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Buckling Analysis of Toroidal Shell by Rayleigh-Ritz Method
Journal of Pressure Vessel Technology, 2019The energy approach is used to analyze the buckling stability of toroidal shells. A closed and an open toroidal shell, as well as a shell segment are considered. Linear strain energy and nonlinear strain energy due to a uniform external pressure are formulated.
Senjanović, Ivo +5 more
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The Rayleigh-Ritz Method: A Graphical Proof
American Journal of Physics, 1969We give a simple graphical proof for the Rayleigh-Ritz variational method for simultaneously obtaining upper bounds to the n lowest eigenvalues of a Hermitean operator.
J. Flores, P. A. Mello
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A Computer Optimization of the Rayleigh-Ritz Method
IEEE Transactions on Microwave Theory and Techniques, 1969A method has been developed to improve the use of the RayIeigh-Ritz procedure. A criterion is established, which is a measure of the cumulative improvement due to the addition of more and more terms in the series expansion. Without calculating the exact roots of determinantal equations, the convergence is accelerated by skipping unnecessary ...
A.S. Vander Vorst +2 more
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The Rayleigh-Ritz and Trefftz Methods
1981The Rayleigh-Ritz method belongs to the so-called direct methods of the calculus of variations, inasmuch as it is applied to problems formulated in an integral rather than a conventional, that is, differential, form. More often than not, the procedure involves the minimization of integrals containing unknown functions and their derivatives, without ...
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On the use of polynomial series with the Rayleigh-Ritz method
Composite Structures, 1997Extensive literature emphasising the use of special sets of polynomials for Rayleigh-Ritz solutions to plate problems exists. It is commonly suggested that convergence can be improved by the use of special sets of polynomials, which are often orthogonal over the plate domain.
R.E. Brown, M.A. Stone
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Rayleigh-Ritz Method for Plate Flexure
Journal of the Engineering Mechanics Division, 1967A method is presented for obtaining two-dimensional plate element displacement functions which may allow continuity in any required derivative of the displacement parameter. These functions for slope and curvature continuity are used to obtain the load deflection characteristics of square plates simply supported or built-in along their edges.
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Collocation, Galerkin, and Rayleigh–Ritz Methods
2019Weighted residual methods (WRM) (also called Petrov-Galerkin methods) provide simple and highly accurate solutions of BVPs. Collocation, Galerkin, and Rayleigh–Ritz methods are examples of the WRMs.
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On the Equivalence of the Galerkin and Rayleigh-Ritz Methods
The Journal of the Royal Aeronautical Society, 1962The Galerkin method for the approximate solution of elasticity problems (see e.g.Ref. 1) is usually presented as an alternative to the Rayleigh-Ritz method. The main distinction between the two methods is stated to be that the former begins with an equation of equilibrium, whereas the latter begins with a total potential energy expression.
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A finite element application of the modified Rayleigh–Ritz method
International Journal for Numerical Methods in Engineering, 1970AbstractConsiderable attention has been devoted in the literature on numerical methods towards securing energy convergence of solutions for, say, linearly elastic plate bending problems. Although energy convergence is necessary it by no means follows that the derived bending moments and shearing forces converge uniformly at a given point and it is this
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Nullspace technique for imposing constraints in the Rayleigh–Ritz method
Journal of Sound and Vibration, 2022Jie Deng, Oriol Guasch, Nansha Gao
exaly