Analysis of geometrical Nonlinearities – with Applications to Timber Structures

Abstract

A large part of the study is concerned with geometrical nonlinearities in structural systems, primarily 3D frame type structures. Parametrizations of finite rotations are studied, and geometric terms associated with transition from pseudo-vector representation to Euler angles are presented. The theories of Cosserat rods and the element independent co-rotational formulation, with emphasis on beam elements, are also presented and discussed. Furthermore, simplifications to the Cosserat rod theory, used in a co-rotational frame, is tested, as well as the use of B-spline basis functions for interpolating displacements and rotations. A consistent linearization of the internal forces, for the use in linearized buckling, is presented for this formulation. A comprehensive finite element computer program has been developed and implemented, and numerical results obtained with this analysis tool are presented and discussed for some typical timber structures. Stability of glue laminated timber arches is the center of attention, but also modelling issues related to a timber footbridge as well as the effect of typical material properties, such as orthotropy and low shear modulus, are discussed.