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  • Engineering General  (57)
  • Wiley-Blackwell  (57)
  • American Institute of Physics
  • Springer Nature
  • 1995-1999  (57)
  • 1
    Electronic Resource
    Electronic Resource
    Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: Application to thermomechanical problems (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 685-716 
    Details
    ISSN: 0029-5981
    Keywords: hourglass and locking control ; large strains ; thermomechanical coupling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a class of ‘assumed strain’ mixed finite element methods based on the Hu-Washizu variational principle is presented. Special care is taken to avoid hourglass modes and shear locking as well as volumetric locking. An unified framework for the 4-node quadrilateral solid and thermal as well as thermomechanical coupling elements with uniform reduced integration (URI) and selective numerical integration (SI) schemes is developed. The approach is simply implemented by a small change of the standard technique and is applicable to arbitrary non-linear constitutive laws including isotropic and anisotropic material behaviours. The implementation of the proposed SI elements is straightforward, while the development of the proposed URI elements requires ‘anti-hourglass stresses’ which are evaluated by classical constitutive equations. Several numerical examples are given to demonstrate the performance of the suggested formulation, including static/dynamic mechanical problems, heat conduction and thermomechanical problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620380411
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  • 2
    Electronic Resource
    Electronic Resource
    NUMERICAL ALGORITHMS FOR SOLUTIONS OF LARGE EIGENVALUE PROBLEMS IN PIEZOELECTRIC RESONATORS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 909-922 
    Details
    ISSN: 0029-5981
    Keywords: piezoelectric resonators ; numerical algorithms ; largescale eigenvalue problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two algorithms for eigenvalue problems in piezoelectric finite element analyses are introduced. The first algorithm involves the use of Lanczos method with a new matrix storage scheme, while the second algorithm uses a Rayleigh quotient iteration scheme. In both solution methods, schemes are implemented to reduce storage requirements and solution time. Both solution methods also seek to preserve the sparsity structure of the stiffness matrix to realize major savings in memory.In the Lanczos method with the new storage scheme, the bandwidth of the stiffness matrix is optimized by mixing the electrical degree of freedom with the mechanical degrees of freedom. The unique structural pattern of the consistent mass matrix is exploited to reduce storage requirements. These major reductions in memory requirements for both the stiffness and mass matrices also provided large savings in computational time. In the Rayleigh quotient iteration method, an algorithm for generating good initial eigenpairs is employed to improve its overall convergence rate, and its convergence stability in the regions of closely spaced eigenvalues and repeated eigenvalues. The initial eigenvectors are obtained by interpolation from a coarse mesh. In order for this multi-mesh iterative method to be effective, an eigenvector of interest in the fine mesh must resemble an eigenvector in the coarse mesh. Hence, the method is effective for finding the set of eigenpairs in the low-frequency range, while the Lanczos method with a mixed electromechanical matrix can be used for any frequency range. Results of example problems are presented to show the savings in solution time and storage requirements of the proposed algorithms when compared with the existing algorithms in the literature.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    A SIMPLE AND EFFICIENT MIXED FINITE ELEMENT FOR AXISYMMETRIC SHELL ANALYSIS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1903-1914 
    Details
    ISSN: 0029-5981
    Keywords: axisymmetric shell ; mixed finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient, perhaps simplest, three-noded mixed finite element is proposed for axisymmetric shell analysis. The key feature in the present formulation is to start with a better variational principle in which the independent unknowns are only the quantities that can be prescribed at the shell edges. If the consistency for field approximations is satisfied, no other numerical consideration is necessary in the present element. Several examples confirm the satisfactory numerical behaviour of the present mixed element.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    SOLID ELEMENTS WITH ROTATIONAL DOFs BY EXPLICIT HYBRID STABILIZATION (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2987-3005 
    Details
    ISSN: 0029-5981
    Keywords: rotation ; finite element ; hexahedral ; hybrid/mixed ; stabilization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two brick elements equipped with Allman's rotation are presented. Strain energy of both elements is sub-integrated by the second order quadrature which gives rise to the hourglass mechanisms. Inasmuch as Allman's rotation is employed, the elements are also plagued by the equal-rotation mechanisms. Variational functional containing independently assumed stress, displacement and rotation is employed to formulate the stabilization devices for the elements. Computational cost of the elements is reduced by incorporating the explicit hybrid stabilization technique. Popular numerical benchmarks are studied and the present elements are found to be competitive to other state-of-the-art elements.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Solution of the differential Riccati equation using the transmission line modelling (TLM) technique (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 25-32 
    Details
    ISSN: 1069-8299
