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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 843-855 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The two matrix equations obtained from the mixed finite element method are uncoupled through the use of the QR decomposition. The procedure obtains the basis for the null space which is composed of solutions to the homogeneous flux-equilibrium equation. The result is that, even for statically indeterminate problems, stresses can be obtained without solving for the displacement field. Furthermore, the stress field can be decomposed directly into contributions from applied forces and from prescribed displacements. The appearance of kinetic modes can easily be monitored. The possibility of utilizing non-conventional basis functions for use in conjunction with the QR decomposition is explored briefly. Simple examples are given to illustrate the theoretical results.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 687-703 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Exact analytical expressions for the eigenvalues of the elastic stiffness matrix are obtained for the four-node, rectangular, quadrilateral element. A procedure is given for identifying alternative hourglass modes and eigenvalues which render the element incompatible but with non-monotonic convergence assured. A convergence study confirms that for the special case of when the hourglass modes coincide with beam bending the element can serve as a beam element. Analytical expressions are given for the resulting element stiffness matrix.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1721-1736 
    ISSN: 0029-5981
    Keywords: material stability ; loss of ellipticity ; discontinuous bifurcation ; numerical solution ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Material instability occurs when ellipticity is lost for symmetric constitutive equations. Prior to loss of ellipticity it is possible that the second-order work of Hill or Drucker becomes negative. There are implications in the literature that numerical solutions cease to be meaningful when a material strain softens and the second-order work is not positive. The instant that the second-order work is zero or negative simultaneously with the additional restriction that the strain increments satisfy compatibility is equivalent to the loss of the ellipticity criterion for symmetric constitutive relations. The loss of ellipticity criterion is the appropriate one for identifying when numerical solutions cease to show convergence and may also be a suitable criterion for identifying the instant at which material failure is initiated. An analytical development is provided for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane. Numerical solutions are given for several sample problems. For all cases, the numerical solutions based on the finite element method conform to the theoretical expectations that unique numerical solutions exist prior to the point at which ellipticity is lost.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1927-1944 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: High-order elements are an option for providing an enhanced rate of convergence. However, it is not widely known that if a high-order element based on a mapping from a master-element space is distorted by displacing one of the side nodes slightly from the traditional midside position then the rate of convergence drops one order. The proof for a three-node element in one dimension has been given previously. Here, a numerical demonstration is presented to show how quickly the rate is lost as the second node is moved from the midpoint. For a six-node triangular element, a similar convergence study is performed in two dimensions in which one of the side nodes is moved off centre along a straight line joining the vertices of the triangle. Again, a loss in the order of convergence is shown although the loss is only apparent for sufficiently small element size. To prevent this drop in the rate of convergence as a side node is displaced, a procedure is given for developing the element stiffness matrix without formulating element basis functions. For the six-node triangle, a complete quadratic representation is retained, but at the expense of element compatibility between nodes. The numerical investigation shows that convergence appears to be retained but that the error associated with the incompatibility is greater than the error obtained with the use of distorted isoparametric elements. The results of this study are particularly appropriate for domains with curved boundaries and for non-linear problems in which node positions are updated according to the deformation history.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 563-573 
    ISSN: 1069-8299
    Keywords: constraints ; boundary conditions ; rigid inclusions ; inextensibility ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Constraints arise naturally in the context of rigid inclusions, incompressibility, inextensible fibres and deformed finite elements. Typical methods for handling constraints in the governing matrix equation include Lagrange multipliers, penalty weights and elimination of variables. Each procedure has a particular undesirable feature. Proposed here is an approach in which each constraint is handled directly and sequentially through a modification of the rows and columns of the governing matrix and force vector. Positive definiteness, symmetry and the dimensions of the matrix remain unchanged. Elementary examples involving both the static and dynamic response of a bar are given to illustrate the procedure.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 35 (1995), S. 387-394 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Rigid, closed-cell, polyurethane foam consists of interconnected polyurethane plates that form cells. When this foam is compressed, it exhibits an initial elastic regime, which is followed by a plateau regime in which the load required to compress the foam remains nearly constant. In the plateau regime, cell walls are damaged and large permanent volume changes are generated. As additional load is applied, cell walls are compressed against neighboring cell walls, and the stiffness of the foam increases and approaches a value equal to that of solid poyurethane. When the foam is loaded in tension, the cell walls are damaged and the foam fractures. A constitutive theory for rigid polyurethane foam has been developed. This theory is based on a decomposition of the foam in two parts: a skeleton and a nonlinear elastic continuum in parallel. The skeleton accounts for the foam behavior in the elastic and plateau regimes and is described using a coupled plasticity with continuum damage theory. The nonlinear elastic continuum accounts for the lock-up of the foam due to internal gas pressure and cell wall interactions. This new constitutive theory has been implemented in both static and dynamic finite element codes. Numerical simulations performed using the new constitutive theory are presented.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Publication Date: 2006-10-24
    Print ISSN: 0148-0227
    Electronic ISSN: 2156-2202
    Topics: Geosciences
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  • 8
    Publication Date: 2019-08-16
    Description: One of the dominant characteristics of Arctic ice as reflected by RADARSAT Geophysical Processor System data is the development and persistence of leads. Experimental data from small specimens as well as in situ data from Arctic ice suggest that failure may occur under compression. Presented here is a decohesive constitutive model for which one of the distinguishing new features is that failure is predicted under uniaxial compression. More generally, the model specifically indicates when a lead is initiated, provides the orientation of the lead, gives the mode of failure, and allows one to numerically determine the width of leads. In addition, the approach allows multiple failure planes, a feature that is necessary to simulate crack branching. Pre-existing planes of weakness such as those formed from previous leads can be incorporated. Sample calculations indicate how such a model can be used for large-scale numerical simulations.
    Keywords: Oceanography
    Type: H23I-04
    Format: text
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  • 9
    Publication Date: 2019-08-17
    Description: We are developing, testing, and validating a new sea ice dynamics model that treats the ice cover as an elastic/decohesive material in the permanent pack and includes the correct frazil/pancake behavior in the marginal zone. Two salient features of present ice dynamics models are that they do not: 1) reproduce the oriented fracture patterns of openings and closings in the pack ice, and 2) accurately model the effects of frazil/pancake ice formation in the ice margin. These poorly modeled areas account for a substantial portion of the ice growth, turbulent heat flux to the atmosphere, salt flux to the ocean, and energy dissipation due to slippage, ridging, and rafting, in the Arctic. Existing sea ice models have shown limited success in predicting the degree to which a lead will open for prescribed or observed forcing conditions. An important aspect of the new model we are developing is that the existence of cracks, along with their orientation, opening, and closing, is predicted. To put this effort in perspective a short history of ice dynamics modeling and data collection is presented. The RGPS data set is used to validate the model. As part of the testing and validation of the model, we are working on a new metric for comparing linear features (leads and ridges) in the data and model to be used in data assimilation for this model. The model framework is presented as well as some results showing the creation and development of leads in a simulation of ice dynamics in the Beaufort Sea. Other presentations by the authors will show other results from this effort.
    Keywords: Oceanography
    Type: H23I-03
    Format: text
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