Implementation of Higher Order Shear Theory on Isotropic Material and Liu's Bending Part on Laminated Composite Flat Shell Elements

Abstract

Plate and shell analysis using classical plate theory (CPT) has a lack of accuracy in predicting the influence of transverse deformation, because of its assumption that the line normal to the surface is remain straight and normal to the midplane before and after deformation. The next revision by constant shear deformation theory or famous as first order shear deformation theory (CSDT/FOSDT) still suffer a disadvantage that have a constant value in the shear term that called shear locking phenomenon. This matter have been corrected by higher order shear deformation theory (HOSDT) using refined assumption that the line normal to the surface should be in a parabolic function and not normal to the midplane, but normal to the surfaces so it fulfill the zero strain in the surfaces. The analysis of bending part of laminated composite flat shell element is applied by higher order lamination theory (HOLT) that adopted from HOSDT. This model is accurate for thicknesses variation and complex material. HOLT model is implemented into finite element procedure to find deflection, stresses and internal forces. It can be concluded that the displacement and stresses in HOLT model is higher than FOLT ones (first order lamination theory) in small ratio of a/h dan its result almost the same value for a/h ratio more than 10. In a square plate case, the displacement get smaller if the fiber arranged into cross-ply sequence. Interlaminar stresses along thickness is not distributed continuously, but they have certain modes that depend on the depth of point position, the lamina or layer number, fiber orthotropic angle of each layer and a/h ratio.