    Keywords: Riccati equation ; transmission line modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this communication, the application of the transmission line modelling (TLM) technique to the solution of the differential Riccati equation is described. A comparison is made between the TLM, fourth-order Runge-Kutta and the first-order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equation is second-order. It is found that, when the system is underdamped, the fourth-order Runge-Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM method yields results that are closest to the analytical solution. Finally, a discussion is presented of the effects of errors in the TLM solution of the Riccati equation on the accuracy of the solution to the continuous Kalman filter estimation equation.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110105
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  • 6
    Electronic Resource
    Electronic Resource
    Vibration of continuous beams using modified beam vibration functions (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 107-114 
    Details
    ISSN: 1069-8299
    Keywords: beam ; vibration ; trial functions ; Ritz method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Free vibration of beams with intermediate point supports is studied by the classical Ritz method within the context of Euler beam theory. For the Ritz method, the displacement of a beam is approximated by a set of admissible trial functions which must satisfy the kinematic conditions at the ends and intermediate supports of the beam. To this end, a polynomial is superimposed on the conventional single-span beam vibration functions to form continuous-span or modified beam vibration functions. These modified beam functions are taken as the admissible trial functions for subsequent formulation. Stiffness and mass matrices are formulated using the conventional procedure and the resulting linear eigen-equation can be solved easily. A number of numerical examples are given to demonstrate the accuracy and efficiency of the present method.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Solution of edge crack problem by using a novel weight function formulation (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 497-505 
    Details
    ISSN: 1069-8299
    Keywords: weight function approach ; edge crack problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fundamental field for the edge crack problem is suggested, and the field is composed of the singular displacement field and the complementary regular field. The boundary displacement of the fundamental field plays the role of the weight function in the edge crack problem. After multiplying the boundary traction in the physical problem with the weight function and performing integration along the boundary, the stress intensity factor at the crack tip is obtainable. Numerical examples are given to demonstrate the use of the suggested weight function approach.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Penalty-equilibrating approach and an innovative formulation of 4-noded hybrid stress elements (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 707-717 
    Details
    ISSN: 1069-8299
    Keywords: hybrid element ; shear locking ; penalty-equilibrating approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a penalty-equilibrating approach which is used to enforce the equilibrium constraints to individual hybrid elements so as to optimize the element performance. The approach has been applied successfully to improve the 4-noded hybrid stress membrane element (P-S) by Pian and Sumihara. It turns out that some defects of the P-S element, e.g. the shear locking phenomenon and the inability to pass the MacNeal's bending test, can be overcome and the element performance is significantly improved, without having to add any extra variables to the P-S element or to modify its stress fields.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Elimination of spurious pressure and kinematic modes in biquadratic nine-node plane element (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3911-3932 
    Details
    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
    URL: http://dx.doi.org/10.1002/nme.1620382302
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  • 10
    Electronic Resource
    Electronic Resource
    FORMULATION AND EXPERIMENTAL VERIFICATION OF A PNEUMATIC FINITE ELEMENT (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1097-1114 
    Details
    ISSN: 0029-5981
    Keywords: finite elements ; pneumatics ; air springs ; containers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many engineering structures completely surround and enclose gas filled volumes. The enclosed gas adds additional stiffness to the surrounding structure. This paper shows how to account for this effect by means of an augmented virtual work principle. The additional term augmenting the virtual work equilibrium statement for the structure is the virtual boundary work done by the pressure of the enclosed gas. The augmented equations are discretized using standard finite element methods, and the additional terms are discussed. The resulting ‘pneumatic’ finite element is shown to be analogous to regular structural finite elements. To assess the accuracy and efficiency and also to illustrate the applicability of the present formulation, a series of four examples was selected. In two of the examples, the behaviour of the end cap of a partially filled plastic food product container is studied. The numerical results using the pneumatic element compare well with an alternative Rayleigh-Ritz solution of the end cap behaviour. The other two examples represent the behaviour of a double bellows air spring shock absorber under static isothermal and dynamic adiabatic conditions. For the static isothermal case, an experimental study was performed with results in good agreement with the pneumatic element solutions. For the dynamic adiabatic loading case, the dynamic stiffness of the air spring was predicted using the pneumatic element. The numerical results agree with experimental data published in an air spring application guide. The examples illustrate that the pneumatic element formulation can be applied to the large deflection analysis of structures that enclose gas filled volumes.
    Additional Material: 9 Ill.
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