Refined shear-deformation models for composite laminates with finite rotations
A refined finite-rotation theory applicable to multilayered shell structures, made of composite material layers, is developed. The displacement field containing seven independent variables is approximated by a cubic series expansion of thickness coordinates. A quadratic shear distribution across the thickness is obtained. The given procedure allows 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. Firstly, this third order theory is applied to a single layered shell. Then, by introducing further constraints three simplified models are obtained: a third-order theory with five independent variables; a Mindlin-Reissner type theory; a Kirchhoff-Love type theory. All these four models differ, however, from each other essentially in the constraints imposed on the first and third order displacement variables, thus a significant advantage can be obtained by a unified finite element development. Finally, the Mindlin-Reissner type theory is generalized to a layerwise model which is most predictive to determine local interlaminar effects, and finite element procedure is applied to obtain five theoretical models. The results are compared by means of appropriate numerical examples concerning linear and nonlinear problems (sandwich plate under sinusoidal and uniform transverse load, cylindrical bending of an asymmetric cross-plied laminate under uniformly distributed transverse load, and hyperboloidal shell under two pairs of opposite point loads). The general conclusion is that a single model can hardly be seen as the best one for all purposes. In reality a decision about the quality of an analysis model can be made under consideration of the requirements of the application field. The models proposed in the paper can enable us to select the best possible one for each individual laminate problem.
scientific article; zbMATH DE number 473182