Abstract
Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material properties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England’s method, the problem can be solved by determining the expressions of four analytic functions. Expanding the transverse load in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.
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Project supported by the National Natural Science Foundation of China (No. 11621062), the Natural Science Foundation of Zhejiang Province (No. LY18A020009), the Science and Technology Project of Ministry of Housing and Urban and Rural Development (No. 2016-K5-052), and the Science Foundation of Zhejiang Sci-Tech University (No. 16052188-Y)
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Yang, Y., Zhang, Y., Chen, W. et al. On asymmetric bending of functionally graded solid circular plates. Appl. Math. Mech.-Engl. Ed. 39, 767–782 (2018). https://doi.org/10.1007/s10483-018-2337-7
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DOI: https://doi.org/10.1007/s10483-018-2337-7