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

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2016-02, Vol.96 (2), p.217-232
• Main Authors: Fallah, F., Nosier, A., Sharifi, M., Ghezelbash, F.
• Format: Article
• Language: English
• Subjects: cylindrical bending; Functionally graded material; nonlinear analysis; perturbation method; post-buckling
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201400136

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. 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.