Development of discontinuous Galerkin method for nonlocal linear elasticity
Name
225080524-MIT.pdf
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Full printable version
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3.88 MB
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Author(s)
Bala Chandran, Ram
Advisor(s)
Raúl Radovitzky.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
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).
Subjects
Computation for Design and Optimization Program.
MIT Department
Massachusetts Institute of Technology. Computation for Design and Optimization Program
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