Acta Mechanica

, Volume 227, Issue 2, pp 495–506 | Cite as

Analytical solutions for an infinite transversely isotropic functionally graded sectorial plate subjected to a concentrated force or couple at the tip

Original Paper
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Abstract

This paper considers the elastic responses of an infinite sectorial plate made of transversely isotropic functionally graded material (FGM), which is subjected to a concentrated force or couple at the tip. There is no load acting on the upper and lower surfaces, and the elastic coefficients can vary arbitrarily through the plate thickness. No constraint is required on the symmetry of the plate in the thickness direction. Based on the displacement assumption for the bending of an FGM plate and by using the complex variable method, this paper presents the general solutions to the basic equations governing transversely isotropic FGM plates, which are expressed in terms of four analytical functions (or complex potentials). The boundary conditions are a combination of those from the plane elasticity and those from the classical plate theory. For a particular boundary value problem, such as the ones considered here for a sectorial plate, with the specific conditions for determining solutions, the four analytic functions can be assumed in appropriate forms, which contain only some unknown constants. Once these constants are determined from the specific conditions, the complete solutions are readily derived too. Among the solutions presented here, the solutions for the infinite FGM sectorial plate under a concentrated couple are absolutely new to the literature, and they are also applicable to isotropic FGM sectorial plates. The solutions degenerate into the ones for a homogeneous sectorial plate, which coincide with the available solutions from the plane elasticity theory. There are three-dimensional correction terms in the mid-plane displacements.

Keywords

Functionally Grade Material Concentrate Force Elasticity Solution Annular Plate Functionally Grade Material Plate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.The Faculty of Mechanical Engineering and MechanicsNingbo UniversityNingboPeople’s Republic of China
  2. 2.Department of Civil EngineeringZhejiang Sci-Tech UniversityHangzhouPeople’s Republic of China
  3. 3.Key Lab of CAD&CGZhejiang UniversityHangzhouPeople’s Republic of China
  4. 4.Department of Engineering MechanicsZhejiang UniversityHangzhouPeople’s Republic of China
  5. 5.Department of Civil EngineeringZhejiang UniversityHangzhouPeople’s Republic of China

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