• Login
    View Item 
    •   SMARTech Home
    • Georgia Tech Theses and Dissertations
    • Georgia Tech Theses and Dissertations
    • View Item
    •   SMARTech Home
    • Georgia Tech Theses and Dissertations
    • Georgia Tech Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    A nonlinear theory of Cosserat elastic plates using the variational-asymptotic method

    Thumbnail
    View/Open
    KOVVALI-DISSERTATION-2015.pdf (3.099Mb)
    Date
    2015-08-26
    Author
    Kovvali, Ravi Kumar
    Metadata
    Show full item record
    Abstract
    One of the most important branches of applied mechanics is the theory of plates - defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions. There is an abundance of plate theories in the literature modeling classical elastic solids that fit this description. Recently, however, there has been a steady growth of interest in modeling materials with microstructures that exhibit length-scale dependent behavior, generally known as Cosserat elastic materials. Concurrently, there has also been an increased interest in the construction of reduced dimensional models of such materials owing to advantages like reduced computational effort and a simpler, yet elegant, resulting mathematical formulation. The objective of this work is the formulation and implementation of a theory of elastic plates with microstructure. The mathematical underpinning of the approach used is the Variational Asymptotic Method (VAM), a powerful tool used to construct asymptotically correct plate models. Unlike existing Cosserat plate models in the literature, the VAM allows for a plate formulation that is free of a priori assumptions regarding the kinematics. The result is a systematic derivation of the two-dimensional constitutive relations and a set of geometrically-exact, fully intrinsic equations gov- erning the motion of a plate. An important consequence is the extraction of the drilling degree of freedom and the associated stiffness. Finally, a Galerkin approach for the solution of the fully-intrinsic formulation will be developed for a Cosserat sur- face analysis which will also be compatible with more traditional plate solvers based on the classical theory of elasticity. Results and validation are presented from linear static and dynamic analyses, along with a discussion on some challenges and solution techniques for nonlinear problems.One of the most important branches of applied mechanics is the theory of plates - defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions. There is an abundance of plate theories in the literature modeling classical elastic solids that fit this description. Recently, however, there has been a steady growth of interest in modeling materials with microstructures that exhibit length-scale dependent behavior, generally known as Cosserat elastic materials. Concurrently, there has also been an increased interest in the construction of reduced dimensional models of such materials owing to advantages like reduced computational effort and a simpler, yet elegant, resulting mathematical formulation. The objective of this work is the formulation and implementation of a theory of elastic plates with microstructure. The mathematical underpinning of the approach used is the Variational Asymptotic Method (VAM), a powerful tool used to construct asymptotically correct plate models. Unlike existing Cosserat plate models in the literature, the VAM allows for a plate formulation that is free of a priori assumptions regarding the kinematics. The result is a systematic derivation of the two-dimensional constitutive relations and a set of geometrically-exact, fully intrinsic equations gov- erning the motion of a plate. An important consequence is the extraction of the drilling degree of freedom and the associated stiffness. Finally, a Galerkin approach for the solution of the fully-intrinsic formulation will be developed for a Cosserat sur- face analysis which will also be compatible with more traditional plate solvers based on the classical theory of elasticity. Results and validation are presented from linear static and dynamic analyses, along with a discussion on some challenges and solution techniques for nonlinear problems.
    URI
    http://hdl.handle.net/1853/54342
    Collections
    • Georgia Tech Theses and Dissertations [22398]
    • School of Aerospace Engineering Theses and Dissertations [1342]

    Browse

    All of SMARTechCommunities & CollectionsDatesAuthorsTitlesSubjectsTypesThis CollectionDatesAuthorsTitlesSubjectsTypes

    My SMARTech

    Login

    Statistics

    View Usage StatisticsView Google Analytics Statistics
    • About
    • Terms of Use
    • Contact Us
    • Emergency Information
    • Legal & Privacy Information
    • Accessibility
    • Accountability
    • Accreditation
    • Employment
    • Login
    Georgia Tech

    © Georgia Institute of Technology

    • About
    • Terms of Use
    • Contact Us
    • Emergency Information
    • Legal & Privacy Information
    • Accessibility
    • Accountability
    • Accreditation
    • Employment
    • Login
    Georgia Tech

    © Georgia Institute of Technology