Generalized plane strain thermoelastic deformation of laminated anisotropic thick plates

Vel, Senthil S.; Batra, R.C.

doi:10.1016/s0020-7683(00)00108-6

Cited by 41 publications

(25 citation statements)

References 30 publications

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“…However, Vel and Batra [23] presented the numerical results, only, for a cross-ply plate simply supported on two opposite edges and subjected to different sets of boundary conditions on the other edges and a clamped plate with [0°/90°/0°] and [45°/-45°/45°] laminations. Vel and Batra [25] simplified three-dimensional equations of linear elasticity to the case of generalized plane-strain deformations and solved them by the Eshelby-Stroh formalism to study the cylindrical bending of an anisotropic laminated plate with either both edges clamped or one edge clamped and the other simply supported or one edge clamped and the other free.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions

Nik

Tahani

2009

J Mech Sci Technol

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The intent of the present study is to employ the extended Kantorovich method for semi-analytical solutions of laminated composite plates with arbitrary lamination and boundary conditions subjected to transverse loads. The method based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation theory, a laminated plate theory is developed. Using the principle of minimum total potential energy, two systems of coupled ordinary differential equations with constant coefficients are obtained. The equations are solved analytically by using the state-space approach. The results obtained are compared with the Levy-type solutions of cross-ply and antisymmetric angle-ply laminates with various admissible boundary conditions to verify the validity and accuracy of the present theory. Also, for other laminations and boundary conditions that there exist no Levy-type solutions the present results are compared with those obtained by other investigators and finite element method. It is found that the present results have very good agreements with those obtained by other methods.

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Section: Introductionmentioning

confidence: 99%

Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions

Nik

Tahani

2009

J Mech Sci Technol

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“…This hypothesis is fully consistent with the original proposal of Weiner and Boley and has also been followed by Thomas and coworkers [14][15][16][17][18][19], who called it Generalized Plane Strain hypothesis. We propose instead the name two-dimensional extended plane strain condition (EPSC) to avoid confusions with a kinematic hypothesis used in plate analysis (see References [20,21]) which has been given that name. In Section 3 we compare the results obtained for the one-dimensional EPSC case, with those reported in the above-mentioned studies.…”

Section: Introductionmentioning

confidence: 99%

Thermal stress evaluation in the steel continuous casting process

Risso

Huespe

Cardona

2005

Numerical Meth Engineering

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“…In the thermally conducting composite solids, the increases in the temperature distribution due to the occurrence of geometrical or material discontinuities, which may result in the increase of thermal stresses and may often lead to the structural failure of the material. Thermal stresses, especially at the interface between two different materials, often represent a significant aspect in the breakdown of laminated composite structures; as a consequence, a number of mechanical models have been proposed to estimate the importance of thermal loadings (Vel and Batra 2001;Batra 1999, 2000). Therefore, there is a need to accurately predict thermal stresses in composite structures.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic symmetric and antisymmetric wave modes with trigonometric functions in laminated plates

Verma

2014

Int J Mech Mater Eng

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Background: Coupling term in coupled thermoelasticity generally is small for all materials and can be neglected. Neglecting the coupling term simplifies the analysis without noticeable effect on the frequency spectrum. In generalized theory of thermoelasticity, effect of increasing the relaxation time is to lower the speeds of the thermal modes. Since the effect of anisotropy of the material is quite pronounced on waves propagating in different directions along the plate. Thus, it is significant to consider the anisotropy of the material in order to accurately model the propagation characteristics. Methods: A theoretical framework is developed for displacements and temperature expression of plane harmonic waves in generalized theory of thermoelasticity using three dimensional thermoelasticity with a thermal relaxation time. Subsequently, the Lamb waves in a single lamina where a compact closed-form dispersion relation is derived by separating thermoelastic symmetric and anti-symmetrical modes using trigonometric functions through the lamina thickness. Results: Propagation of guided thermoelastic waves in a homogeneous, orthotropic, thermally conducting plate is investigated within the framework of the generalized theory of thermoelasticity. The results show that both elastic and thermal modes are attenuated, the thermal modes exhibit much larger attenuation than the elastic modes. The attenuation of the former is quite small. Results obtained are extended to a general laminate with an arbitrary layup. On employing boundary conditions on both mid-plane and top surfaces is developed to decouple the wave modes for symmetric and anti-symmetrical modes for laminates. Conclusions: Propagation of guided thermoelastic waves in a homogeneous, orthotropic, thermally conducting plate is investigated employing generalized theory of thermoelasticity which includes a thermal relaxation time in the heat conduction equation in order to model the finite speed of the thermal wave. Both elastic and thermal modes are attenuated; the thermal modes exhibit much larger attenuation than the elastic modes. The effect of increasing the relaxation time is to lower the speeds of the thermal modes. The effect of anisotropy of the material is quite pronounced on waves propagating in different directions. Thus, it is important to consider the anisotropy of the material in order to accurately model the propagation characteristics.

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Generalized plane strain thermoelastic deformation of laminated anisotropic thick plates

Cited by 41 publications

References 30 publications

Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions

Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions

Thermal stress evaluation in the steel continuous casting process

Thermoelastic symmetric and antisymmetric wave modes with trigonometric functions in laminated plates

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