Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019


composites. Delamination was also considered in his analysis. Using finite strip method Ashour (Ashour, 2009) studied vibration of skew plate. Rango et al. (Rango, et al., 2015) relied on trigonometric shear deformation theory to calculate the natural frequencies. Upadhyay and Shukla (Upadhyay & Shukla, 2013) and Shojaee et al. (Shojaee, et al., 2017) made use of Hamilton’s principle to do so.


However, HSDT was used in (Upadhyay & Shukla, 2013) whereas (Shojaee, et al., 2017) used FSDT.


Ardestani et al. (Ardestani, et al., 2017) and Zhang et al. (Zhang, et al., 2017) used HSDT and TSDT respectively while modelling thick skew laminates. In both the works isogeometric method was adopted. Similarly, meshless methods were adopted by Fallah and Delzendeh (Fallah & Delzendeh, 2018) and Liew et al. (Liew, et al., 2004). The moving least square Ritz (MLS-Ritz) method was used by Zhou and Zheng (Zhou & Zheng, 2008) and Zhang (Zhang, 2017). Fallah et al. (Fallah, et al., 2011) considered the use of multi-term extended Kantorovich method most appropriate for skew plate analysis. The Rayleigh-Ritz approach was used by quite a few researchers Like Mizusawa et al. (Mizusawa, et al., 1979) (Mizusawa, et al., 1980), Liew and Lam (Liew & Lam, 1990), Liew et al. (Liew, et al., 1993), Singh and Chakraverty (Singh & Chakraverty, 1994), Zeng and Bert (Zeng & Bert, 2001), Kumar et al. (Kumar, et al., 2015) (Kumar, et al., 2017), He et al. (He, et al., 2017). Wang (Wang, 1997) used B-spline Rayleigh-Ritz method based first order shear deformation theory for free vibration analysis of laminated composite skew plates. For analysis of free vibration of laminated composite skew plates, Anlas and Gooker (Anlas & Göker, 2001) used orthogonal polynomials with Ritz method. Makhecha et al. (Makhecha, et al., 2001) investigated dynamic responses of thick skew sandwich plates using C0QUAD-8 finite element based on a realistic higher-order theory. Effect of skew angle and thickness ratio on the dynamic characteristics of sandwich laminates subjected to


Table 1. Research works on skew plates. Source


Eftekhari and Jafari (Eftekhari & Jafari, 2013) Wang (Wang, 1997a) Wang (Wang, 1997b)


Kiani et al. (Kiani, et al., 2018) Malekzadeh (Malekzadeh, 2008) Bert and Malik (Bert & Malik, 1996)


Malekzadeh and Zarei (Malekzadeh & Zarei, 2014) Wang and Wu (Wang & Wu, 2013) Wang and Yuan (Wang & Yuan, 2018) Wang et al. (Wang, et al., 2014) Zamani et al. (Zamani, et al., 2012)


Malekzadeh and Fiouz (Malekzadeh & Fiouz, 2007)


Adineh and Kadkhodayan (Adineh & Kadkhodayan, 2017)


Malekzadeh and Karami (Malekzadeh & Karami, 2006)


thermal and mechanical loads have been studied. A high precision thick plate element has been developed by Sheikh and Haldar (Sheikh, et al., 2004) for free vibration analysis of composite plates in different situations. Numerical examples of plates having different shapes, boundary conditions, thickness ratio and fiber orientations have been analysed. Examples of plates having an internal cut-out and concentrated mass have also been studied. A simple C0 isoparametric finite element model based on a higher order shear deformation theory has been presented by Garg et al. (Garg, et al., 2006) for free vibration of isotropic, orthotropic and layered composite and sandwich skew laminates. Numerical results have been presented for natural frequencies of cross-ply and angle-ply with different lamination parameters, skew angles and boundary conditions. A nine node isoparametric plate bending element formulation has been developed by Pandit et al. (Pandit, et al., 2007) for free vibration analysis of isotropic and laminated composite plates. Numerical examples of isotropic and composite plates having different fiber orientations, aspect ratios, and thickness ratios have been solved and compared. Examples of plates having an internal cut-out and uniformly distributed mass on the plate have also been studied. Bending response of functionally graded skew sandwich plates has been analysed by Taj et al. (Taj, et al., 2014). A comprehensive list of works on skew isotropic and composite plates is presented in Table 1. From this review, the followings insights into the analysis of skew composite laminates are gained: • FSDT is by far the most popularly used theory for analysis of skew laminates.


• FEM, DQM and Rayleigh-Ritz are the most commonly applied numerical methods for this problem.


• Works involving static and dynamic analysis of skew shells are very limited.


• Works involving static and dynamic analysis of skew shells with cutouts are negligible.


Theory FSDT FSDT FSDT FSDT FSDT FSDT


Malekzadeh and Karami (Malekzadeh & Karami, 2005) FSDT Malekzadeh (Malekzadeh, 2007)


FSDT FSDT


FSDT FSDT


3D elasticity FSDT


Method


R-DQM Plate RRM RRM RM


DQM DQM DQM DQM DQM DQM DQM DQM DQM DQM DQM


DQM


Structure ProblemType Vibration Vibration Buckling Vibration Vibration Vibration Vibration Vibration Vibration Vibration Buckling Vibration Vibration Bending Vibration


Plate Plate Shell Plate Plate Plate Plate Plate Plate Plate Plate Plate Plate Plate


Plate Vibration


A-362


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