradient-elastic bar and plane strain/stress models are formulated in a variational form within an H2 Sobolev space setting. For both problems, the existence and uniqueness of the solution is established by proving the continuity and coercivity of the associated symmetric bilinear form. For completeness, the full sets of boundary conditions of the problems are derived and, in particular, the new types of boundary conditions featured by the gradient-elastic models are given the additional attributes singly and doubly. By utilizing the continuity and coercivity of the continuous problems, corresponding error estimates are formulated for conforming Galerkin formulations. Finally, numerical results, with isogeometric Cpâ1-continuous discretizations for NURBS basis functions of order pâ¥2, confirm the theoretical results and illustrate the essentials of both static and vibration problems.
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Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Jarkko Niiranen, Sergei Khakalo, Viacheslav Balobanov, Antti H. Niemi,