Vibrations of thick isotropic plates with higher order shear and normal deformable Plate theories

Batra, R.C.; Aimmanee, Sontipee

doi:10.1016/j.compstruc.2004.11.023

Cited by 50 publications

(18 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Batra and Vidoli [38] showed that for a thick beam results from the mixed plate theory are in better agreement with the LET solutions than those from the compatible theory of the same order. Qian et al [39] and Batra and Aimmanee [40] have used the compatible (mixed) theory of different orders to show that in-plane modes of free vibration in a thick plate are well captured when K = 3. Qian and Batra [41] have extended the compatible theory to analyze thermo-elastic deformations.…”

Section: Introductionmentioning

confidence: 99%

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

Shah

Batra

2016

Mechanics of Advanced Materials and Structures

View full text Add to dashboard Cite

We analyze static infinitesimal deformations of doubly curved shells using a third-order shear and normal deformable theory (TSNDT) and delineate effects of the curvilinear length/thickness ratio, R/a, a/h, radius of curvature/curvilinear length, and the ratio of the two principal radii on through-the-thickness stresses, strain energies of the in-plane and the transverse shear and normal deformations, and strain energies of stretching and bending deformations for loads that include uniform normal tractions on a major surface and equal and opposite tangential tractions on the two major surfaces. In the TSNDT the three displacement components at a point are represented as complete polynomials of degree three in the thickness coordinate. Advantages of the TSNDT include not needing a shear correction factor, allowing stresses for monolithic shells to be computed from the constitutive relation and the shell theory displacements, and considering general tractions on bounding surfaces. For laminated shells we use an equivalent single layer TSNDT and find the in-plane stresses from the constitutive relations and the transverse stresses with a onestep stress recovery scheme. The in-house developed finite element software is first verified by comparing displacements and stresses in the shell computed from it with those from either analytical or numerical solutions of the corresponding 3D problems. The strain energy of a spherical shell is found to approach that of a plate when R/a exceeds 10. For a thick clamped shell of aspect ratio 5 subjected to uniform normal traction on the outer surface, the in-plane and the transverse deformations contribute equally to the total strain energy for R/a greater than 5. However, for a cantilever shell of aspect ratio 5 subjected to equal and opposite uniform tangential tractions on the two major surfaces, the strain energy of in-plane deformations equals 95-98% of the total strain energy. Numerical results presented herein for several problems provide insights into different deformation modes, help designers decide when to consider effects of transverse deformations, and use the TSNDT for optimizing doubly curved shells.

show abstract

Section: Introductionmentioning

confidence: 99%

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

Shah

Batra

2016

Mechanics of Advanced Materials and Structures

View full text Add to dashboard Cite

show abstract

“…Fethi Kadıoğlu, Gülçin Tekin Istanbul Technical University Turkey Batra and Aimmanee [11] studied vibration of thick isotropic plates with higher order shear and normal deformable plate theories. Aagaah et al [12] examined natural frequencies of laminated composite plates using third order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Cross ply Laminated Composite Thick Plates

Kadıoğlu¹,

Tekin²

2015

Second International Conference on Advances in Civil, Structural and Mechanical Engineering - ACSM 2015

View full text Add to dashboard Cite

“…Batra and Jin [8] used the FSDT coupled with the FEM to study the free vibrations of an FG anisotropic rectangular plate with various edge conditions. Also, Batra and Aimmanee [9] studied a higher order shear and normal deformable plate theory by FEM. Many studies conducted on FGMs are related to the analysis of free vibration by applying FSDT (see [10][11][12] and the references there in).…”

Section: Introductionmentioning

confidence: 99%

Second Order Shear Deformation Theory (SSDT) for Free Vibration Analysis on a Functionally Graded Quadrangle Plate

Shahrjerdi¹,

Mustapha²

2011

Recent Advances in Vibrations Analysis

View full text Add to dashboard Cite

Vibrations of thick isotropic plates with higher order shear and normal deformable Plate theories

Cited by 50 publications

References 29 publications

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

Stretching and bending deformations due to normal and shear tractions of doubly curved shells using third-order shear and normal deformable theory

Free Vibration Analysis of Cross ply Laminated Composite Thick Plates

Second Order Shear Deformation Theory (SSDT) for Free Vibration Analysis on a Functionally Graded Quadrangle Plate

Contact Info

Product

Resources

About