# Browsing by Subject "finite element"

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Item A Viscoelastic-Viscoplastic Analysis of Fiber Reinforced Polymer Composites Undergoing Mechanical Loading and Temperature Changes(2013-08-09) Jeon, JaehyeukShow more This study presents a combined viscoelastic (VE)-viscoplastic (VP) analysis for Fiber Reinforced Polymer (FRP) composites subject to simultaneous mechanical load and conduction of heat. The studied FRP composites consist of unidirectional fibers, which are considered as linearly elastic with regards to their mechanical response, and isotropic polymeric matrix, which shows viscoelastic-viscoplastic response under various stresses and temperatures. Due to the viscoelastic and viscoplastic behavior of the polymeric matrix, the overall FRP composites exhibit a combined time-dependent and inelastic behavior. A simplified micromechanical model, consisting of a unit-cell with four fiber and matrix subcells, is formulated to homogenize the overall heat conduction and viscoelastic-viscoplastic responses of the FRP composites. The micromechanical model is compatible with a displacement based finite element (FE) and is implemented at the Gaussian integration points within the continuum finite elements, which is useful for analyzing the overall time-dependent response of FRP composite structures under various boundary conditions. The Schapery nonlinear integral model combined with the Perzyna viscoplastic model is used to describe the viscoelastic-viscoplastic response of the polymer constituents. An integrated time integration algorithm is formulated at the micromechanics level in order to solve the nonlinear viscoelastic-viscoplastic constitutive model at the matrix subcells and obtain the overall nonlinear response of the FRP. The viscoelastic-viscoplastic micromechanical model is validated usingexperimental data on off-axis glass/epoxy FRP composites available in literature. The overall response of the FRP composites determined from the simplified micromechanical model is also compared with the ones generated from microstructures of FRP with various fiber arrangements dispersed in homogeneous polymer matrix. The microstructural models of the FRP with detailed fiber arrangements are generated using FE. The effects of thermal stresses, due to the mismatches in the coefficient of thermal expansions of the fibers and polymeric matrix, and stress concentrations/discontinuities near the fiber and matrix interfaces on the overall thermo-mechanical deformation of FRP composites are studied using the two micromechanical models discussed above. Finally, an example of structural analysis is performed on a polymeric smart sandwich composite beam, having FRP skins and polymeric foam core with piezoelectric sensors integrated to the FRP skins, undergoing three point bending at an elevated temperature. The creep displacement is compared to experimental data available in literature.Show more Item Application of a Constrained Optimization Technique to the Imaging of Heterogeneous Objects Using Diffusion Theory(2011-02-22) Sternat, Matthew RyanShow more The problem of inferring or reconstructing the material properties (cross sections) of a domain through noninvasive techniques, methods using only input and output at the domain boundary, is attempted using the governing laws of neutron diffusion theory as an optimization constraint. A standard Lagrangian was formed consisting of the objective function and the constraints to satisfy, which was minimized through optimization using a line search method. The chosen line search method was Newton's method with the Armijo algorithm applied for step length control. A Gaussian elimination procedure was applied to form the Schur complement of the system, which resulted in greater computational efficiency. In the one energy group and multi-group models, the limits of parameter reconstruction with respect to maximum reconstruction depth, resolution, and number of experiments were established. The maximum reconstruction depth for one-group absorption cross section or multi-group removal cross section were only approximately 6-7 characteristic lengths deep. After this reconstruction depth limit, features in the center of a domain begin to diminish independent of the number of experiments. When a small domain was considered and size held constant, the maximum reconstruction resolution for one group absorption or multi-group removal cross section is approximately one fourth of a characteristic length. When finer resolution then this is considered, there is simply not enough information to recover that many region's cross sections independent of number of experiments or flux to cross-section mesh refinement. When reconstructing fission cross sections, the one group case is identical to absorption so only the multi-group is considered, then the problem at hand becomes more ill-posed. A corresponding change in fission cross section from a change in boundary flux is much greater then change in removal cross section pushing convergence criteria to its limits. Due to a more ill-posed problem, the maximum reconstruction depth for multi-group fission cross sections is 5 characteristic lengths, which is significantly shorter than the removal limit. To better simulate actual detector readings, random signal noise and biased noise were added to the synthetic measured solutions produced by the forward models. The magnitude of this noise and biased noise is modified and a dependency of the maximum magnitude of this noise versus the size of a domain was established. As expected, the results showed that as a domain becomes larger its reconstruction ability is lowered which worsens upon the addition of noise and biased noise.Show more Item Developing & tailoring multi-functional carbon foams for multi-field response(2009-05-15) Sarzynski, Melanie DianeShow more As technological advances occur, many conventional materials are incapable of providing the unique multi-functional characteristics demanded thus driving an accelerated focus to create new material systems such as carbon and graphite foams. The improvement of their mechanical stiffness and strength, and tailoring of thermal and electrical conductivities are two areas of multi-functionality with active interest and investment by researchers. The present research focuses on developing