New approaches for linear and nonlinear analyses of thin-walled members in the framework of Generalized Beam Theory

Abstract

The Generalized Beam Theory (GBT) is a reliable tool for the linear and nonlinear analysis of thin-walled members (TWMs). Based on expressing the displacement field as a linear combination of assumed deformation fields (i.e., trial functions) and unknown amplitude functions (i.e., linear coordinates), it relies on two steps: (a) selection of the deformation fields (i.e., cross-section analysis); and (b) solution of an equivalent 1D problem (i.e., member analysis). This thesis proposes new approaches for the GBT-based analysis of TWMs, in particular: (a) a novel approach for the cross-section analysis, (b) a GBT formulation for the partial interaction analysis of multi-component TWMs, (c) a displacement - based GBT for composite perforated TWMs, and (d) a nonlinear GBT for the analysis of arbitrary TWMs. The novel cross-section analysis is based on the so-called dynamic approach (GBT-D) and relies on the solution of a very limited number of constrained eigenvalue problems. It is much simpler to use than the classic static approach, in addition to provide even better results from the point of view of accuracy and symmetry of obtained displacement fields. The proposed cross-section analysis is suited for developing a GBT-based formulation for the study of the linear-elastic behavior of multi-component TWMs. The novelty of the approach consists on its ability to accurately model the partial interaction between the different components forming the cross-section in both longitudinal and transverse directions. The displacement-based GBT for the analysis of composite TWMs is based on a variable transform which allows to express the unknown linear coordinates in terms of cross-section nodal degrees-of-freedom (DOFs). The proposed approach leads to a beam-like finite element equivalent to an assembly of flat quadrilateral shell elements. Finally, the nonlinear GBT is developed according to the nonlinear Galerkin method, which calls for the evaluation of nonlinear (passive) trial functions, to be used in conjunction with linear (active) ones, in describing the displacement field. Within this framework, equilibrium paths can be determined by using few linear (and corresponding passive) trial functions, supplying good results when compared with burdensome finite-element solutions.