FINITE ELEMENT ANALYSIS AND DESIGN OF LAMINATED COMPOSITE SHELL USING HIGHER ORDER SHEAR DEFORMATION THEORY

Abstract

Laminated composites shells have been widely used in civil, mechanical, aerospace, marine and other branches of engineering due to their high strength/stiffness to weight ratio and good tailoring capability compared to the conventional materials. However, laminated composite materials are weak in shear due to its low shear modulus compared to extensional rigidity. This dissertation work presents analysis (static and free vibration) of skew composite shells by developing a Co finite element (FE) model based on higher order shear deformation theory (HSDT). Many commercial software packages (e.g., Ansys, Abaqus etc.) are developed based on FE method for the analysis of laminated composite structures. However, almost all of these software packages have the capability of modeling the transverse shear deformation using 2D elements up to a certain extent based on FSDT. On the other hand, the laminated structures can also be modeled by using three-dimensional solid elements. But a huge number of elements will be required to model the multi-layered laminates since each layer will require at least one element in the thickness direction and the element size in the other directions cannot be made large in order to maintain its aspect ratio. Thus it will require a huge computational effort which may not be encouraged in practical applications. Therefore, a computer code is developed for the mathematical formulation based on HSDT for present problem. FORTRAN 90 language has been used to develop a computer code for the mathematical formulation for the analysis of laminated composite shells. In the present theory the transverse shear stresses are taken as zero at the shell top and bottom. A realistic parabolic variation of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Sander's approximations are considered to include the effect of three curvature terms in the strain components of composite shells. The Co finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Many problems of laminated composite shells are solved using the present finite element model based on HSDT for normal as well as skew configurations considering different geometry, boundary conditions, ply orientation, loadings and skew angles. The results obtained are iii Abstract presented in the form of tables and figures. For the purpose of validation of the proposed model, a large number of these results are compared with the published results. It has been found in the literature that so far there is no result available on the present problem of laminated composite skew shell based on HSDT. The results are mostly found for laminated composite shells with normal geometry with simply supported boundary conditions. Actually, very few results are available for orthotropic skew shells based on FSDT. The design of laminated composite spherical and cylindrical shells is also been carried out with the help of present FE model. A typical design problem of spherical shell structure including shell superstructure and RCC substructure is solved considering shell materials as RCC and FRP separately. The comparative cost analysis between RCC shell structure and FRP shell structure is also performed. iv