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.
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Citation: XIAO, S. and YUE, Z. Q. Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy. Applied Mathematics and Mechanics (English Edition), 44(3), 411–430 (2023) https://doi.org/10.1007/s10483-023-2958-8
Project 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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Xiao, S., Yue, Z. Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy. Appl. Math. Mech.-Engl. Ed. 44, 411–430 (2023). https://doi.org/10.1007/s10483-023-2958-8
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DOI: https://doi.org/10.1007/s10483-023-2958-8
Key words
- functionally graded material (FGM)
- transverse isotropy
- elasticity
- closed-form singular solution
- Green’s function
- point load vector