A contribution to the finite element formulation for the analysis of composite sandwich shells

The ultimate goal of the present research is to come up with an accurate and efficient analysis approach for composite and sandwich shells, which is simple enough to be capable of implementing into a FE code without significantly affecting its computational efficiency, and at the same time gives good accuracy in predicting the behavior of layered shells. It has to be capable of accurately modeling both overall behavior, and the local distribution of strains and stresses in all layers and all constituents in the composite laminae.; Two different approaches are utilized in the attempt to fulfill the final research objective of the present work. First, a homogenization procedure for the FE analysis of sandwich shells is developed. The procedure works on the material constitutive level. A homogenization of the sandwich shell is performed at each call of the corresponding constitutive subroutine. Thus the sandwich nature of the problem is hidden from the main FE program. As a consequence there is no need to develop a new shell element formulation, but instead the available homogeneous shell elements in the utilized FE code can be used for the analysis of sandwich shells. However, the defined homogenization procedure works with first order shear deformable shell elements, which sets a limit to the accuracy with which the transverse distribution of the unknowns is represented. To overcome this, a higher order shear deformable shell element is formulated and implemented into a general nonlinear explicit FE code. Using the differential equilibrium equations and the interlayer requirements, special treatment is developed for the transverse shear, resulting in a continuous, piecewise quartic distribution of the transverse shear stresses through the shell thickness. A similar approach is applied to the transverse normal stresses, which are represented by a continuous piecewise cubic function. The FE implementation is cast into a 4-noded quadrilateral shell element with 9 degrees of freedom per node. Only C0 continuity of the displacement functions is required in the shell plane, which makes the present formulation applicable to the most popular 4-noded bilinear isoparametric shell elements. Expressions are developed for the critical time step oft he explicit time integration for orthotropic homogeneous and layered shells based on the developed third order formulation.; Finally, to be able to analyze shells with woven composite layers, two micromechanical models for analysis of woven fabric composites are developed. Both models utilize the representative volume cell approach and divide a representative unit of the woven lamina into sub-cells of homogeneous material. Starting with the average strains in the representative volume cell and based on continuity requirements at the sub-cell interfaces, the strains and stresses in the composite constituents are determined as well as the average stresses in the lamina. Equivalent homogenized material properties are also determined. Their very good accuracy together with the simplicity of formulation makes these models attractive for the nonlinear FE analysis of composite laminates and can be efficiently utilized in explicit and implicit FE codes.; The formulations developed within the research provide an efficient analysis approach to layered shells including sandwich shells with composite facings. Furthermore, the developed micromechanical models can be used to determine the stress and strain fields in the composite layer constituents. This would enable important strength and durability phenomena as failure, damage, and property degradation of the constituents to be included into the FE analysis of layered shells.