On asymmetric bending of functionally graded solid circular plates

• Published in: Applied mathematics and mechanics Vol. 39; no. 6; pp. 767 - 782
• Main Authors: Yang, Yingwu, Zhang, Ying, Chen, Weiqiu, Yang, Bo
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.06.2018; Springer Nature B.V; Department of Civil Engineering, Zhejiang Agriculture and Forestry University, Hangzhou 311300, China%Department of Civil Engineering, Zhejiang Sci-Tech University,Hangzhou 310018, China%Department of Engineering Mechanics, Yuquan Campus, Zhejiang University,Hangzhou 310027, China
• Edition: English ed.
• Subjects: Analytic functions; Applications of Mathematics; Circular plates; Classical Mechanics; Elastic bending; Elasticity; Fluid- and Aerodynamics; Fourier series; Functionally gradient materials; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Transverse loads; transversely isotropic; O343.1; 74B05; elasticity solution; functionally graded material; circular plate; biharmonic load
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-018-2337-7

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.