The objective of the present investigation is to study the elastic non-linear behaviour of spatial structures, using the finite element method. The use of the finite element method for such analyses, results in the formulation of a large set of non-linear algebraic equations, the solution of which can be computationally very expensive. It is this concern with the computational cost of solving these equations that prompts the development in this thesis of a more efficient Newton-type iterative solution strategy based on extrapolation ideas.
In addition to the computational cost, problems exist in developing a sufficiently reliable and robust solution technique capable of traversing critical points, and continuing the computations into the post-buckled region. A comprehensive review of available solution techniques indicates the present superiority of the constrained arc length methods. The feasibility of this method for analysing the post-buckled equilibrium paths of spatial frames exhibiting a diverse range of instability behaviour is demonstrated.
A faceted shell element, free from the deficiencies of incompatible translational displacements, singularity with co-planar elements, inability to model intersections and low order membrane strain representation; associated with existing flat shell elements, is presented. This shell element utilises the linear strain triangle for membrane representation and a plate element developed in this study to approximate the bending action. Extension of this faceted element to large displacement, moderate rotation and large displacement, finite rotation analysis; using a total Lagrangian and corotational description of motion respectively, is elaborated on. Application of this element to both the linear and non-linear elastic analysis of several plate and shell structures, indicates that its convergence characteristics are good.