Bending Solutions of Sectorial Thick Plates Based on Reissner Plate Theory

ABSTRACT

This paper is concerned with the bending of sectorial and annular sectorial thick plates with the radial edges simply supported. The Reissner plate theory has been adopted to cater for the effect of transverse shear deformation. In solving the aforementioned plate problems, we derive the relationships between the bending solutions of the Reissner plate theory and the classical thin plate theory. The relationships enable one to deduce the bending solutions of the Reissner plate theory using the corresponding classical thin plate results, which can be determined readily or are already available in the literature. Several sectorial plate problems are solved, and the Reissner plate results are checked against existing numerical results as well as results obtained using other higher-order plate theories.

Key Words:

• Plate bending
• Classical thin plate theory
• Reissner plate theory
• Relationships
• Sectorial plates
• Annular sectorial plates

Mathematics Subject Classification:

• Partial differential equations
• Generalized Fourier transform

Notes

^a Based on the Mindlin plate theory with shear correction factor κ² = 5/6.

^b Based on the Reissner plate theory, where w¯ = wD/[qa ⁴]×10³, M¯ _rr  = M _rr D/[qa ²]×10², M¯ _ΘΘ = M _ΘΘ D/[qa ²]×10², Q¯ _r  = Q _r D/[qa]×10², Q¯ _Θ = Q _Θ D/[qa]×10², and β = a/2.

^a Based on the Mindlin plate theory with shear correction factor κ² = 5/6.

^b Based on the Reissner plate theory, where w¯ = wD/[qa ⁴]×10³, M¯ _rr  = M _rr D/[qa ²]×10², M¯ _ΘΘ = M _ΘΘ D/[qa ²]×10², Q¯ _r  = Q _r D/[qa]×10², Q¯ _Θ = Q _Θ D/[qa]×10², and β = a/2.

^a Based on two-dimensional and three-dimensional finite strip method.

^b Based on the Reissner plate theory.

^a Finite element method with sectorial plate elements based on the Reissner plate theory.

^b Based on the analytical solution of the Reissner plate theory, where w¯ = wD/[qa ⁴]×10³ and M¯ _rr  = M _rr D/[qa ²]×10².

^a Based on the Mindlin plate theory with shear correction factor κ² = 5/6.

^b Based on the Reissner plate theory, where w¯ = wD/[qa ⁴]×10³, M¯ _rr  = M _rr D/[qa ²]×10², M¯ _ΘΘ = M _ΘΘ D/[qa ²]×10², Q¯ _r  = Q _r D/[qa]×10², Q¯ _Θ = Q _Θ D/[qa]×10², and β = a/2.

^a Based on the Mindlin plate theory with shear correction factor κ² = 5/6.

^b Based on the Reissner plate theory, where w¯ = wD/[qa ⁴]×10³, M¯ _rr  = M _rr D/[qa ²]×10², M¯ _ΘΘ = M _ΘΘ D/[qa ²]×10², Q¯ _r  = Q _r D/[qa]×10², Q¯ _Θ = Q _Θ D/[qa]×10² and β = a/2.

^a Based on differential quadrature element method on theReissner–Mindlin plates.

^b Based on the Mindlin plate theory with shear correction factor κ² = 5/6.

^c Based on analytical solution of Reissner plate theory, where w¯ = wD/[qa ⁴]×10³, M¯ _rr  = M _rr D/[qa ²]×10², andM¯ _ΘΘ = M _ΘΘ D/[qa ²]×10².