models to facilitate and assess multi-functional carbon foams in an effort to expand knowledge. The foundation of the models relies on a unique approach to finite element meshing which captures the morphology of carbon foams. The developed models also include ligament anisotropy and coatings to provide comprehensive information to guide processing researchers in their pursuit of tailorable performance. Several illustrations are undertaken at multiple scales to explore the response of multi-functional carbon foams under coupled field environments providing valuable insight for design engineers in emerging technologies. The illustrations highlight the importance of individual moduli in the anisotropic stiffness matrix as well as the impact of common processing defects when tailoring the bulk stiffness. Furthermore, complete coating coverage and quality interface conditions are critical when utilizing copper to improve thermal and electrical conductivity of carbon foams.Show more Item Direct Forcing Immersed Boundary Methods: Finite Element Versus Finite Volume Approach(2012-12-07) Frisani, Angelo 1980-Show more Two immersed boundary methods (IBM) for the simulation of conjugate heat transfer problems with complex geometries are introduced: a finite element (IFEM) and a finite volume (IFVM) immersed boundary methods are discussed. In the IFEM a projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations (NSEs) and energy equation in conjunction with the immersed boundary method for solving fluid flow and heat transfer problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body-fitted mesh. Dirichlet boundary constraints are satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the ?immersed? boundary) and vice versa, it is possible to impose the extra constraint to the NSEs as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisfy the divergence-free constraint. The IFEM approach presented shows third order accuracy in space and second order accuracy in time when the simulation results for the Taylor-Green decaying vortex are compared to the analytical solution. For the IFVM a ghost-cell approach with sharp interface scheme is used to enforce the boundary condition at the fluid/solid interface. The interpolation procedure at the immersed boundary preserves the overall second order accuracy of the base solver. The developed ghost-cell method is applied on a staggered configuration with the Semi-Implicit Method for Pressure-Linked Equations Revised algorithm. Second order accuracy in space and first order accuracy in time are obtained when the Taylor-Green decaying vortex test case is compared to the IFVM analytical solution. Computations were performed using the IFEM and IFVM approaches for the two-dimensional flow over a backward-facing step, two-dimensional flow past a stationary circular cylinder, three-dimensional flow past a sphere and two and three-dimensional natural convection in an enclosure with/without immersed body. The numerical results obtained with the discussed IFEM and IFVM were compared against other IBMs available in literature and simulations performed with the commercial computational fluid dynamics code STAR-CCM+/V7.04.006. The benchmark test cases showed that the numerical results obtained with the implemented immersed boundary methods are in good agreement with the predictions from STAR-CCM+ and the numerical data from the other IBMs. The immersed boundary method based of finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.Show more Item Finite Element Studies of Colloidal Mixtures Influenced by Electric Fields(2011-10-21) Drummond, Franklin JerrelShow more A further understanding of colloidal mixture behavior under applied electric fields would greatly benefit the design of smart material systems such as electrorheological fluidic devices and microfluidic reconfigurable antennas. This thesis presents a finite element analysis of colloidal mixture electrokinetic behavior. Computations of particle forces as a function of applied frequency and particle shape were performed. An effective medium property method was also studied. Fluidic and electric forces were obtained with various applied excitation frequencies throughout three locations in a coplanar microelectrode domain. This domain consists of two 50 nanometers thick gold electrodes separated by a 30 micrometers gap. The three locations are 1.2 micrometers, 40 micrometers, and 90 micrometers from the gap center. Total force vectors were computed by integrating Maxwell and Cauchy stress tensors to determine whether the particles are pushed toward or away from the electrode gap at frequencies of 10 Hz, 1 kHz, and 100 kHz. It was determined that particles were pushed outside the gap at median frequencies of 1kHz (indicating ac electroosmotic force domination) and began to be pushed back toward the gap at higher frequencies of 100 kHz (indicating dielectrophoretic force intensification). Particle shape effects were examined by calculating the electrical interparticle force between two particles at various incidences with respect to a uniform electric field. Particle attraction occurs when the line between the particle centers is aligned with the electric field; repulsion occurs when this center line is perpendicular. The incidence angle at which the particles switch from attraction to repulsion is defined as ?cr. The aspect ratio and particle edge separation distances used in this study were 1, 5,12.92 and 0.25 micrometers, 0.50 micrometers, 2.0 micrometers, respectively. The results indicate that higher aspect ratio particles tend to have smaller ?cr values and larger interparticle force magnitudes for given separation distances. Finally, effective dielectric constant simulations utilizing periodic crystalline arrangements of colloidal structure were performed. The results show good agreement with the Maxwell Garnett mixing rule at volume fractions above 30 percent. Less canonical structures of cubic particles were also modeled.Show more Item Modeling Time-dependent Responses of Piezoelectric Fiber Composite(2011-02-22) Li, Kuo-AnShow more The existence of polymer constituent in piezoelectric fiber composites (PFCs) could lead to significant viscoelastic behaviors, affecting overall performance of PFCs. High mechanical and electrical stimuli often generate significant amount of heat, increasing temperatures