Three-dimensional layerwise modeling of layered media with boundary integral equations

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dc.contributor.authorKokkinos, Filis-Triantaphyllos T.en
dc.contributor.committeechairReddy, Junuthula N.en
dc.contributor.committeememberGriffin, Odis Hayden Jr.en
dc.contributor.committeememberHendricks, Scott L.en
dc.contributor.committeememberRagab, Saad A.en
dc.contributor.committeememberRenardy, Yuriko Y.en
dc.contributor.committeememberKatsikadelis, J. T.en
dc.contributor.departmentEngineering Mechanicsen
dc.date.accessioned2014-03-14T21:09:26Zen
dc.date.adate2009-02-13en
dc.date.available2014-03-14T21:09:26Zen
dc.date.issued1995-12-15en
dc.date.rdate2009-02-13en
dc.date.sdate2009-02-13en
dc.description.abstractA hybrid method is presented for the analysis of layers, plates, and multi-layered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multi-layered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. A one-dimensional finite element model is used for the analysis of the multi-layered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of the typical infinite layer, which are applied in the two-dimensional boundary integral equation model to produce the integral representation of the solution. The boundary integral equation model is two-dimensional, displacement-based and assumes piecewise continuous distribution of the displacement components through the system's thickness. The developed model describes the three-dimensional displacement field, the stress field, the strains and the interlaminar stresses over the entire domain of the problem as continuous functions of the position. This detailed three-dimensional analysis is achieved by incorporating only contour integrals. The boundary integral equations are discretized using the boundary element method and a numerical model is developed for the single numerical layer (element). This model is extended to the case of a multilayered system by introducing appropriate continuity conditions at the interfaces between the layers (firmly bonded layers, or separation, slip and friction between the layers). Assembly of the element matrices yields the global system of equations, which can be solved via iterative techniques. In addition, numerical techniques are developed for the evaluation of the boundary and domain integrals involved in the construction of the element matrices. The singular boundary integrals are computed using a special coordinate transformation, along with a subdivision of the boundary element and a transformation of the Gauss points. The domain integrals (regular, singular or near-singular) are transformed to regular definite integrals along the boundary through a semi-analytical approach. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems. It can also be used to study plates resting on elastic foundations or plates with internal supports. The proposed method can be applied in an obvious manner to anisotropic materials and vibration problems.en
dc.description.degreePh. D.en
dc.format.extentxi, 177 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-02132009-170805en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-02132009-170805/en
dc.identifier.urihttp://hdl.handle.net/10919/37340en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1995.K71.pdfen
dc.relation.isformatofOCLC# 34647247en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectfinite element modelsen
dc.subjectfundamental solutionsen
dc.subjectthick platesen
dc.subjectlaminated platesen
dc.subjectsandwich platesen
dc.subjectlayerwise theoryen
dc.subjectboundary element modelsen
dc.subjectBEM and FEM couplingen
dc.subject.lccLD5655.V856 1995.K71en
dc.titleThree-dimensional layerwise modeling of layered media with boundary integral equationsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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