A higher-order polynomial shear deformation theory for geometrically nonlinear free vibration response of laminated composite plate

Swain, Puspa Ranjan; Adhikari, Balakrishna; Dash, P. R.

doi:10.1080/15376494.2017.1365981

Cited by 18 publications

(10 citation statements)

References 26 publications

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“…The achievements of the last decade in the shear deformation theory of thin-walled structures have been discussed in review articles [ 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 ], among others.…”

Section: Introductionmentioning

confidence: 99%

Some Inconsistencies in the Nonlinear Buckling Plate Theories—FSDT, S-FSDT, HSDT

Kołakowski

Jankowski

2021

Materials

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Bending and membrane components of transverse forces in a fixed square isotropic plate under simultaneous compression and transverse loading were established within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), and the classical plate theory (CPT). Special attention was drawn to the fact that bending components were accompanied by transverse deformations, whereas membrane components were not, i.e., the plate was transversely perfectly rigid. In the FSDT and the S-FSDT, double assumptions concerning transverse deformations in the plate hold. A new formulation of the differential equation of equilibrium with respect to the transverse direction of the plate, using a variational approach, was proposed. For nonlinear problems in the mechanics of thin-walled plates, a range where membrane components should be considered in total transverse forces was determined. It is of particular significance as far as modern composite structures are concerned.

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Section: Introductionmentioning

confidence: 99%

Some Inconsistencies in the Nonlinear Buckling Plate Theories—FSDT, S-FSDT, HSDT

Kołakowski

Jankowski

2021

Materials

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“…Hence, the complete investigations on the nonlinear analysis of structure can be found in various studies. 6–10 However, a few relevant literatures, which guided the present research have been discussed. In this regard, Gnapathi et al.…”

Section: Introductionmentioning

confidence: 99%

“…Swain et al. 10 investigated the large amplitude free vibration of a laminated composite plate using Green Lagrange strain field based on a higher order quasi 3-D theory. Further, Adhikari and Dash 16 formulated a finite element procedure for the large amplitude free vibration of the laminated composite plates based on an inverse trigonometric shear deformation theory (ITSDT).…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear static and dynamic analysis of CNT reinforced laminated composite plates: A finite element study

Adhikari

Singh

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, a finite element study is conducted using the Green Lagrange strain field based on vonKarman assumptions for the geometric nonlinear static and dynamic response of the laminated functionally graded CNT reinforced (FG-CNTRC) composite plate. The governing equations for determining the nonlinear static and dynamic behavior of the FG-CNTRC plate are derived using the Lagrange equation of motion based on Reddy's higher order theory. Using the direct iteration technique, the nonlinear eigenvalues for analyzing the free vibration response are obtained and the nonlinear dynamic responses of the FG-CNTRC plate are encapsulated based on the nonlinear Newmark integration scheme. The impact of the amplitude of vibration on mode switching phenomena and the consequence of the duration of the pulse on the free vibration regime of the plate are outlined. Also, the effect of time dependent loads is studied on the normal stresses of the plate. Furthermore, the impact on the nonlinear static and dynamic response of the laminated FG-CNTRC plate of various parameters such as span-thickness ratio (b/h ratio), aspect ratio (a/b ratio), different edge constraints, CNT fiber gradation, etc. are also studied.

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“…In contrast, the numerical methods can predict the behavior of arbitrary laminated composite plates in practice within acceptable tolerances. Nowadays, laminated composite plates have been largely analyzed by such numerical methods as the finite element methods (FEM) [23][24][25][26][27][28][29][30][31], meshless methods [27,32,33] and isogeometric methods [13,[34][35][36][37]. The recently developed meshless and isogeometric methods can represent high-order displacement approximations and then satisfy the C 1 -continuous requirement of the HSDT.…”

Section: Introductionmentioning

confidence: 99%

A MITC3+ element improved by edge-based smoothed strains for analyses of laminated composite plates using the higher-order shear deformation theory

et al. 2020

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In this paper, a new three-node triangular plate element is proposed to analyze laminated composite plates based on the higher-order shear deformation theory (HSDT). Originating from the MITC3+ shell finite elements, the displacement fields of the HSDT are interpolated by usual linear functions of the three-node triangular element and a cubic supplemented function associated with a node located at the centroid of the element. The transverse shear strain fields are separately approximated according to the MITC3+ shear-locking removal technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. Applying the divergence theorem, the surface integration of the in-plane stiffness matrices is transformed into the line integration on the boundary of the smoothing domains. The performance of the so-called ES-MITC3+ plate elements is validated through several numerical examples. The numerical results of the static, frequency and buckling analyses when this new element is used converge to the exact solutions and agree well with those given in other references.

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A higher-order polynomial shear deformation theory for geometrically nonlinear free vibration response of laminated composite plate

Cited by 18 publications

References 26 publications

Some Inconsistencies in the Nonlinear Buckling Plate Theories—FSDT, S-FSDT, HSDT

Some Inconsistencies in the Nonlinear Buckling Plate Theories—FSDT, S-FSDT, HSDT

Geometrically nonlinear static and dynamic analysis of CNT reinforced laminated composite plates: A finite element study

A MITC3+ element improved by edge-based smoothed strains for analyses of laminated composite plates using the higher-order shear deformation theory

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