scholarly journals Parallel finite-element implementation for higher-order ice-sheet models

2012 ◽  
Vol 58 (207) ◽  
pp. 76-88 ◽  
Author(s):  
Mauro Perego ◽  
Max Gunzburger ◽  
John Burkardt
Keyword(s):  
Finite Element ◽  
Computational Models ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Integrated Model ◽  
Higher Order ◽  
Order Model ◽  
Length Scales ◽  
First Order ◽  
Finite Element Approximations

AbstractHigher-order models represent a computationally less expensive alternative to the Stokes model for ice-sheet modeling. In this work, we develop linear and quadratic finite-element methods, implemented on parallel architectures, for the three-dimensional first-order model of Dukowicz and others (2010) that is based on the Blatter-Pattyn model, and for the depth-integrated model of Schoof and Hindmarsh (2010). We then apply our computational models to three of the ISMIP-HOM benchmark test cases (Pattyn and others, 2008). We compare results obtained from our models with those obtained using a reliable Stokes computational model, showing that our first-order model implementation produces reliable and accurate solutions for almost all characteristic length scales of the test geometries considered. Good agreement with the reference Stokes solution is also obtained by our depth-integrated model implementation in fast-sliding regimes and for medium to large length scales. We also provide a comprehensive comparison between results obtained from our first-order model implementation and implementations developed by ISMIP-HOM participants; this study shows that our implementation is at least as good as the previous ones. Finally, a comparison between linear and quadratic finite- element approximations is carried out, showing, as expected, the better accuracy of the quadratic finite-element method.

Transverse Stresses in Antisymmetric Angle Ply Sandwich Plates – Analytical Evaluation of Refined Higher Order Shear Deformation Theories

2010 ◽  
Vol 123-125 ◽  
pp. 599-602 ◽  
Author(s):  
K. Swaminathan ◽  
Govind R. Sangwai
Keyword(s):  
Computational Models ◽  
Processing Technique ◽  
Higher Order ◽  
Transverse Load ◽  
Sandwich Plates ◽  
Order Model ◽  
Simply Supported ◽  
First Order ◽  
Shear Deformation Theories ◽  
Transverse Stresses

In the present work two higher order computational models with 9 and 12 DOF already available in the literature for which analytical formulations and solutions for the stress analysis not yet reported are considered. In addition to these models, few higher order models and the first order model developed by other investigators are also considered for the evaluation. A simply supported plate subjected to sinusoidal transverse load with SS-2 boundary conditions is considered for the analysis. Solutions are obtained using Navier's technique. Transverse stresses are computed by post processing technique and the accuracy of models in predicting the stresses is evaluated.

Computational Models for Multilayered Composite Shells with Application to Tires

1996 ◽  
Vol 24 (1) ◽  
pp. 11-38 ◽  
Author(s):  
G. M. Kulikov
Keyword(s):  
Type Theory ◽  
Computational Models ◽  
Geometrical Nonlinearity ◽  
Higher Order ◽  
Stress Strain ◽  
Strain Fields ◽  
First Order ◽  
Timoshenko Type ◽  
Joint Influence ◽  
Discrete Layer

Abstract This paper focuses on four tire computational models based on two-dimensional shear deformation theories, namely, the first-order Timoshenko-type theory, the higher-order Timoshenko-type theory, the first-order discrete-layer theory, and the higher-order discrete-layer theory. The joint influence of anisotropy, geometrical nonlinearity, and laminated material response on the tire stress-strain fields is examined. The comparative analysis of stresses and strains of the cord-rubber tire on the basis of these four shell computational models is given. Results show that neglecting the effect of anisotropy leads to an incorrect description of the stress-strain fields even in bias-ply tires.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

scholarly journals Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

2011 ◽  
Vol 4 (3) ◽  
pp. 1569-1610
Author(s):  
J. J. Fürst ◽  
O. Rybak ◽  
H. Goelzer ◽  
B. De Smedt ◽  
P. de Groen ◽  
...  
Keyword(s):  
Velocity Field ◽  
Finite Difference ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Higher Order ◽  
Velocity Fields ◽  
Force Balance ◽  
Staggered Grid ◽  
Comparison Results ◽  
Resultant Velocity

Abstract. We present a novel finite difference implementation of a three-dimensional higher-order ice sheet model that performs well both in terms of convergence rate and numerical stability. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, an existing discretisation that operates exclusively on the regular grid serves as a reference. Participation in the ISMIP-HOM benchmark indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This allows a direct comparison not only of the resultant velocity fields but also of the solver's convergence behaviour which holds main differences. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the precision for the resultant velocity field can be chosen higher in the novel finite difference implementation. For high precisions, the old discretisation experiences difficulties to converge due to large variation in the velocity fields of consecutive Picard iterations. Finally, changing discretisation prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher precision and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. Transient applications also benefit from the increased computational efficiency.

