Exact solution of certain problems by finite- element method.
01 Jan 1969-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 7, Iss: 1, pp 178-180
About: This article is published in AIAA Journal.The article was published on 1969-01-01. It has received 43 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.
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TL;DR: In this article, the spectral element method in frequency domain is employed to analyze continuous beams and bridges subjected to a moving load, and a modified Static Green's function is used as a modifying function to improve the moment and shear force.
59 citations
TL;DR: In this article, the authors trace the development of the finite element method from its origins in aircraft structural engineering to the present day, where it provides the essential tool for solution of a great variety of problems in engineering and physics.
Abstract: The article traces the important steps of the development of the finite element method from its origins in aircraft structural engineering to the present day, where it provides the essential tool for solution of a great variety of problems in engineering and physics. The emphasis and the choice of the “landmarks” stresses the aspects which are general and essentially of mathematical nature applicable to a wide range of situations. For this reason no mention is made of perhaps equally important developments to new application fields such as metal forming, electromagnetics, geomechanics etc.
42 citations
TL;DR: In this article, a finite element displacement formulation based on Reissner's thick plate theory is presented for the bending analysis of annular and sector plates, and an annular element with six and twenty degrees of freedom, respectively, are developed.
30 citations
TL;DR: The first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework is presented in this paper, where a steplength parametrization of mesh dimensions is used to modify the shape functions.
Abstract: This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations Parametrized linear shape functions are directly inserted into a FIC functional The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process Both constant- and variable-coefficient cases are studied It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation The inclusion of the Ritz-FIC models in the context of templates is examined This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions
28 citations
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TL;DR: In this article, a review and reinterpretation of the existing finite element methods and other alternative schemes are presented, and a comparison of the relative merits of the various methods is made.
Abstract: Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.
417 citations
TL;DR: In this paper, some general stability criteria for non-dissipative swirling flows are derived, and extended to the case of an electrically conducting fluid in the presence of axial magnetic field and current.
Abstract: Some general stability criteria for non-dissipative swirling flows are derived, and extended to the case of an electrically conducting fluid in the presence of axial magnetic field and current. In particular, it is shown that the analogy between a rotating and a stratified fluid holds in this case, and that an important determinant of stability is a Richardson number'' based on the analog of the density gradient and the shear in the axial flow. (auth)
324 citations
TL;DR: In this paper, a compatible triangular plate element for normal and in-plane displacements was proposed for both inplane and out-plane displacement, and the nine degree of freedom element, strain energy, simply supported and clamped plates were discussed.
Abstract: Compatible triangular plate elements for normal and in-plane displacements, discussing nine degree of freedom element, strain energy, simply supported and clamped plates
134 citations
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