Chinese Journal of Theoretical and Applied Mechani ›› 2010, Vol. 42 ›› Issue (2): 325-331.DOI: 10.6052/0459-1879-2010-2-2007-576

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Three-dimensional analysis for static bending and free vibration of functionally graded rectangular plate

Fengxi Zhou Shirong Li   

  1. Northwest Center for Disaster Mitigation in Civil Engineering, Ministry of Education, Lanzhou 730050, China College of Civil Science and Engineering, Yangzhou University, Yangzhou 225009, China
  • Received:2007-11-26 Revised:2008-02-19 Online:2010-03-18 Published:2010-03-18

Abstract: The state equation of functionally graded rectangular plate were established with the state variables of three displacement components and three stress components, based on the three-dimensional linear elastic theory by using of state space method. Considering simply supported boundary conditions, the static bending and free vibration problems of a three-dimensional functionally graded rectangular plate were numerically solved by shooting method with that the material properties through the thickness coordinate are assumed to obey the exponent law dependence. Effects of the volume fraction distributions of constituent materials, and thickness-to-side ratio of functionally graded rectangular plate on the dynamical and static responses were studied. The present algorithm can be used to research the three-dimensional elastic response of functionally graded materials.

Key words: functionally graded material, three-dimensional analysis, state space approach, shooting method, static bending, free vibration