An Efficient Layerwise Shear-Deformation Theory and Finite Element Implementation

A computationally efficient, layerwise shear-deformation theory for improving the accuracy of stress and strain predictions in the analysis of laminated shells with arbitrary thickness is presented. The theory is two-dimensional and displacement-based. The in-plane displacement field is modeled using the superposition of overall first-order shear deformation and layerwise functions that accommodate the complexity of zigzag-like in-plane deformation through the laminate thickness. By imposing the inter-laminar shear traction continuity, which is ignored by most conventional laminate theories, the accuracy of stress and strain predictions is improved. Moreover, the relations between structural variables that are defined for each layer are obtained through the use of inter-laminar continuity of stress and displacement. The relations are used to reduce the number of independent variables such that the number of structural variables is independent of the number of layer, which makes the model computationally attractive. The developed theory is implemented using finite-element technique. The accuracy and the range of application of the present theory are evinced using a cylindrical shell and a laminated plate with different thickness, for which exact elasticity solutions exist.