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

Sha XIAO, Zhongqi YUE

doi:10.1007/s10483-023-2958-8

2023 , Vol. 44 >Issue 3: 411 - 430

DOI: https://doi.org/10.1007/s10483-023-2958-8

Articles

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

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1. Key Laboratory of Urban Security and Disaster Engineering of China Ministry of Education, Beijing University of Technology, Beijing 100124, China;
2. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China

Received date: 2022-08-29

Revised date: 2022-11-09

Online published: 2023-02-27

Supported by

the National Natural Science Foundation of China (No. 42207182) and the Research Grants Council of the Hong Kong Special Administrative Region Government of China (Nos. HKU 17207518 and R5037-18)

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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

Cite this article

Sha XIAO, Zhongqi YUE . Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy[J]. Applied Mathematics and Mechanics, 2023 , 44(3) : 411 -430 . DOI: 10.1007/s10483-023-2958-8

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