Vibration analysis of thin shallow shells using spectral element method

Bahrami, Saeed; Shirmohammadi, Fatemeh; Saadatpour, M.M.

doi:10.1016/j.apm.2017.02.001

Cited by 20 publications

(6 citation statements)

References 13 publications

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“…ψ j (ξ α ) being the Lagrange interpolation functions of order p. Substituting the approximations in the virtual kinetic energy of Equation (25) and in the virtual strain energy of Equation (27), the mass and the stiffness matrices are obtained. It is important to mention that the terms involved in the stiffness matrix are extensive, and a computer program of algebraic manipulation is required; in this case, they were obtained using Maple.…”

Section: Finite Element Modelmentioning

confidence: 99%

“…In the work of Lee & Han [26], a similar formulation to the one presented by these authors in 2001 [25] is used, but this time it is applied to laminated composite plates and shells. Recently, Bahrami et al [27] reported a vibration analysis of thin shallow shells with the spectral interpolation functions and subjected to impact loads. Tornabene et al [28] presented formulations based on differential and integral quadrature methods for the free vibration analysis of composite plates and shells; they considered nonuniform thickness.Żak & Krawczuk [29] presented a finite element with six degrees of freedom and spectral interpolation functions for dynamic analysis of isotropic shell-like structures; the transverse deformation was considered and the structures studied were of uniform thickness.…”

Section: Introductionmentioning

confidence: 99%

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Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

2020

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In this paper, a seven-parameter spectral/hp finite element model to obtain natural frequencies in shell type structures is presented. This model accounts for constant and variable thickness of shell structures. The finite element model is based on a Higher-order Shear Deformation Theory, and the equations of motion are obtained by means of Hamilton’s principle. Analysis is performed for isotropic linear elastic shells. A validation of the formulation is made by comparing the present results with those reported in the literature and with simulations in the commercial code ANSYS. Finally, results for shell like structures with variable thickness are presented, and their behavior for different ratios r/h and L/r is studied.

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Section: Finite Element Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

2020

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“…Изучению конструкций в виде пологих оболочек в настоящее время уделяется значительное внимание во всем мире. Проводятся исследования устойчивости [1][2][3] и колебаний конструкций [4][5][6][7], в том числе в нелинейной постановке [8; 9] и различных форм срединной поверхности [10][11][12]. Интересны работы, анализирующие поведения слоистых [13][14][15] и ортотропных пологих оболочек [16], результаты которых могут быть использованы для моделирования железобетонных и армоцементных конструкций.…”

Section: Introductionunclassified

Stability of shallow shells with local changes in strength characteristics

Kolesnikov

Osadchaya²

2022

Struct. Mech. of Eng. Const. and Build

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The authors deal with the structures of buildings in the form of shallow shells with some damage. The derivation of equations is given taking into account the geometric nonlinearity of the work of a thin-walled structure. A technique for solving systems of equations using the Bubnov - Galyorkin method is given. The work of the structure with various ways of fixing the edges is simulated. Damage is specified by changing the modulus of elasticity in an arbitrary section of the structure. The influence of the shape and location of the defect on the value of the critical load is investigated. The results of the studies carried out are given in a dimensionless form and illustrated by graphs, which makes it convenient to use them in engineering calculations. Recommendations are given for correcting the shape and thickness of coating structures in the form of shallow shells in order to maintain their bearing capacity in the event of defects. The proposed method can be used to determine and investigate the stress-strain state of structures in the form of shallow shells, taking into account the geometric nonlinearity of work in the presence of defects in them. The constructed graphs of the dependence of the critical load on various parameters make it possible to evaluate the operation of structures, taking into account changes in various factors at various stages of the structure's operation. The use of varying characteristics of the reduction in the modulus of elasticity, which appears because of the occurrence of a defect, shows results that are close to real conditions.

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“…Numerical strategies have also been proposed as an alternative to FEM: Wu and Li. [41] employed the Di↵erential Quadrature method for conical shells modelled by the FSDT; Tornabene et al [42,19,24,43] employed the closely related Generalized Di↵erential Quadrature method for studying doubly-curved shells in the context of both ESL and LW theories; Ferreira et al [44] proposed the use of a collocation method based on radial basis functions for the study of doublycurved shells modelled via LW theories; Behrami et al [45] developed a Spectral Element Method for the vibration analysis of thin shallow shells.…”

Section: Introductionmentioning

confidence: 99%