On shear correction factors in the non-linear theory of elastic shells

Abstract

Theoretical values of two correction factors α s = 5/6 and α t = 7/10 are established for the respective transverse shear stress resultants and stress couples within the general, dynamically and kinematically exact, six-field theory of elastic shells. These values do not depend on the shell material symmetry, geometry of the base surface, the shell thickness, or any kind of kinematic and/or dynamic constraints. The analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section. The appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with α s and α t as the respective correction factors. Four numerical examples of highly non-linear shell structures illustrate the influence of different values of α s and α t on the results. In particular, some influence of α t is noticed on the placement of bifurcation points. In dynamic problem of flight of three intersecting plates analysed with Newmark-type temporal algorithm, the value of α t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure.