Refined shear-deformation models for composite laminates with finite rotations

Abstract

For arbitrary multilayered shell structures made particularly of composite material layers a refined finite-rotation theory with seven independent displacement variables is developed, approximating the displacement field by a cubic series expansion of thickness coordinates. This model allows a quadratic shear deformation distribution across the thickness. Procedures are given permitting a unique determination of the first order displacement term in the case of finite rotations. Kinematic relations are formulated in two alternative forms suitable for both classical and isoparametric finite element formulations. The constitutive relations presented model orthotropic material properties varying arbitrarily across the thickness. This third order single-layer theory is then transformed, by introducing further constraints, into three simplified models : a third order theory with five independent displacement variables, a Mindlin-Reissner type theory and a Kirchhoff-Love type theory. These four models differ, however, from each other essentially in the constraints imposed on the first and third order displacement variables : a significant advantage for a unified finite element development. Finally, the Mindlin-Reissner type theory is generalized to a layer-wise model being the most predictive one in dealing with local interlaminar effects. The theoretical models are transformed into adequate finite shell elements and then compared by means of appropriate examples concerning their prediction capability. Also examples are given demonstrating their applicability to finite-rotation phenomena.