Development of discontinuous Galerkin method for nonlocal linear elasticity
Citable URI:
http://hdl.handle.net/1721.1/41730
| Title: | Development of discontinuous Galerkin method for nonlocal linear elasticity |
| Author: | Bala Chandran, Ram |
| Other Contributors: | Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Advisor: | Raúl Radovitzky. |
| Department: | Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Publisher: | Massachusetts Institute of Technology |
| Issue Date: | 2007 |
| Abstract: | A number of constitutive theories have arisen describing materials which, by nature, exhibit a non-local response. The formulation of boundary value problems, in this case, leads to a system of equations involving higher-order derivatives which, in turn, results in requirements of continuity of the solution of higher order. Discontinuous Galerkin methods are particularly attractive toward this end, as they provide a means to naturally enforce higher interelement continuity in a weak manner without the need of modifying the finite element interpolation. In this work, a discontinuous Galerkin formulation for boundary value problems in small strain, non-local linear elasticity is proposed. The underlying theory corresponds to the phenomenological strain-gradient theory developed by Fleck and Hutchinson within the Toupin-Mindlin framework. The single-field displacement method obtained enables the discretization of the boundary value problem with a conventional continuous interpolation inside each finite element, whereas the higher-order interelement continuity is enforced in a weak manner. The proposed method is shown to be consistent and stable both theoretically and with suitable numerical examples. |
| Description: |
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. Includes bibliographical references (p. 75-81). |
| URI: | http://hdl.handle.net/1721.1/41730 |
| Keywords: | Computation for Design and Optimization Program. |
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