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Raúl Radovitzky. Bala Chandran, Ram Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program 2008-05-19T16:12:48Z 2008-05-19T16:12:48Z 2007 2007 http://hdl.handle.net/1721.1/41730 225080524 Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. Includes bibliographical references (p. 75-81). 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. by Ram Bala Chandran. S.M. 103 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Computation for Design and Optimization Program. Development of discontinuous Galerkin method for nonlocal linear elasticity Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="bfc57dcb-3a8e-431d-b854-140b8556a78c"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Development of discontinuous Galerkin method for nonlocal linear elasticity</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2007</PublicationDate> <Authors> <Author> <DisplayName>Bala Chandran, Ram</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Computation for Design and Optimization Program.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>