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  • RPI SCOREC - Technical Reports
    isotropic solid The theoretical foundations of this theory are reviewed with emphasis on constitutive modeling Alternate mixed penalty and velocity pressure finite element formulations are used to solve the nonlinear biphasic governing equations including the effects of a strain dependent permeability and a hyperelastic solid phase under finite deformation The resulting first order nonlinear system of equations are discretized in time using an implicit finite difference scheme and solved using the Newton Raphson method Both formulations are used to develop quadrilateral and triangular elements in 2 D and hexahedral and tetrahedral elements in 3 D Numerical examples including those representative of soft tissue material testing and simple human joints are used to validate the formulations and to illustrate their applications While not the central objective of this work important insights have been gained from selected linear biphasic analyses A focus of this work is the comparison of the alternate formulations for nonlinear problems While it is demonstrated that both formulations produce a range of converging elements the velocity pressure formulation is found to be more efficient computationally A significant contribution of this work is the implementation and testing of a biphasic description with a transversely isotropic hyperelastic solid phase This

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=232 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    discretization Two important classes of problems of comparable complexity are addressed one each in the areas of linear and nonlinear case A fast efficient multilevel solution scheme is developed for large systems of nonlinear equations arising from finite element discretization The proposed solver results from an innovative combination of the BFGS quasi Newton method and FAS version of the multigrid method that preserves the desirable features of both the methods while minimizing most of their significant drawbacks The numerical experiments on history dependent elasto plastic problems demonstrate the potential of the new solution methodology for large scale nonlinear systems The problem considered in the linear case belongs to the class of nonpositive definite symmetric systems resulting from hybrid formulations that weakly enforces compatibility and traction continuity conditions between independently modeled substructures Two distinct approaches are investigated the domain decomposition method and the global local type method In the domain decomposition approach the nonpositive definite system is transformed into an equivalent positive definite system that can be solved by either iterative or direct method without pivoting A multigrid like algorithm is developed that uses the collocation problem as the auxiliary grid and a new computationally efficient preconditioner for smoothing The superiority

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=233 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    for Shell Analysis Year 1995 Journal Computational Mechanics Volume 16 1995 Pages 328 340 Abstract A new quadrature scheme and a family of hierarchical assumed strain elements have been developed to enhance the performance of the displacement based hierarchical shell

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=234 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    Laminated Composites Year 1995 Journal International Journal for Numerical Methods in Engineering Volume 39 21 Pages 3641 3662 Abstract The s version of finite element method is developed for laminated plates and shells By this technique the global domain is idealized using 2D Equivalent Single Layer model The regions where ESL model errs badly in capturing localized phenomena are superimposed by a stack of 3D elements Assumed strain formulation and

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=235 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    and Curvature Based Mesh Control Year 1994 Volume 75 Pages 67 96 Publisher Springer Verlag Editor Abstract Specific Issues associated with the automatic generation of finite element meshes for curved geometric domains are considered A review of the definition of when a triangulation is a valid mesh a geometric triangulation for curved geometric domains is given Consideration is then given to the additional operations necessary to maintain the validity of

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=236 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    et al 1 2 describes a reactive vapor infiltration RVI process for manufacturing fiber reinforced ceramic composites where silicon carbide SiC or alumina Al2 3 fibers are mixed with molybdenum Mo powder and pressed at room temperature to form a porous preform The preform is exposed to a silicon tetra chloride SiCl4 and hydrogen H2 flow where molecular surface reactions liberate Si which when absorbed into the preform reacts with Mo to form a molybdenum di silicide MoSi2 matrix As a first step in modeling the RVI process we present a mathematical model of the diffusion of Si into a compressed powder Mo pellet to form the MoSi2 matrix The production of an intermediate Mo5Si3 silicide layer the growth of the MoSi2 layer and the volume expansion of the pellet are predicted The model consisting of a nonlinear ordinary and partial differential system is solved using a state of the art adaptive software system 3 that includes capabilities for automatic quadtree structured mesh generation mesh refinement coarsening h refinement method order variation p refinement and mesh motion r refinement Computational solutions of one and two dimensional problems indicate that the adaptive software is a robust and effective tool for addressing

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=237 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    Dey and Ramamoorthy Ravichandran Title List of Error and Warning Messages in Finite Octree Mesh Generator Year 1994 Pages 34 Abstract This report lists all current error and warning messages given by Finite Octree during mesh generation The direct meaning of these messages and possible indirect cause are also explained There could be more than one possible indirect cause for a given message but tips are provided on indirect cause

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=238 (2015-07-15)
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  • RPI SCOREC - Technical Reports
    in Engineering Volume 38 Pages 1597 1610 Abstract We present a new approach for the fast efficient solution of large system of nonlinear equations arising from the finite element discretization The proposed nonlinear solver builds on the advantages of the popular methods of solution that are currently being employed while eliminating most of their undesirable features It combines the well known BFGS method with the FAS version of multigrid method

    Original URL path: http://www.scorec.rpi.edu/reports/view_report.php?id=239 (2015-07-15)
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