Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019
TgSDT predicted buckling loads to be about 65% of those predicted by FSDT for certain thick-walled cylinders. Stein and Bains (Stein, et al., 1990) studied buckling of plates due to compressive load using sinusoidal terms for displacement fields. Touratier
(Touratier, 1991)
(Touratier, 1992) presented TgSDTs that accounted for cosine shear stress distribution and free boundary conditions for shear stress upon the top and bottom surfaces of the plate. His theory was based on the kinematical approach, where the shear was represented by a sinusoidal function. He further extended it for shells (Touratier & Faye, 1995). Bhimaraddi and Stevens (Bhimaraddi & Stevens, 1986), Stein (Stein, 1986), Becker (Becker, 1994) (Becker, 1993) and Lu and Liu (Lu & Liu, 1992) have also made some valuable contributions towards development of TgSDTs.
Using Hamilton's principle and Lagrange multipliers, Soldatos (Soldatos, 1992) developed a TgSDT for homogenous monoclinic plates. Beakou and Touratier (Beakou & Touratier, 1993) developed a 32 degree of freedom finite element that was used in conjunction with a TgSDT in which the transverse shear deformation was represented by cosine functions. They carried out static, buckling and dynamic analysis of composite shells. Muller and Touratier (Muller & Touratier, 1995) made a comparative study on the theory of Kirchhoff-love, Schmidt-Levinson theory, Reissner-Mindlin theory, Reddy theory and Touratier theory. Shimpi and Ghugal (P. Shimpi, 2000) used a sinusoidal function to represent the shear deformation. However, it contained only three variables, even less than FSDT. Kassapoglou and Lagace (Kassapoglou & Lagace, 1986) used a TgSDT to calculate the interlaminate stress field at straight free edges in symmetric composite plates under uniaxial load. They also extended the theory for angle-ply and cross-ply plates (Kassapoglou & Lagace, 1987). Later the method was further extended by Kassapoglou (Kassapoglou, 1990) to study the effect of combined loads on the free edges interlaminate stress. Similarly, Webber and Morton (Webber & Morton, 1993) used TgSDT to study free edge stress fields in laminated plates due to thermal effects.
3.
LITERATURE REVIEW ON ANALYSIS OF SKEW PLATES
In this section, a brief literature survey on static and dynamic analysis of composite skew plates is presented. Some papers on isotropic plates/shells are also reviewed to maintain continuity. However, works on functionally graded structures are excluded. The structural behavior of isotropic skew plates has been studied previously by many investigators like Kennedy and Huggins (Kennedy, 1964), Kennedy and Tamberg (Kennedy & Tamberg, 1969), Mizusawa et al. (Mizusawa, et al., 1979) among others.
York and Williams (York & Williams, 1995) relied on CLPT to study buckling of skew plates. Reddy and Palaninathan (Reddy & Palaninathan, 1995) used the
finite element method for buckling analysis of laminated skew plates. They used a high precision triangular plate bending element with three nodes located at vertices having 12 degrees of freedom per node. Auricchio and Taylor (Auricchio & Taylor, 1995) developed a new formulation for a triangular element. Using FSDT they calculated the cylindrical bending of simply supported skew plates. Ganapathi and Prakash (Ganapathi & Prakash, 2006) too used FSDT to estimate buckling of skew panels.
Bardell (Bardell, 1992) determined the natural frequencies for isotropic plates. McGee and Butalia (McGee & Butalia, 1994) used FSDT and HSDT in conjunction with a nine node Lagrangian isoparametric quadrilateral element based finite element analysis for estimating the natural frequencies of a cantilever skew plate. Using the same high precision triangular plate bending element that they developed in 1995, Reddy and Palaninathan (Reddy & Palaninathan, 1999) conducted an FE analysis to accurately predict the Eigenfrequencies of a skew plate. Singha and Ganapathi (Singha & Ganapathi, 2004) estimated the large amplitude free flexural vibrations using HSDT. Sundararajan et al. (Sundararajan, et al., 2005) conducted a finite element analysis using the 8-node quadrilateral element to calculate the nonlinear free flexural vibrations. Dey and Singha (Dey & Singha, 2006) carried out a dynamic stability analysis of composite skew plates subjected to periodic in-plane load. Singha and Daripa (Singha & Daripa, 2007) used a 4-node shear flexible quadrilateral high precision plate bending element to study nonlinear vibrations in a symmetric laminated skew panel. Nguyen-Van et al. (Nguyen-Van, et al., 2008) too relied on FSDT to estimate the Eigenfrequencies of skew plates. Park et al. (Park, et al., 2009) modelled delamination in composite skew plates using finite element method and studied their effect on natural frequencies. They considered HSDT for considering the shear deformation across the thickness of the plate.
Eftekhari and Jafari (Eftekhari & Jafari, 2012) developed a higher order FEM formulation to accurately model skew plates. Chalak et al. (Chalak, et al., 2014) carried out both static and dynamic analysis of skew rectangular laminated sandwich plates considering a higher order zigzag theory (HOZT). Experimental and numerical simulation in a commercial FE package was carried out by Srinivasa et al. (Srinivasa, et al., 2014) to study the natural frequencies of skew laminates. Yadav et al. (Yadav, et al., 2015) comprehensively studied the effect of skewness in stiffened plates using a commercial finite element
package. Garcia-Macaisa et al. (Garcı́a-Macı́as, et al., 2016) used a four-node skew element while considering FSDT to account for shear deformation. Zhang et al. (Zhang, et al., 2015b) also used a FSDT and moving least square-Ritz method. Zghal et al. (Zghal, et al., 2018) used a HSDT to carry out free vibration analysis of nanocomposite shells reinforced with carbon nanotubes. Lee (Lee, 2018) also used a HSDT and finite element analysis to assess the dynamic stability of multiscale
©2019: The Royal Institution of Naval Architects
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