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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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Rayleigh–Ritz variation method and connected-moments expansions
Physica Scripta, 2009We compare the connected-moments expansion (CMX) with the Rayleigh–Ritz variational method in the Krylov space (RRK). As a benchmark model we choose the same two-dimensional anharmonic oscillator already treated earlier by means of the CMX. Our results show that the RRK converges more smoothly than the CMX. We also discuss the fact that the CMX is size
Paolo Amore, Francisco M Fernández
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Beam‐Buckling Analysis via Automated Rayleigh‐Ritz Method
Journal of Structural Engineering, 1994This paper presents an automated Rayleigh-Ritz method for the elastic buckling analysis of doubly symmetric I-beams subjected to arbitrary loading conditions. Moreover, the beams may have various types of end-supporting conditions, internal discrete rigid braces, and internal supports.
C. M. Wang, L. Wang, K. K. Ang
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Modified Fourier Series and Rayleigh-Ritz Method
2015Although the governing equations and associated boundary equations for laminated beams, plates and shells presented in Chap. 1 show the possibility of seeking their exact solutions of vibration, however, it is commonly believed that very few exact solutions are possible for plate and shell vibration problems.
Guoyong Jin, Tiangui Ye, Zhu Su
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On the Numerical Stability of the Rayleigh–Ritz Method
SIAM Journal on Numerical Analysis, 1977The numerical stability of the Rayleigh–Ritz method is investigated from the point of view of Mikhlin stability and of the condition number of the Rayleigh–Ritz matrix, and it is shown that the condition number approach is more appropriate for floating-point computation.
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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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Rayleigh-Ritz Method, Secular Determinant, and Anharmonic Oscillators
Physical Review D, 1973The standard Rayleigh-Ritz procedure yielding the successive truncations of the secular determinant is applied to any anharmonic oscillator (${x}^{2m}$ and in any finite number of dimensions). In this way we obtain a rigorously convergent as well as numerically very effective approximation procedure for any eigenvalue and eigenvector of the ...
S. Graffi, V. Grecchi
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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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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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