Vibroacoustic Comparisons and Acoustic Power Insulation Mechanisms of Multidirectional Stiffened Laminated Plates

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
Fourier Transform ◽  
High Efficiency ◽  
Three Dimensional ◽  
Acoustic Power ◽  
Higher Order ◽  
Laminated Plates ◽  
Transverse Displacement ◽  
Third Order ◽  
First Order ◽  
Implicit Equations

Vibroacoustic characteristics of multidirectional stiffened laminated plates with or without compliant layers are explored in the wavenumber and spatial domains with the help of the two-dimensional continuous Fourier transform and discrete inverse fast Fourier transform. Implicit equations of motion for the arbitrary angle ply laminated plates are derived from the three-dimensional higher order and Reddy third order shear deformation plate theories. The expressions of acoustic power of the stiffened laminated plates with or without complaint layers are formulated in the wavenumber domain, which is a significant method to calculate acoustic power of the stiffened plates with multiple sets of cross stiffeners. Vibroacoustic comparisons of the stiffened laminated plates are made in terms of the transverse displacement spectra, forced responses, acoustic power, and input power according to the first order, Reddy third order, and three-dimensional higher order plate theories. Sound reduction profiles of compliant layers are further examined by the theoretical deductions. This study shows the feasibility and high efficiency of the first order and Reddy third order plate theories in the broad frequency range and allows a better understanding the principal mechanisms of acoustic power radiated from multidirectional stiffened laminated composite plates with compliant layers, which has not been adequately addressed in its companion paper. (Cao and Hua, 2012, “Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers,” ASME J. Vib. Acoust., 134(5), p. 051001.)

Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates

2005 ◽  
Vol 72 (6) ◽  
pp. 809-817 ◽  
Author(s):  
Jun-Sik Kim ◽  
Maenghyo Cho
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Laminated Plates ◽  
Sandwich Plates ◽  
First Order ◽  
Transverse Shear Strains

A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

scholarly journals Hydrodynamic Model Of Glaciers and Ice Sheets Interacted With Ocean

1990 ◽  
Vol 14 ◽  
pp. 347-347
Author(s):  
V.L. Mazo
Keyword(s):  
Shear Stress ◽  
Hydrodynamic Model ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Longitudinal Stress ◽  
First Order ◽  
Longwave Approximation ◽  
Different Parts

Tidewater glaciers and large ice sheets, e.g. the Antarctic ice sheet and a late-Würm Arctic ice sheet, are complex but single dynamic systems composed of terrestrial, marine and floating parts. Morphology and dynamics of the different parts are different. The terrestrial parts are convex and their dynamics are controlled by shear stress only (the longitudinal stress is zero); the floating parts are concave and their dynamics are controlled by longitudinal stress only (the shear stress is zero). To connect the different parts we should consider transitional zones where shear and longitudinal stresses are comparable.To describe glacier and ice-sheet dynamics, longwave approximation of the first order is used. In this approximation it is impossible to connect terrestrial and floating parts dynamically, only morphologically and kinematically. It means that the first-order longwave approximation is not sufficient.If the transitional zone between the terrestrial and floating parts is long in comparison to ice thickness (in hydrodynamics the term “weak” is used) we can do the next step in the longwave approximation to describe the single dynamical system consisting of the terrestrial and floating parts and the weak transitional zones (ice streams). It is a purely hydrodynamical approach to the problem without ad hoc hypothesis.The presented model is a non-stationary three-dimensional hydrodynamic model of glaciers and ice sheets interacted with ocean, involving the conditions of ice continuity and dynamic equilibrium, ice rheology, and boundary conditions on the free surface (dynamic and kinematic) and on the bed (ice freezing or sliding). Longwave approximation is used to reduce the three-dimensional model to a two-dimensional one. The latter consists of (1) evolution equations for grounded and floating parts and weak transitional zones; (2) boundary conditions on the fronts (e.g. the conditions of calving); (3) equations governing the junctions of the parts (the most important junction is the grounded line) with the conditions connecting the evolution equations.

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