Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions

• Published in: International journal for numerical methods in engineering Vol. 79; no. 1; pp. 25 - 44
• Main Authors: Lü, C. F., Lim, C. W., Chen, W. Q.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 02.07.2009; Wiley
• Subjects: 3-D elasticity; Computational techniques; Convergence; differential quadrature method; Elasticity; Exact sciences and technology; Exact solutions; Formalism; Functionally gradient materials; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical methods in physics; Mathematical models; multi-directional functionally graded plates; Physics; Plates; semi-analytical analysis; Solid mechanics; state-space method; Static elasticity (thermoelasticity...); Structural and continuum mechanics; State space method; Modeling; multidirectional functionally graded plates; Orthotropic material; Plate; Exact solution; Quadrature; differential quadrature method; 3-D elasticity; state-space method; semi-analytical analysis; Functionnally graded material; Differential method
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2555

Semi‐analytical 3‐D elasticity solutions are presented for orthotropic multi‐directional functionally graded plates using the differential quadrature method (DQM) based on the state‐space formalism. Material properties are assumed to vary not only through the thickness but also in the in‐plane directions following an exponential law. The graded in‐plane domain is solved numerically via the DQM, while exact solutions are sought for the thickness domain using the state‐space method. Convergence studies are performed, and the present hybrid semi‐analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate. Finally, effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed. Copyright © 2009 John Wiley & Sons, Ltd.