Carrera unified formulation (CUF) for the shells of revolution. II. Navier close form solutions

Carrera, Erasmo; Zozulya, V. V.

doi:10.1007/s00707-022-03373-6

Cited by 6 publications

(1 citation statement)

References 30 publications

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“…The classical theories such as Kirchhoff and Mindlin shear deformation theories can be derived as special cases of CUF [28,29]. As a powerful general theory, CUF had been successfully applied to shell structures [30][31][32]. In CUF, the displacement fields of structures are generalized and expressed by the polynomials, such as Taylor series and Lagrange polynomials, and the precision of the CUF is primarily determined by the terms of polynomial expansions.…”

Section: Materials Elastic Theory Methodsmentioning

confidence: 99%

Three-Dimensional Vibration Model of Cylindrical Shells via Carrera Unified Formulation

Liang

Liu

et al. 2023

Materials

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In this paper, we present a novel and unified model for studying the vibration of cylindrical shells based on the three-dimensional (3D) elastic theory and the Carrera Unified Formulation. Our approach represents a significant advancement in the field, as it enables us to accurately predict the vibrational behavior of cylindrical shells under arbitrary boundary conditions. To accomplish this, we expand the axial, circumferential, and radial displacements of the shell using Chebyshev polynomials and Taylor series, thereby reducing the dimensionality of the expansion and ensuring the precision and rigor of our results. In addition, we introduce three groups of artificial boundary surface springs to simulate the general end boundary conditions of the cylindrical shell and coupling springs to strongly couple the two surfaces of the cylindrical shell φ = 0 and φ = 2π to ensure continuity of displacements on these faces. Using the energy function of the entire cylindrical shell model, we obtain the characteristic equation of the system by finding the partial derivatives of the unknown coefficients of displacement in the energy function. By solving this equation, we can directly obtain the vibration characteristics of the cylindrical shell. We demonstrate the convergence, accuracy, and reliability of our approach by comparing our computational results with existing results in the literature and finite element results. Finally, we present simulation results of the frequency features of cylindrical shells with various geometrical and boundary parameters in the form of tables and figures. Overall, we believe that our novel approach has the potential to greatly enhance our understanding of cylindrical shells and pave the way for further advancements in the field of structural engineering. Our comprehensive model and simulation results contribute to the ongoing efforts to develop efficient and reliable techniques for analyzing the vibrational behavior of cylindrical shells.

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