A twelfth order theory of transverse bending of transversely isotropic plates. (English) Zbl 0535.73039

Reissner, E.

Z. Angew. Math. Mech. 63, 285-289 (1983).

It is known that there are differences between stress concentration factors and stress couple concentration factors for the problem of the effect of a small circular hole on states of uniform transverse bending or twisting in homogeneous isotropic elastic plates. In this paper a variational method is used for the derivation of a twelfth order two- dimensional theory of transversely isotropic plates, which includes the known sixth order theory of shear deformable plates as a special case via constitutive-coefficient specialisation. It is also shown that the twelfth order system may be reduced to two simultaneous second order and two simultaneous fourth order Laplace operator equations. This leads to the possibility of obtaining closed form solutions for polar coordinate boundary value problems.

Reviewer: W.A.Bassali

MSC:

74K20	Plates
74G70	Stress concentrations, singularities in solid mechanics
74E10	Anisotropy in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

stress concentration factors; stress couple concentration factors; small circular hole; uniform transverse bending; twisting; twelfth order two- dimensional theory of transversely isotropic plates; reduced to two simultaneous second order and two simultaneous fourth order Laplace operator equations; closed form solutions for polar coordinate boundary value problems

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