Non-conventional approaches to statical and dynamical analysis of geometrically nonlinear structure

Abstract

The purpose of the work presented in this thesis is to implement two innovative approaches in order to analyze elastic instability problems both in statical and in dynamical eld. The proposed formulations have their main feature in the possibility of describing large rotations without the use of rotation matrices in order to overcome complex manipulations required to obtain conservative descriptions and well-posed transformation matrices. The basis is a total Lagrangian description, where the rigid body motions (translations and rotations) are separated from the total deformation that consequently can be treated using the small-deformation linearized theory. The principal di erence between the suggested two models concerns the chosen parameterization of nite rotations, with distances applied to twoand three-dimensional nite elements in the rst and slopes applied to two node nite element beams in the second one. The theoretical features of the the approaches are presented and their main items are discussed referring to some implementations to planar and spatial beam and thin plate models. An incursion into dynamics has also been performed. The present approach is featured by the fact that the formulation is simple, the expressions in the equations of the nonlinear system are explicit and computationally e cient, and the analysis is robust and economical. A large amount of numerical analysis is performed and the good agreement with the results reported in the literature shows the accuracy and capability of the proposed approaches for numerical implementations.