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  • 1
    Electronic Resource
    Electronic Resource
    Myocardial material property determination in the in vivo heart using magnetic resonance imaging (1996)
    Springer
    The international journal of cardiovascular imaging 12 (1996), S. 153-167 
    Details
    ISSN: 1573-0743
    Keywords: finite element analysis (FEA) ; material properties ; magnetic resonance imaging (MRI)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Objectives: To determine nonlinear material properties of passive, diastolic myocardium using magnetic resonance imaging (MRI) tissue-tagging, finite element analysis (FEA) and nonlinear optimization.Background: Alterations in the diastolic material properties of myocardium may pre-date the onset of or exist exclusive of systolic ventricular dysfunction in disease states such as hypertrophy and heart failure. Accordingly, significant effort has been expended recently to characterize the material properties of myocardium in diastole. The present study defines a new technique for determining material properties of passive myocardium using finite element (FE) models of the heart, MRI tissue-tagging and nonlinear optimization. This material parameter estimation algorithm is employed to estimate nonlinear material parameters in thein vivo canine heart and provides the necessary framework to study the full complexities of myocardial material behavior in health and disease.Methods and results: Material parameters for a proposed exponential strain energy function were determined by minimizing the least squares difference between FE model-predicted and MRI-measured diastolic strains. Six mongrel dogs underwent MRI imaging with radiofrequency (RF) tissue-tagging. Two-dimensional diastolic strains were measured from the deformations of the MRI tag lines. Finite element models were constructed from early diastolic images and were loaded with the mean early to late left ventricular and right ventricular diastolic change in pressure measured at the time of imaging. A nonlinear optimization algorithm was employed to solve the least squares objective function for the material parameters. Average material parameters for the six dogs wereE=28,722 ± 15,984 dynes/cm2 andc=0.00182 ± 0.00232 cm2/dyne.Conclusion: This parameter estimation algorithm provides the necessary framework for estimating the nonlinear, anisotropic and non-homogeneous material properties of passive myocardium in health and disease in thein vivo beating heart.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01806218
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  • 2
    Electronic Resource
    Electronic Resource
    Generalized stress intensity factors in linear elastostatics (1995)
    Springer
    International journal of fracture 72 (1995), S. 223-240 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The solution of two-dimensional linear elastostatic problems in the neighborhood of singular points is discussed. A reliable and efficient method for computing the eigenpairs that characterize the exact solution and their coefficients, called the generalized stress intensity factors, by the finite element method is demonstrated. Examples, representing three very different kinds of singular points demonstrate that the method works well and produces results of high accuracy. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00037312
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  • 3
    Electronic Resource
    Electronic Resource
    Mathematical three-dimensional solid modeling of biventricular geometry (1993)
    Springer
    Annals of biomedical engineering 21 (1993), S. 199-219 
    Details
    ISSN: 1573-9686
    Keywords: Cardiac representation ; Ventricular geometry ; Finite element analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The characterization of regional myocardial stress distribution has been limited by the use of idealized mathematical representations of biventricular geometry. State-of-the-art computer-aided design and engineering (CAD/CAE) techniques can be used to create complete, unambiguous mathematical representations (solid models) of complex object geometry that are suitable for a variety of applications, including stress-strain analyses. We have used advanced CAD/CAE software to create a 3-D solid model of the biventricular unit using planar geometric data extracted from anex vivo canine heart. Volumetric analysis revealed global volume errors of 4.7%, −1.3%, −1.6%, and −1.1% for the left ventricular cavity, right ventricular cavity, myocardial wall, and total enclosed volumes, respectively. Model errors for 34 in-plane area and circumference determinations (mean ±SD) were 5.3±6.7% and 3.8±2.7%. Error analysis suggested that model volume errors may be due to operator variability. These results demonstrate that solid modeling of theex vivo biventricular unit yields an accurate mathematical representation of myocardial geometry which is suitable for meshing and subsequent finite element analysis. The use of CAD/CAE solid modeling in the representation of biventricular geometry may thereby facilitate the characterization of regional myocardial stress distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02368177
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  • 4
    Electronic Resource
    Electronic Resource
    Derivation of stiffness matrices for problems in plane elasticity by Galerkin's method (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 301-310 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Solution of plane elastic problems by piecewise linear approximation is outlined. This method is based upon Galerkin error distribution technique, which leads to simultaneous algebraic equations identical to those associated with the Finite Element Method. In addition, this method permits definition of the discretization error, which can be computed once the displacement components are known. Properties of the interpolation functions are discussed, and a sequence of internally compatible plane elastic elements is defined.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010308
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  • 5
    Electronic Resource
    Electronic Resource
    Linear equality constraints in finite element approximationThis paper was presented at the Seventh U.S. National Congress of Applied Mechanics, University of Colorado, 3-7 June, 1974. (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 563-580 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The typical numerical problem associated with finite element approximations is a quadratic programming problem with linear equality constraints. When nodal variables are employed, the coefficient matrix of the constraint equations, [A], acquires a block-diagonal structure. The transformation from polynomial coefficients to nodal variables involves finding a basis for [A] and computing its inverse.Simultaneous satisfaction of completeness and C1 (or higher) continuity requirements establishes linear relationships among the nodal variables and precludes inversion of the basis by exclusively element-level operations.Linear dependencies among the constraint equations and among the nodal variables can be evaluated by the simplex method. The computational procedure is outlined.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090306
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    A posteriori error indicators for the p-version of the finite element method (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1851-1870 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The existence of local a posteriori error indicators for the p-version of the finite element method is demonstrated through numerical examples. The optimal sequence of p-distributions can be closely followed on the basis of the indicators.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191209
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  • 7
    Electronic Resource
    Electronic Resource
    Convergence of stress maxima in finite element computations (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 683-697 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of stress maxima, computed directly from finite element solutions, is investigated with respect to a family of exact solutions characterized by varying degrees of smoothness. The performances of h- and p-extensions and the product and trunk spaces are evaluated and documented with respect to a family of benchmark problems. In uniform p-extensions a characteristic pattern in the convergence of stress maxima was observed. There does not appear to be a clear-cut advantage of the product space over the trunk space in this respect. The much faster convergence of stress maxima in the case of p-extensions, as compared with h-extensions, is evident from the results.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100903
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  • 8
    Electronic Resource
    Electronic Resource
    Hierarchic plate and shell models based on p-extensionThis paper is dedicated to Professor Ivo Babuša on the occasion of his sixtieth birthday. A summary of the work reported herein was presented at a conference at which Professor Babuša was honoured for his numerous contributions in the fields of engineering and applied mathematics. The conference, entitled: ‘The Impact of Mathematical Analysis on the Numerical Solution of Engineering Problems’, was held at the University of Maryland, College Park, MD September 17-19, 1986. (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 1855-1881 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests and (3) observation of the convergence of quantities of interest.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620260812
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Stress computations for nearly incompressible materials by the p-version of the finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2175-2190 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the case of nearly incompressible elastic materials the strain energy, the shear stress and the difference of normal stresses can be computed accurately by direct methods when the p-version of the finite element method is used. Computation of the sum of the normal stresses requires special procedures. In this paper such procedures are described and examples are presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280913
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  • 10
    Electronic Resource
    Electronic Resource
    Hierarchic models for laminated composites (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 503-535 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The principles governing the formulation of hierarchic models for laminated composites are discussed. The essential features of the hierarchic models described herein are: (a) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness, and (b) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity. Examples are presented.
    Additional Material: 29 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330304
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