Finite element analysis of laminated anisotropic shells with lainated anisotropic stiffness

Abstract

Thesis: Finite Element Analysis of Laminated Anisotropic Shells with Stiffeners Introduction Laminated anisotropic stiffened shells are widely used in many engineering fields. This is due to the fact that fibre-reinforced composites, which offer a high strength-to-weight ratio, have come into vogue. Designers can now tailor-make structures by a suitable choice of layering schemes and materials, knowing the loads acting on the structure.

To arrive at a proper design, it is necessary to have an accurate method of structural analysis. Continuum methods for such shells are often very complex due to bending–stretching coupling inherent in laminated anisotropic construction. On the other hand, the finite element method (FEM) can be effectively employed to tackle such problems.

This thesis contributes to the finite element analysis of laminated anisotropic shells with laminated anisotropic stiffeners.

Shell Element Formulation A doubly curved quadrilateral thin shell finite element for the analysis of laminated anisotropic shells of revolution is presented.

This element has 48 degrees of freedom and four nodes, bounded by two meridians and two parallel circles.

The shell thickness is constant and assumed to be made up of an arbitrary number of bonded layers, each with different thicknesses, linear elastic orthotropic material properties, and orientations of principal axes.

Displacement states over the midsurface are chosen using one-dimensional first-order Hermite interpolation polynomials.

This choice ensures proper rigid mode representation and compatibility with stiffener finite elements.

Stiffener Element Formulation Finite element formulations for laminated anisotropic stiffeners under line member assumptions are presented.

Each stiffener element has two nodes with eight degrees of freedom per node.

Stiffener stiffness matrices are developed as degenerate cases of the parent shell elements.

The following stiffener elements were developed:

Laminated anisotropic curved stiffener finite element compatible with a rectangular shallow shell element.

Laminated anisotropic parallel circle stiffener finite element compatible with the doubly curved quadrilateral shell of revolution element.

Laminated anisotropic meridional stiffener finite element compatible with the doubly curved quadrilateral shell of revolution element.

Adaptations for curved laminated anisotropic closed-section stiffener finite elements are also presented.

Computational Studies Computer software was developed to systematically evaluate the performance of the finite elements.

Eigenvalue analyses and benchmark problems with known solutions were conducted.

Solutions for typical problems of laminated anisotropic unstiffened and stiffened shells of positive, zero, and negative Gaussian curvatures are presented.

For shells reinforced by eccentric stiffeners, suitable transformations ensuring compatibility along the shell–stiffener junction are described.

Applications An interesting feature of the laminated anisotropic curved stiffener finite elements presented in this thesis is their effective application in analysing the elastic response of fusion magnets.