A High-Order Theory of Plate Deformation—Part 1: Homogeneous Plates

Lo, King Him; Christensen, Richard M.; Wu, Edward M.

doi:10.1115/1.3424154

Cited by 578 publications

(175 citation statements)

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“…Finally, the axial stress σ x could be obtained by using stress-strain relationship (constitutive relation) as given in Eqs. (10) and (11). The transverse shear stress τ xz can be obtained either by using the constitutive relation [Eqs.…”

Section: Axial Stress and Transverse Shear Stressesmentioning

confidence: 99%

Flexural analysis of cross-ply laminated beams using layerwise trigonometric shear deformation theory

Ghugal

Shinde

2013

Lat. Am. j. solids struct.

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In the present work, a layerwise trigonometric shear deformation theory is used for the analysis of two layered (90/0) cross ply laminated simply supported and fixed beams subjected to sinusoidal load. The displacement field of the present theory consists of trigonometric sine function in terms of thickness coordinate to take into account the effect of transverse shear deformation. Theory satisfies the transverse shear stress free boundary conditions at top and bottom surfaces of the beam. This model satisfies the constitutive relationship between shear stress and shear strain in both the layers and the axial displacement compatibility at the interface. Virtual work principle is employed to obtain governing equations and boundary conditions. Closed form solution technique has the limitation of simply supported boundary condition. In the present work general solution technique is developed, which can be used for any type of boundary and loading conditions. The transverse shear stresses are obtained using constitutive relation as well from the use of equilibrium equations. The results of displacements and stresses obtained by present theory are compared with the available results in the literature.

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Section: Axial Stress and Transverse Shear Stressesmentioning

confidence: 99%

Flexural analysis of cross-ply laminated beams using layerwise trigonometric shear deformation theory

Ghugal

Shinde

2013

Lat. Am. j. solids struct.

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“…The stiffness coefficients D 1 through D 27 appeared in governing equations (14)(15)(16)(17) and boundary conditions (18)(19)(20)(21)(22)(23)(24)(25)(26)(27) …”

Section: Appendixmentioning

confidence: 99%

“…. unknowns, Lo et al [16,17] with 11 unknowns, Kant [7] with six unknowns, Bhimaraddi and Stevens [2] with five unknowns, Reddy [23] with eight unknowns, Hanna and Leissa [5] with four unknowns. Srinivas et al [27] used an exact three dimensional plate theory to study the vibration of simply supported homogenous and laminated thick rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of thick orthotropic plates using trigonometric shear deformation theory

Ghugal¹,

Sayyad²

2011

Lat. Am. j. solids struct.

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In this paper a trigonometric shear deformation theory is presented for the free vibration of thick orthotropic square and rectangular plates. In this displacement based theory the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The most important feature of the theory is that the transverse shear stress can be obtained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate. Hence the theory obviates the need of shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for frequency of bending mode, shear mode and thickness stretch mode of free vibration of simply supported orthotropic square and rectangular plates are compared with those of other refined theories and exact solution from theory of elasticity wherever applicable.

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“…The eigenvalue problem and the sensitivity analysis are carried out using a third-order shear deformation theory whose pioneering works are described in [16,17] and has been applied to discrete ®nite element models by Mallikarjuna and Kant [18], among others. Full details regarding the model development and implementation for dynamics can be found in [19,20].…”

Section: Numerical Modelmentioning

confidence: 99%

Combined numerical–experimental model for the identification of mechanical properties of laminated structures

Araújo

Soares²,

Freitas³

et al. 2000

Composite Structures

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A combined numerical±experimental method for the identi®cation of six elastic material modulus of generally thick composite plates is proposed in this paper. This technique can be used in composite plates made of di erent materials and with general stacking sequences. It makes use of experimental plate response data, corresponding numerical predictions and optimisation techniques. The plate response is a set of natural frequencies of¯exural vibration. The numerical model is based on the ®nite element method using a higher-order displacement ®eld. The model is applied to the identi®cation of the elastic modulus of the plate specimen through optimisation techniques, using analytical sensitivities. The validity, e ciency and potentiality of the proposed technique is discussed through test cases. Ó

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A High-Order Theory of Plate Deformation—Part 1: Homogeneous Plates

Cited by 578 publications

References 0 publications

Flexural analysis of cross-ply laminated beams using layerwise trigonometric shear deformation theory

Flexural analysis of cross-ply laminated beams using layerwise trigonometric shear deformation theory

Free vibration of thick orthotropic plates using trigonometric shear deformation theory

Combined numerical–experimental model for the identification of mechanical properties of laminated structures

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