A scaled boundary finite element method for static and dynamic analyses of cylindrical shells

Li, Jianghuai; Shi, Zhiyu; Liu, Lei

doi:10.1016/j.enganabound.2018.10.024

Cited by 37 publications

(6 citation statements)

References 61 publications

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“…After substituting the structure of solutions (5) into variational equation (1) and integrating the triple integrals numerically, the boundary problem is reduced to solving a system of linear algebraic equations for the desired constants u p ijk , σ ps ijk and T g ijk . The found values are used to determine all the characteristics of the stress-strained state of the calculated elastic shell region.…”

Section: The Research Results Of the Formulated Boundary Value Problemsmentioning

confidence: 99%

“…In the study of the considered boundary-value problems, a software-implemented algorithm of the a posteriori integral estimation of the accuracy of approximate solutions of mixed variational problems was used [22]. This enabled us to automate the search in structure (5) of such a number of approximations in which the process of convergence of solutions is stable and the final results become reliable. Presented in the numerators of Table 1, the numerical results of the calculation of a shell with a large elliptical hole (μ = 2.5; r 1 /r 2 = 0.5) practically do not differ from those in the denominators of the results of [2].…”

Section: Discussion Of the Results Of Calculating The Stress Concentrmentioning

confidence: 99%

“…In [5], on the basis of FEM, a scaling technique is developed for static and dynamic analysis of cylindrical shells, which is used to provide an accurate representation of the shell boundaries within the framework of the three-dimensional linear theory of elasticity. In [6], the main attention is paid to obtaining a new finite element of a thin-walled shell, the practical application of which is promised to be presented in further publications.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

Salo

Rakivnenko

Nechiporenko

et al. 2019

EEJET

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Section: The Research Results Of the Formulated Boundary Value Problemsmentioning

confidence: 99%

Section: Discussion Of the Results Of Calculating The Stress Concentrmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

See 1 more Smart Citation

Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

Salo

Rakivnenko

Nechiporenko

et al. 2019

EEJET

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“…Recently, many researchers have investigated the SBFEM (Chongshuai et al, 2018;Li et al, 2019;Song, 2004Song, , 2009Song et al, 2018;Zou et al, 2019;Wolf, 2002). The equation of singular stress at cracks by the SBFEM is derived by Song and Wolf, (2002).…”

Section: Introductionmentioning

confidence: 99%

Application of scaled boundary finite element method for vibration-based structural health monitoring of breathing cracks

Sepehry

Ehsani

Zhu

et al. 2020

Journal of Vibration and Control

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The dynamic response of the host structure to a high-frequency actuation is usually used for the detection of tiny damage in structures in the form of breathing crack. The simulation of the microcrack’s effect on the response is essential for several damage identification targets. The conventional finite element method suffers from very small mesh size requirements to address the high-frequency problems, resulting in very large mass and stiffness matrices. In this study, the scaled boundary finite element method was applied to model different schemes of structural health monitoring of a structure with breathing cracks based on high-frequency vibration. The scaled boundary finite element method discretizes only the boundary of the model and thus substantially reduces the size of structural matrices. The node-to-node contact strategy was introduced to the scaled boundary finite element method to capture the contact problem that occurs during the vibration of the breathing crack. As breathing crack vibration results in some nonlinear effects, the simulation of three phenomena was of interest: higher harmonic generation, frequency shift, and vibro-acoustic modulation. A shooting method was used for efficient time integration and description of the frequency response function in the nonlinear regime. According to the results, the scaled boundary finite element method is of great power, efficiency, and accuracy to treat the contact problems, especially in high-frequency regimes. Moreover, the nonlinear methods provide certain advantages over the linear techniques in the early detection of incipient damage.

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“…Comparing with the FEM (Fu et al, 2020; Li and Yu, 2018; Li et al, 2017a, 2018a, 2018b, 2018d, 2019a, 2020; Yu et al, 2018), the analytical formulations of the stiffness matrix along the thickness direction can be given out. Owing to these unique characteristics of the semi-analytical scheme and only discretization of the boundary, the SBFEM has been adopted in many engineering fields, such as modelling both the unbounded and bounded domains (Bazyar and Song, 2008; Birk et al, 2012; Chen et al, 2014; Song, 2009), voided materials (Sladek et al, 2015, 2016), parametrization (Arioli et al, 2019), weak discontinuities (Natarajan et al, 2020), the interaction of acoustic-structures (Li et al, 2018c; Liu et al, 2019b), uniform beams (Li et al, 2017b), cylindrical shells (Li et al, 2019b), and so on. The general solution of the SBFEM governing equation for plates is in the analytical form of a matrix exponent corresponding to the transverse coordinate.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity

Zhang

Fang

et al. 2020

Journal of Intelligent Material Systems and Structures

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A three dimensional elasticity analysis for the transverse free vibration characteristics of functionally graded magneto-electro-elastic plates based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration algorithm (PIA) is presented. The material properties of magneto-electro-elastic plates are changing along the in-plane direction with arbitrary mathematical functions. In the proposed methodology, the strategies of only discretizing the in-plane surface and utilizing the two-dimensional spectral elements to construct diagonal coefficient matrices are adopted, which contributes to decreasing the calculation effort. The derivation process begins with the three dimensional governing equations of magneto-electro-elastic materials. Neither the plate mechanical kinematics nor invoking assumptions on the spatial distributions of electric and magnetic quantities are adopted. Built upon the introduced scaled boundary coordinates, the principle of virtual work and the technique of dual vectors, a first order ordinary differential SBFEM matrix equation for the in-plane functionally graded magneto-electro-elastic plates is obtained. Its general solution is analytically denoted as the matrix exponent. To improve the computation accuracy of the matrix exponent, the PIA is utilized to form the stiffness matrix. By virtue of the kinetic energy technique, it is convenient to construct the mass matrix of the in-plane functionally graded magneto-electro-elastic plates based on the SBFEM for the first time. Finally, comparisons of flexural frequency parameters with those from exact solutions and other numerical methods are provided. The accuracy, effectiveness, and versatility of the employed technique are validated. Moreover, additional numerical exercises are conducted to exhibit the influences of boundary conditions, material gradation functions, and aspect ratios on the free vibration behaviors of in-plane functionally graded magneto-electro-elastic rectangular, circular, and perforated plates.

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A scaled boundary finite element method for static and dynamic analyses of cylindrical shells

Cited by 37 publications

References 61 publications

Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

Calculation of stress concentrations in orthotropic cylindrical shells with holes on the basis of a variational method

Application of scaled boundary finite element method for vibration-based structural health monitoring of breathing cracks

Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity

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