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Journal ArticleDOI

A frontal solution program for finite element analysis

01 Jan 1970-International Journal for Numerical Methods in Engineering (John Wiley & Sons, Ltd)-Vol. 2, Iss: 1, pp 5-32
TL;DR: The program given here assembles and solves symmetric positive–definite equations as met in finite element applications, more involved than the standard band–matrix algorithms, but more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes.
Abstract: The program given here assembles and solves symmetric positive–definite equations as met in finite element applications. The technique is more involved than the standard band–matrix algorithms, but it is more efficient in the important case when two-dimensional or three-dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print-out.
Citations
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Journal ArticleDOI
TL;DR: In this article, a general formulation for the curved, arbitrary shape of thick shell finite elements is presented along with a simplified form for axisymmetric situations, which is suitable for thin to thick shell applications.
Abstract: A general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation. A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation. A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations. Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used. The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.

1,205 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position to obtain a more accurate solution to the problem of determining the stress intensity at the tip of a crack.
Abstract: It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.

1,057 citations

Journal ArticleDOI
TL;DR: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps.
Abstract: On etend la methode frontale pour resoudre des systemes lineaires d'equations en permettant a plus d'un front d'apparaitre en meme temps

956 citations


Cites methods from "A frontal solution program for fini..."

  • ...Irons' frontal method [ 20 ] treats the symmetric positive-definite case....

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  • ...The aim of this work is to use the ideas of frontal elimination [ 20 , 19] to permit...

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Journal ArticleDOI
TL;DR: Four decades after the development of the first dynamic substructuring techniques, there is a necessity to classify the different methods in a general framework that outlines the relations between them, and a certain vision on substructureuring methods is proposed.
Abstract: Four decades after the development of the first dynamic substructuring techniques, there is a necessity to classify the different methods in a general framework that outlines the relations between them. In this paper, a certain vision on substructuring methods is proposed, by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept. Thereafter, based on the dual and primal assembly of substructures, a general framework for the classification of the methods is presented. This framework allows us to indicate how the various classes of methods, proposed along the years, can be derived from a clear mathematical description of substructured problems. Current bottlenecks in experimental dynamic substructuring, as well as solutions found in literature, will also be briefly discussed.

668 citations

References
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Book
01 Jan 1965
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Abstract: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography Index.

7,422 citations

Journal ArticleDOI
TL;DR: In this paper, the boundary layer separation associated with a compression corner was investigated in the GALCIT Mach 6 wind tunnel, and a supplementary study was performed in the JPL supersonic wind tunnel.
Abstract: An experimental investigation of the boundary layer separation associated with a compression corner was conducted in the GALCIT Mach 6 wind tunnel, and a supplementary study was performed in the JPL supersonic wind tunnel. Special emphasis was placed on the development of a wind tunnel model which approximated true two-dimensional flow, and which could be run in either a highly cooled or an adiabatic configuration. The basic measurements consist of the model surface pressure and temperature, and Pitot surveys of the boundary layer. The surface pressure distributions for the adiabatic wall configurations are compared with the theory of Lees and Reeves (modified by Klineberg and Lees). The surface pressure distribution for the cold wall was compared with the adiabatic configuration for a laminar interaction, and the dependence on Reynolds number for both laminar and transitional interactions are observed. The "free interaction" similarity suggested by Chapman is empirically tested and found to be a good approximation for the adiabatic configuration, but it fails to correlate the cooled with the adiabatic case. The scaling suggested by Curle was tested and found to eliminate this deficiency.

160 citations

Journal ArticleDOI
TL;DR: A survey of selected computational aspects of linear algebra, addressed to the nonspecialist in numerical analysis, and some current methods of solving systems of linear equations, and computing eigenvalues of symmetric and unsymmetric matrices are outlined.
Abstract: : This is a survey of selected computational aspects of linear algebra, addressed to the nonspecialist in numerical analysis. Some current methods of solving systems of linear equations, and computing eigenvalues of symmetric and unsymmetric matrices are outlined. A bibliography containing 62 titles is included.

33 citations

Journal ArticleDOI
TL;DR: In this paper, the iterative method of determining mean elements for Vinti's spheroidal satellite theory was used as a valid alternative to the procedure of numerical factorization.
Abstract: the iterative method of determining mean elements for Vinti's spheroidal satellite theory presented in this paper may be used as a valid alternative to the procedure of numerical factorization. However, if the latter procedure is applied, then substantial corrections to the orbital elements are not to be expected through use of the iterative method, inasmuch as any such corrections account for errors of third or higher orders. Without use of numerical factorization, the decrease in size of the position and velocity residuals through application of the iterative method is impressive, but, even when the factorization process is employed, most residuals experience noteworthy decreases after only two iterations of this method.

20 citations