• Steel and Composite Structures
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• v.37 no.5
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• pp.621-632
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• 2020

This research deals with the study of vibrational behavior of armchair and zigzag single-walled carbon nanotubes invoking extended Love shell theory. The effects of different physical and material parameters on the fundamental frequencies are investigated. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. To discretize the governing equation in eigen-value form, wave propagation approach is developed. Complex exponential functions have been used and the axial model depends on boundary condition that has been described at the edges of carbon nanotubes to calculate the axial modal dependence. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes and current results shows a good stability with comparison of other studies.

• Computers and Concrete
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• v.34 no.5
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• pp.591-609
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• 2024

Two novel laminate constitutive equations (LCE) for the static analysis of anisotropic shells are presented and implemented in this work. The LCE, developed for both two-dimensional (2D) and three-dimensional (3D) analysis, are more general than those obtained using the Kirchhoff-Love (K-L) equations, Reissner-Minddlin (R-M) type models, refined 2D/3D models, and some general anisotropic doubly-curved shell theories. Our study presents a 2D LCE model that accounts for classical mechanical couplings based on previous models plus additional couplings including extensional-twisting-shearing, extensional-twisting, Gauss bending-twisting-shearing, and Gauss bending-shearing mechanical couplings related to the third fundamental, or Gauss tensor. Moreover, the developed 3D LCE model accounts for all 2D mechanical couplings cited above plus additional mechanical couplings due to the section warping tensor, which arises from the stretching-through-the-thickness variable. These mechanical couplings are pertinent to the optimal design of a composite and are often disregarded in various static and dynamic analysis studies. Neglecting these new mechanical couplings in the design and analysis of laminated composite shells (LCS) can result in significant errors, from both physical and mechanical viewpoint. As such, we recommend employing new complete constitutive relations that integrate these pertinent mechanical couplings for the aforementioned study. Based on our analysis of the impact of additional couplings, we have developed several mathematical formulations that address several challenges encountered in laminated shell theory. As we increase the shell's thickness ratio, our research examines the effects of these couplings on mechanical behavior, buckling shape, critical buckling pressure, and failure analysis through computational modelling and various tests. The examination of the thickness ratio of composite shells illustrates the contrast between our newly developed LCE and some existing LCE as the shells increase in thickness.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.749-765
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• 2008

Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love's first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.