Non-linear thermo-mechanical cylindrical bending of functionally graded plates

Fallah, Famida; Nosier, A.

doi:10.1243/09544062jmes772

Cited by 6 publications

(14 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…shows the results for center deflection of an FG plate under thermal loading

((), P_{z} = 0)

by using the two‐parameter expansion in . It is observed that the results are of good accuracy in comparison with the exact solution . In addition, when deflection and normal stress resultant are used as the perturbation parameters, the method is accurate even with the second‐order expansion.…”

Section: Numerical Results and Discussionmentioning

confidence: 84%

“…The results of seven different analyses of a simply‐supported FG plate under thermal loading, including the one‐parameter expansion of N T and T c with different perturbation parameters (deflection

w (x_{1})

, rotation

ψ (x_{2})

, and normal stress resultant N x ) and the two‐parameter expansion of N T and M T , for center deflection and axial stress versus

Δ T

are displayed and compared with the exact solution in Figs. and , respectively.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…In Figs. and the results for center deflection and axial stress, respectively, in simply‐supported and clamped FG plates

((), h / (2 a) = 0.02, n = 1)

under thermo‐mechanical loading are compared with the exact solution . In Fig.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…It is then readily seen that by imposing the homogeneous boundary conditions of a clamped FG plate (see Eq. ), only a trivial solution for the displacement field is obtained (see also ).…”

Section: General Developmentsmentioning

confidence: 99%

“…Within Mindlin's first-order shear deformation plate theory, the displacement field for cylindrical bending of an FG plate is assumed as follows [13]:…”

Section: Equilibrium Equationsmentioning

confidence: 99%

See 4 more Smart Citations

On perturbation method in mechanical, thermal and thermo‐mechanical loadings of plates: cylindrical bending of FG plates

et al. 2015

View full text Add to dashboard Cite

The performance of perturbation method in nonlinear analyses of plates subjected to mechanical, thermal, and thermo‐mechanical loadings is investigated. To this end, cylindrical bending of FG plates with clamped and simply‐supported edges is considered. The governing equations of Mindlin's first‐order shear deformation theory with von Kármán's geometric nonlinearity are solved using one‐ and two‐parameter perturbation methods and the results are compared with the results of an analytical solution. The material properties are assumed to vary continuously through the thickness of the plate according to a power‐law distribution of the volume fraction of the constituents. It is shown that the accuracy of any‐order expansion in perturbation method depends not only on the perturbation parameter, but also on the location chosen for the perturbation parameter and, in general, the solution becomes more accurate when the perturbation parameter is specified at the location where its corresponding response quantity is a maximum. Under thermal loading the possibility of using different parameters as the perturbation parameter for various boundary conditions is investigated. It is observed that, instead of a one‐parameter perturbation method, a two‐parameter perturbation method must be used in the thermal analysis of FG plates. Also, buckling and post‐buckling behavior of FG plates in cylindrical bending is investigated. It is shown that under thermal loading, a bifurcation‐type buckling occurs in clamped FG plates. In addition, a snap‐through buckling may occur in simply‐supported FG plates under thermo‐mechanical loading.

show abstract

“…shows the results for center deflection of an FG plate under thermal loading

((), P_{z} = 0)

Section: Numerical Results and Discussionmentioning

confidence: 84%

w (x_{1})

, rotation

ψ (x_{2})

, and normal stress resultant N x ) and the two‐parameter expansion of N T and M T , for center deflection and axial stress versus

Δ T

are displayed and compared with the exact solution in Figs. and , respectively.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…In Figs. and the results for center deflection and axial stress, respectively, in simply‐supported and clamped FG plates

((), h / (2 a) = 0.02, n = 1)

under thermo‐mechanical loading are compared with the exact solution . In Fig.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…It is then readily seen that by imposing the homogeneous boundary conditions of a clamped FG plate (see Eq. ), only a trivial solution for the displacement field is obtained (see also ).…”

Section: General Developmentsmentioning

confidence: 99%

“…Within Mindlin's first-order shear deformation plate theory, the displacement field for cylindrical bending of an FG plate is assumed as follows [13]:…”

Section: Equilibrium Equationsmentioning

confidence: 99%

See 3 more Smart Citations