Spelling suggestions: "subject:"figher order finite element methods"" "subject:"gaigher order finite element methods""
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Multiscale analysis of nanocomposite and nanofibrous structuresUnnikrishnan, Vinu Unnithan 15 May 2009 (has links)
The overall goal of the present research is to provide a computationally based
methodology to realize the projected extraordinary properties of Carbon Nanotube (CNT)-
reinforced composites and polymeric nanofibers for engineering applications. The
discovery of carbon nanotubes (CNT) and its derivatives has led to considerable study
both experimentally and computationally as carbon based materials are ideally suited for
molecular level building blocks for nanoscale systems. Research in nanomechanics is
currently focused on the utilization of CNTs as reinforcements in polymer matrices as
CNTs have a very high modulus and are extremely light weight.
The nanometer dimension of a CNT and its interaction with a polymer chain
requires a study involving the coupling of the length scales. This length scale coupling
requires analysis in the molecular and higher order levels. The atomistic interactions of the
nanotube are studied using molecular dynamic simulations. The elastic properties of neat
nanotube as well as doped nanotube are estimated first. The stability of the nanotube
under various conditions is also dealt with in this dissertation.
The changes in the elastic stiffness of a nanotube when it is embedded in a
composite system are also considered. This type of a study is very unique as it gives
information on the effect of surrounding materials on the core nanotube. Various
configurations of nanotubes and nanocomposites are analyzed in this dissertation.
Polymeric nanofibers are an important component in tissue engineering; however,
these nanofibers are found to have a complex internal structure. A computational strategy is developed for the first time in this work, where a combined multiscale approach for the
estimation of the elastic properties of nanofibers was carried out. This was achieved by
using information from the molecular simulations, micromechanical analysis, and
subsequently the continuum chain model, which was developed for rope systems. The
continuum chain model is modified using properties of the constituent materials in the
mesoscale. The results are found to show excellent correlation with experimental
measurements.
Finally, the entire atomistic to mesoscale analysis was coupled into the macroscale
by mathematical homogenization techniques. Two-scale mathematical homogenization,
called asymptotic expansion homogenization (AEH), was used for the estimation of the
overall effective properties of the systems being analyzed. This work is unique for the
formulation of spectral/hp based higher-order finite element methods with AEH. Various
nanocomposite and nanofibrous structures are analyzed using this formulation.
In summary, in this dissertation the mechanical characteristics of nanotube based
composite systems and polymeric nanofibrous systems are analyzed by a seamless
integration of processes at different scales.
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Higher-Order Spectral/HP Finite Element Technology for Structures and Fluid FlowsVallala, Venkat Pradeep 16 December 2013 (has links)
This study deals with the use of high-order spectral/hp approximation functions in the finite element models of various nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. For many of these classes of problems, the high-order (typically, polynomial order p greater than or equal to 4) spectral/hp finite element technology offers many computational advantages over traditional low-order (i.e., p < 3) finite elements. For instance, higher-order spectral/hp finite element procedures allow us to develop robust structural elements for beams, plates, and shells in a purely displacement-based setting, which avoid all forms of numerical locking. The higher-order spectral/hp basis functions avoid the interpolation error in the numerical schemes, thereby making them accurate and stable. Furthermore, for fluid flows, when combined with least-squares variational principles, such technology allows us to develop efficient finite element models, that always yield a symmetric positive-definite (SPD) coefficient matrix, and thereby robust direct or iterative solvers can be used. The least-squares formulation avoids ad-hoc stabilization methods employed with traditional low-order weak-form Galerkin formulations. Also, the use of spectral/hp finite element technology results in a better conservation of physical quantities (e.g., dilatation, volume, and mass) and stable evolution of variables with time in the case of unsteady flows. The present study uses spectral/hp approximations in the (1) weak-form Galerkin finite element models of viscoelastic beams, (2) weak-form Galerkin displacement finite element models of shear-deformable elastic shell structures under thermal and mechanical loads, and (3) least-squares formulations for the Navier-Stokes equations governing flows of viscous incompressible fluids. Numerical simulations using the developed technology of several non-trivial benchmark problems are presented to illustrate the robustness of the higher-order spectral/hp based finite element technology.
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