ABSTRACT
Most of the shear correction methods for the first-order plates and shells are based on matching certain gross response predicted by the first order theory with those obtained from the 3-D elastic theory, such as, matching the transverse shear strain energy, the propagation velocity of a flexural wave, or the natural frequency of the thickness shear vibration mode. In this paper, an assumed strain based shear correction method for the first-order shear theory based plate and shell elements has been derived from the general variational principles. The derived shear correction method is the optimal result in certain FEM space and easy to implement. The used general variational principle is based on the thermodynamic potential, making the derived shear correction method suitable for different materials. The shear correction factor for homogeneous elastic material is evaluated using the assumed strain based shear correction method, and the result of 0.8 is obtained. The proposed shear correction method is then applied to an elastic-linear hardening plastic deep beam for verification, and the conformable result is obtained as compared with the plane strain result.
