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  • Engineering General  (287)
  • 04. Solid Earth::04.08. Volcanology::04.08.06. Volcano monitoring
  • Wiley-Blackwell  (287)
  • Springer  (3)
  • American Institute of Physics
  • Springer Nature
  • 1
    Electronic Resource
    Electronic Resource
    A coupling scheme for boundary and finite elements using a joint element (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 161-172 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A coupling scheme for boundary and finite elements using a joint element is proposed. The scheme is based on the finite element discretization (i.e. the equivalent FE procedure). Footing problems founded on multiple layers are solved. Furthermore, the scheme is extended to a non-linear analysis.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610090205
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  • 2
    Electronic Resource
    Electronic Resource
    A new numerical method for transient thermal stress problems (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 987-1000 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new numerical method of calculating unsteady-state heat conduction and thermal stresses by using improved coefficient matrix patterns on the nodal points of a structure is given. Good agreement is obtained between our results and the rigorous results, and this method seems to yield better accuracy than other well-known approximate methods for two-dimensional transient thermal stress problems.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140704
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  • 3
    Electronic Resource
    Electronic Resource
    Reconsiderations on singularity or crack tip elements (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1525-1544 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Various singularity finite elements proposed so far are reviewed and their correlations are discussed. The method adopted in the comparative study is based on the singularity mapping or transformation technique. It is suggested that a compact design of computational routines is materialized by using the element which embodies singularity transformation and can be compatible with the notion of using the variable-number-nodes element in the general-purpose computer programs.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620141008
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  • 4
    Electronic Resource
    Electronic Resource
    On curved finite elements for the analysis of circular arches (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1635-1651 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper proposes a straightforward criterion to warrant the displacement functions being used in the finite element approximation of circular arches. The criterion was established by studying the natural shape function, i.e. the exact solution of the deformed shape, of the circular arch element. The exact stiffness matrix [K]exact is derived from the natural shape and is confirmed to be the inverse of the well-known flexibility matrix [F]exact in the curved beam theory. The present paper compares the inverse [K]-1 of the stiffness matrix derived from the assumed displacement function with the [F]exact. It is shown that the procedure also guarantees the implicit inclusion of rigid-body modes in the pertinent stiffness matrix [K]. Case studies on typical approximate displacement functions assure the appropriateness as well as the ease of application of the proposed method.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111102
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  • 5
    Electronic Resource
    Electronic Resource
    Element-free Galerkin methods (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 229-256 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.
    Additional Material: 26 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370205
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  • 6
    Electronic Resource
    Electronic Resource
    A variationally coupled FE-BE method for transient problems (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 91-105 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variationally coupled finite element-boundary element method is developed for transient problems. A single variational statement is obtained for the entire domain and the unknown tractions, which may be discontinuous on the interface and are often a source of difficulties, are eliminated. Moreover, no interface conditions need be taken into consideration at the level of the discretized equation. The discrete equations for the coupled system can be obtained directly without any intermediate steps. The method generalizes a coupling method previously developed by the authors for statics. Numerical examples show that the solutions obtained by the present method agree very well with those obtained by analytical solutions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370107
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  • 7
    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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  • 8
    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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  • 9
    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.
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  • 10
    Electronic Resource
    Electronic Resource
    A geometrically non-linear tensorial formulation of a skewed quadrilateral thin shell finite element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2855-2875 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 48-degree-of-freedom (d.o.f.) skewed quadrilateral thin shell finite element, including the effect of geometrical non-linearity, is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures. The element surface is described by a variable-order polynomial in curvilinear co-ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co-ordinates. The directions of the curvilinear co-ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element. In the present case of a skewed quadrilateral with non-orthogonal curvilinear coordinates, the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish, such as in the case of orthogonal co-ordinates. The tensor form is used in the setup of the shape functions, geometric derivatives, stiffness matrix and computer code. This allows for the treatment of shells with irregular shapes and variable curvatures. To evaluate the efficiency and accuracy of this formulation, a systematic list of examples is chosen: (i) linear and non-linear static analysis of square and rhombic plates, cylindrical and spherical shells; (ii) linear vibrations of trapezoidal flat and curved plates; (iii) large amplitude vibrations of a rhombic plate. For the square plate and cylindrical and spherical shell, shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element. All results are compared with alternative available solutions including those obtained using regular rectangular meshes. Pinched thin cylindrical and spherical shells are studied using different skewed meshes and various Gauss integration meshes, and no membrane locking phenomenon is observed.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281210
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