of the PFCs. At elevated temperatures, most materials, especially polymers show pronounced time-dependent behaviors. Predicting time-dependent responses of the PFCs becomes important to improve reliability in using PFCs. We study overall performance of PFCs having unidirectional piezoceramic fibers, such as PZT fibers, dispersed in viscoelastic polymer matrix. Two types of PFCs are studied, which are active fiber composites (AFCs) and macro fiber composites (MFCs). AFCs and MFCs consist of unidirectional PZT fibers dispersed in epoxy placed between two interdigitated electrode and kapton layers. The AFCs have a circular fiber cross-section while the MFCs have a square fiber cross-section. Finite element (FE) models of representative volume elements (RVEs) of active PFCs, having square and circular fiber cross-sections, are generated for composites with 20, 40, and 60 percent fiber contents. Two FE micromechanical models having one fiber embedded in epoxy matrix and five fibers placed in epoxy matrix are considered. A continuum 3D piezoelectric element in ABAQUS FE is used. A general time-integral function is applied for the mechanical, electrical, and piezoelectric properties in order to incorporate the time-dependent effect and histories of loadings. The effective properties of PZT-5A/epoxy and PZT-7A/LaRC-SI piezocomposites determined from the FE micromechanical models are compared to available experimental data and analytical solutions in the literature. Furthermore, the effect of viscoelastic behaviors of the LaRC-SI matrix at an elevated temperature on the overall electro-mechanical and piezoelectric constants are examined.Show more Item Structural and Aerodynamic Interaction Computational Tool for Highly Reconfigurable Wings(2011-10-21) Eisenbeis, Brian JosephShow more Morphing air vehicles enable more efficient and capable multi-role aircraft by adapting their shape to reach an ideal configuration in an ever-changing environment. Morphing capability is envisioned to have a profound impact on the future of the aerospace industry, and a reconfigurable wing is a significant element of a morphing aircraft. This thesis develops two tools for analyzing wing configurations with multiple geometric degrees-of-freedom: the structural tool and the aerodynamic and structural interaction tool. Linear Space Frame Finite Element Analysis with Euler-Bernoulli beam theory is used to develop the structural analysis morphing tool for modeling a given wing structure with variable geometric parameters including wing span, aspect ratio, sweep angle, dihedral angle, chord length, thickness, incidence angle, and twist angle. The structural tool is validated with linear Euler-Bernoulli beam models using a commercial finite element software program, and the tool is shown to match within 1% compared to all test cases. The verification of the structural tool uses linear and nonlinear Timoshenko beam models, 3D brick element wing models at various sweep angles, and a complex wing structural model of an existing aircraft. The beam model verification demonstrated the tool matches the Timoshenko models within 3%, but the comparisons to complex wing models show the limitations of modeling a wing structure using beam elements. The aerodynamic and structural interaction tool is developed to integrate a constant strength source doublet panel method aerodynamic tool, developed externally to this work, with the structural tool. The load results provided by the aerodynamic tool are used as inputs to the structural tool, giving a quasi-static aeroelastically deflected wing shape. An iterative version of the interaction tool uses the deflected wing shape results from the structural tool as new inputs for the aerodynamic tool in order to investigate the geometric convergence of an aeroelastically deflected wing shape. The findings presented in this thesis show that geometric convergence of the deflected wing shape is not attained using the chosen iterative method, but other potential methods are proposed for future work. The tools presented in the thesis are capable of modeling a wide range of wing configurations, and they may ultimately be utilized by Machine Learning algorithms to learn the ideal wing configuration for given flight conditions and develop control laws for a flyable morphing air vehicle.Show more Item Viscoelastic Analysis of Sandwich Beams Having Aluminum and Fiber-reinforced Polymer Skins with a Polystyrene Foam Core(2010-07-14) Roberts-Tompkins, Altramese L.Show more Sandwich beams are composite systems having high stiffness-to-weight and strength-to-weight ratios and are used as light weight load bearing components. The use of thin, strong skin sheets adhered to thicker, lightweight core materials has allowed industry to build strong, stiff, light, and durable structures. Due to the use of viscoelastic polymer constituents, sandwich beams can exhibit time-dependent behavior. This study examines and predicts the time-dependent behavior of sandwich beams driven by the viscoelastic foam core. Governing equations of the deformation of viscoelastic materials are often represented in differential form or hereditary integral form. A single integral constitutive equation is used to model linear viscoelastic materials by means of the Boltzmann superposition principle. Based on the strength of materials approach, the analytical solution for the deformation in a viscoelastic sandwich beam is determined based on the application of the Correspondence Principle and Laplace transform. Finite element (FE) method is used to analyze the overall transient responses of the sandwich systems subject to a concentrated point load at the midspan of the beam. A 2D plane strain element is used to generate meshes of the three-point bending beam. User material (UMAT) subroutine in ABAQUS FE code is utilized to incorporate the viscoelastic constitutive model for the foam core. Analytical models and experimental data available in the literature are used to verify the results obtained from the FE analysis. The stress, strain, and deformation fields during creep responses are analyzed. Parameters such as the viscosity of the foam core, the ratio of the skin and core thicknesses, the ratio of the skin and core moduli, and adhesive layers are varied and their effect on the timedependent behavior of the sandwich system is examined.Show more