Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

doi:10.1007/s10483-023-2958-8

Abstract

Abstract: The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material (FGM) model with transverse isotropy. The FGMs are approximated with $n$-layered materials. Each of the $n$-layered materials is homogeneous and transversely isotropic. The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions. The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties. The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions. Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Key words: functionally graded material (FGM), transverse isotropy, elasticity, closed-form singular solution, Green's function, point load vector

2010 MSC Number:

35A08
35G60

Sha XIAO, Zhongqi YUE. Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy. Applied Mathematics and Mechanics (English Edition), 2023, 44(3): 411-430.

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