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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the issue of invariance for various hybrid/mixed models with and without incompatible displacement modes is addressed. Special emphasis is directed to assumed spaces of the primary variables which are based on the natural co-ordinates. It is found that if the assumed spaces of all primary variables are invariant to orthogonal transformations, any derived models would automatically be invariant. In contrast to the traditional concept of choosing the starting stress/strain interpolants based on either global or local co-ordinate systems, it is shown that it is not necessary to employ either complete or balanced polynomial expansions of natural co-ordinates in order to preserve the element invariance. Based on one of the newly proposed classes of stress/strain interpolants, 8-node invariant-assumed stress brick elements are proposed which are close to Loikkanen and Irons' assumed stress counterpart of Wilson's Q6 brick element.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: assumed natural strain ; plate bending ; triangular ; finite element ; six-node ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a six-node triangular C0 plate bending element is developed by the assumed natural strain method. In the element, all the sampled natural transverse shear strains are chosen such that the latter has a favourable constraint index and the strains are optimized with respect to a linear pure moment field. The element passes the patch tests, yields satisfactory accuracy and shows no sign of shear locking in all the problems considered. Copyright © 1998 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article discusses two alternative methods of formulating the recently proposed quadrilateral plane element Qcs6, which is based on a generalized functional with multiple stress fields. The first method is derived by an extended Hu-Washizu Principle with the presence of incompatible modes and enforcement of energy orthogonality, while the second one is established on a non-conventional discrete local stress smoothing. Both methods can be applied to other structural element formulations with enhanced efficiency.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the formulation of a hybrid stress quadrilateral Kirchhoff plate bending element based on an extended complementary energy functional first proposed by Tong. With the inclusion of a Lagrange multiplier in the functional to enforce a constraint on the assumed moment space, the construction of the C1 deflection profile inside the element is no longer necessary. The continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way. Special attention is paid to the selection of assumed moment space such that the element stability, convergency, invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low. Quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading. Numerical examples are presented and the accuracy achieved is found to be satisfactory.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an efficient way to devise higher-order hybrid elements by generalizing the admissible matrix formulation recently proposed by the author. The assumed stress or strain is first decomposed into the constant, lower- and higher-order modes. In the absence of any higher-order modes, the resulting hybrid element would be identical to the corresponding sub-integrated displacement element. By a natural and straightforward method of orthogonalizing the higher-order modes with respect to the constant and lower-order modes, the element stiffness can be partitioned into a lower- and a higher-order matrix. With further refinements, the method devised can readily be applied to a number of higher-order hybrid elements with enhanced finite element consistency and computational efficiency.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: finite element ; assumed strain formulation ; Mindlin/Reissner ; plate bending ; triangular ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a six-node triangular C0 plate bending element is developed by the assumed strain formulation. The sampled transverse shear strains in the element are chosen such that the latter has a favourable constraint index of shear locking and the strains are optimized with respect to a linear pure bending displacement/rotation field. It happens that the optimal strains are the mean strains along the element edges and medians. Numerical examples reveal that the element is free from shear locking and passes all the patch tests for plate bending elements. Moreover, the element accuracy is close to that of a state-of-the-art seven-node assumed strain element. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an investigation of using orthogonal constant and higher order stress modes in formulating efficient hybrid elements by equipping the primary idea of Bergan and Hanssen. Two sample elements modified from Pian-Sumihara 5-β plane and Pian-Tong 18-β hexahedral assumed contravariant stress elements are derived. With the suggested admissible simplifications of the flexibility matrices incorporated into the two new elements, new plane and hexahédral elements requiring respectively no and a negligible amount of computing efforts for inverting the flexibility matrices are formed. All, proposed elements are stable, invariant, contain no empirically determined factor and strictly pass the patch test. Popular benchmark problems are studied and the accuracy of the proposed elements is close to their parent models.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A robust two-field hexahedral element capable of handling plate/shell, beam and nearly incompressible material analyses without locking are presented. Starting with the assumed stress element of Pian and Tong,7 parasitic strain components leading to locking in plate, shell and beam analyses are first identified. Locking can be alleviated by scaling down selectively the parasitic strain components in the leverage matrix. Unfortunately, the element then fails the patch test. However, patch test correction and reduction in computation can be achieved by the recently proposed admissible matrix formulation. The resulting element is lock-free and very efficient. All matrices involved in constructing the stiffness matrix can be derived explicitly. The accuracy of the element is tested by popular bench-mark problems.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, control of spurious mechanisms for sub-integrated 20-node and transition hexahedral elements is devised by an assumed stress approach. The higher-order stress modes for stabilizing the sub-integrated elements are identified by examining the spurious mechanisms. With an admissible simplification of the flexibility matrix, row vectors of the leverage matrix can be used as stabilization vectors. Numerical examples for the stabilized 20-node element are presented. Accuracy of the derived element is far better than the fully integrated displacement elements. Meanwhile, the former also consumes marginally less CPU time than the latter.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 0029-5981
    Keywords: spurious mechanism ; spurious pressure ; hybrid element ; stabilization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In two-dimensional penalty finite element analysis of incompressible materials, Q9/3P, the 9-node quadrilateral with three assumed quasi-pressure modes, is the most popular element not bothered by spurious pressure. In constructing the penalty matrix of Q9/3P, it is necessary to form a 3×18 matrix and a 3×3 symmetric matrix. The inverse of the symmetric matrix is then post- and pre-multiplied by the 3×18 matrix and its transpose, respectively. By employing a rank subtraction technique, a new and more efficient implementation scheme is devised for the penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff. On the other hand, there are two spurious kinematic modes should the element be sub-integrated. In the proposed Q9/3P element, the two mechanisms will be annihilated by judiciously chosen higher-order assumed stress modes in conjunction with a modified Hellinger-Reissner functional. It will be demonstrated that the element is of good accuracy and high efficiency.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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