The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Kumar, Y. Shravan

doi:10.1177/1077546317694724

Cited by 83 publications

(33 citation statements)

References 196 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In order to conduct vibration analysis of composite plate, finite element model is developed using first order shear deformation theory and Hamilton's principle derived from the Rayleigh-Ritz method. With some modifications, Rayleigh-Ritz method has been extensively used by many researchers to find the natural frequencies and mode shapes of the beams, shells and plates [40]. Nomenclature…”

Section: Analytical Analysismentioning

confidence: 99%

Experimental, Numerical and Finite Element Vibration Analysis of Delaminated Composite Plate

2019

View full text Add to dashboard Cite

The vibration of the delaminated composites concerns the structure safety and dynamic behavior of the composite structures as it can be vital in the presence of delamination. In this research paper, the finite element simulations, analytical simulations and the experimental work are combined to analyze the vibration behavior at different delamination size, different stacking sequences and different boundary conditions. The finite element analysis software packages like Ansy and Abqus are used to fetch the vibration response of carbon fiber reinforced polymer composite plate for different boundary conditions, stacking sequences and delamination sizes. Rayleigh-Ritz method was used to derive the governing equations to find the natural frequencies and the results were computed using Matlab tool. It is seen that the natural frequencies of carbon fiber reinforced polymer decreased with an increase in delamination size subjected to all boundary conditions. The higher values of natural frequencies found for all sides clamped boundary conditions. Stacking sequence of (0/90/45/90) showed higher values of natural frequencies subjected to all-sided clamped boundary conditions. Results from this analysis can be considered as a base point for the safe, reliable design of composite structures with and without delamination.

show abstract

Section: Analytical Analysismentioning

confidence: 99%

Experimental, Numerical and Finite Element Vibration Analysis of Delaminated Composite Plate

2019

View full text Add to dashboard Cite

show abstract

“…-Discussions on this paper will be accepted by xxxxxxx xx, xxxx.  https://doi.org/10.18400/tekderg.839435 rectangular, elliptical or circular plates analyzed by the Rayleigh-Ritz method have been demonstrated in the review paper [5].…”

Section: Introductionmentioning

confidence: 99%

Buckling of Laminated Elliptical and Super-Elliptical Thin Plates

Altunsaray

Bayer

2022

Teknik Dergi

View full text Add to dashboard Cite

In this computational study the buckling analysis of symmetrically laminated elliptical and super-elliptical thin plates was carried out. The plates were considered as clamped or simply supported at the boundary. The minimum buckling load was determined using the Rayleigh-Ritz method and the Galerkin Method based on the Classical Laminated Plate Theory (CLPT). The influence of the solution methods, shape functions, boundary conditions, super-elliptical power, lamination type, aspect ratio, and thickness on the critical buckling load were investigated using a parametric study. The verification of the isotropic case was performed comparing some results in the open literature, and reliable agreement was obtained. Convergence studies of the composite case with increasing terms (up to 10 terms) were achieved and sufficient accuracy was provided. During the preliminary design stage of composite structures, many design parameters such as panel sizes, panel thickness, stacking sequences, boundary conditions and loading conditions are taken into consideration. It is possible to evaluate these parameters quickly by using appropriate shape function with the Rayleigh-Ritz method.

show abstract

“…Использование сложных математических моделей требует применения численных методов, точность и особенности применения которых также могут оказывать влияние на получаемые результаты [16,17].…”

Section: Introductionunclassified

Analysis of the stability of the computational algorithm to a change in the geometric parameters of cylindrical shell structures

Bakusov

Semenov

2021

PNRPU Mechanics Bulletin

View full text Add to dashboard Cite

This study deals with testing sustainability of a computational algorithm to a change in geometric parameters of cylindrical shell structures. A change in geometry implies the replacement of one type of a cylindrical shell (elliptic, hyperbolic, parabolic) with another so that the quantitative change (the difference in elevations) in the area under consideration is minimal. On the one hand, this test allows to assessing the correctness of the algorithm itself and is relevant for algorithms that use both numerical methods and symbolic calculations. On the other hand, it allows to evaluating the possibility of simplifying calculations by approximating a complex surface with a simpler one both in understanding the surface definition itself and in expressing its basic characteristics such as Lame coefficients and main curvatures. A mathematical model of deformations of shell structures based on the hypotheses of Timoshenko (Mindlin - Reisner) are used in the work. The model takes into account transverse shifts, geometric nonlinearity and orthotropy of the material, and its written in the form of a functional of the total potential strain energy. The calculation algorithm is built on the basis of the Ritz method to reduce the variational problem of the minimum functional to the solution of a system of nonlinear algebraic equations, and on the method of continuing the solution with the best parameter for its solution. All calculations were carried out in dimensionless parameters. Three types of cylindrical panels are calculated, and critical loads of buckling and deflection fields at subcritical and supercritical moments are obtained. It is shown that for the considered class of problems the previously proposed mathematical model and computational algorithm are resistant to changes in the geometry of the structure.

show abstract

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Cited by 83 publications

References 196 publications

Experimental, Numerical and Finite Element Vibration Analysis of Delaminated Composite Plate

Experimental, Numerical and Finite Element Vibration Analysis of Delaminated Composite Plate

Buckling of Laminated Elliptical and Super-Elliptical Thin Plates

Analysis of the stability of the computational algorithm to a change in the geometric parameters of cylindrical shell structures

Contact Info

Product

Resources

About