Static and Dynamic Analysis of Shallow Shells with Functionally Graded and Orthotropic Material Properties

Sládek, J.; Sládek, V.; Zhang, Ch.; Solek, P.

doi:10.1080/15376490701810480

Cited by 22 publications

(12 citation statements)

References 27 publications

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“…The dimensionless quantities used are listed in Table 1. The results of dimensionless deflection of a shallow spherical shell with the laterally unrestrained BC subjected to a UDL are also compared with the results obtained from the MLPG formulation [5], as shown in Figure 4a. The bottom surface of the shell is subjected to a UDL of 2.07 × 10 6 N/m 2 directed upwards (bottom surface loading).…”

Section: Resultsmentioning

confidence: 99%

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On thermo-mechanical nonlinear behaviour of shallow shells

Khazaeinejad

Usmani

2016

International Journal of Non-Linear Mechanics

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The structural performance of thin shells is largely dictated by their curvature and the degree of lateral restraint at the shell edges. The present study is an attempt to theoretically investigate the influence of such factors on nonlinear thermo-mechanical response of shallow shells with single and double curvatures. For the mechanical loading, a transverse load is assumed and for the thermal loading, a through-depth thermal gradient is applied on the shallow shell. Two types of boundary conditions are considered for the shallow shell, both of which constrain transverse deflections of the shell but allow rotations parallel to the shell boundaries to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). The fundamental nonlinear equations of shallow shells are derived based on the quasi-static conditions. The validity and reliability of the proposed approach is assessed by calculating several numerical examples for shallow shells under various mechanical and thermal loads. It is found that the proposed formulation, in particular, can adequately capture the nonlinear behaviour of laterally restrained shallow shells.

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Section: Resultsmentioning

confidence: 99%

“…Research in this area has been often focused towards developing efficient shell elements using numerical methods (e.g. see [1][2][3][4][5][6][7][8][9]). …”

Section: Introductionmentioning

confidence: 99%

On thermo-mechanical nonlinear behaviour of shallow shells

Khazaeinejad

Usmani

2016

International Journal of Non-Linear Mechanics

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“…A nice review about the alleviation of the volumetric locking in the MLS meshfree methods can be found in Belytschko et al (2004). Earlier results with application of meshless methods to shallow shell problems (Krysl and Belytschko, 1996;Li et al, 2000Li et al, , 2008Noguchi et al, 2000;Sladek et al, 2007Sladek et al, , 2008Jarak et al, 2007;Soric and Jarak, 2010;Sladek et al, 2013a,b) showed excellent results for conventional elastic materials. In mesh-based methods, the mesh describes the geometry of the surface, and the elements provide local parametrical spaces where the shape functions and the local parameterizations of the surface can be defined.…”

Section: Introductionmentioning

confidence: 89%

Modelling of orthorhombic quasicrystal shallow shells

Sládek

Zhang

et al. 2015

European Journal of Mechanics - A/Solids

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“…Sofiyev [25] studied the non-linear vibration of truncated conical shells made of functionally graded materials using the large deformation theory along with the von Karman-Donnell-type of kinematic non-linearity. Sladek et al [26] employed first-order shear deformation theory description of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness. A meshless local Petrov-Galerkin (MLPG) formulation was applied to solve the 2-D problem.…”

Section: Introductionmentioning

confidence: 99%

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

Asanjarani

Kargarnovin

Satouri

et al. 2015

Mechanics of Advanced Materials and Structures

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Based on the First order Shear Deformation Theory (FSDT), the free vibration of the functionally graded (FG) truncated conical shells is analyzed. The truncated conical shell materials are assumed to be isotropic and inhomogeneous in the longitudinal direction. The twoconstituent (FG) shell consists of ceramic and metal. These constituents are graded through the length, from one end of the shell to the other end. Using Hamilton's principle the derived governing equations are solved using Differential Quadrature Method (DQM). Fast rate of convergence of this method is tested and its advantages over other existing solver methods are observed. The primary results of this study were obtained for four different ends boundary conditions and for some special cases acquire results were compared with those available in the * Graduate Student † Corresponding author, (Ali.Asanjarani@Gmail.com) Downloaded by [University of Connecticut] at 20:02 11 April 2015 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 literature. Furthermore, effects of geometrical parameters, material graded power index, and boundary conditions on the natural frequencies of the FG truncated conical shell are carried out.

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Static and Dynamic Analysis of Shallow Shells with Functionally Graded and Orthotropic Material Properties

Cited by 22 publications

References 27 publications

On thermo-mechanical nonlinear behaviour of shallow shells

On thermo-mechanical nonlinear behaviour of shallow shells

Modelling of orthorhombic quasicrystal shallow shells

Natural frequency analysis of functionally graded material truncated conical shell with lengthwise material variation based on first-order shear deformation theory

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