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Abstract
In several industries such as civil, mechanical, and aerospace, thinwalled structures are often used due to the high strength and effective use of the materials. Because of the increased consumption there has been increasing focus on optimizing and more detailed calculations. However, finely detailed calculations will be very time consuming, if not impossible, due to the large amount of degrees of freedom needed. The present thesis deals with a novel modebased approach concerning more detailed calculation in the context of distortion of the cross section which model distortion by a limited number of degrees of freedom. This means that the classical Vlasov thinwalled beam theory for open and closed cross sections is generalized as part of a semidiscretization process by including distortional displacement fields. A novel finiteelementbased displacement approach is used in combination with a weak formulation of the shear constraints and constrained wall widths. The weak formulation of the shear constraints enables analysis of both open and closed cell crosssections by allowing constant shear flow. Variational analysis is used to establish and identify the uncoupled set of homogeneous and nonhomogeneous differential equations and the related solutions.
The developed semidiscretization approach to Generalized Beam Theory (GBT) is furthermore extended to include the geometrical stiffness terms for column buckling analysis based on an initial stress approach. Through variations in the potential energy a modified set of coupled homogeneous differential equations of GBT including initial stress is establish and solved. In this context instability solutions are found for simply supported columns and by solving the reduced order differential equations the crosssection displacement mode shapes and buckling load factor are given.
In order to handle arbitrary boundary conditions as well as the possibility to add concentrated loads as nodal loads the formulation of a generalized onedimensional semidiscretized thinwalled beam element including distortional contributions is developed. From the full assembled homogenous solution as well as the full assembled nonhomogeneous solution the generalized displacements of the exact full solution along the beam are found.
This new approach is a considerable theoretical development since the obtained GBT equations including distributed loading found by discretization of the cross section are now solved analytically and the formulation is valid without special attention and approximation also for closed single or multicell cross sections. Furthermore, the found eigenvalues have clear mechanical meaning, since they represent the attenuation of the distortional eigenmodes and may be used in the automatic meshing of approximate distortional beam elements. The magnitude of the eigenvalues thus also gives the natural ordering of the modes.
The results are compared to results found using other computational methods taking distortion of the cross section into account. Thus, the results are compared to results found using the commercial FE program Abaqus as well as the free available software GBTUL and CUFSM concerning conventional GBT and the finite strip method, respectively. Reasonable matches are obtained in all cases which confirm that this new approach to GBT provides reasonable results with a very small computational cost making it a good alternative to the classical FE calculations and other available methods.
The developed semidiscretization approach to Generalized Beam Theory (GBT) is furthermore extended to include the geometrical stiffness terms for column buckling analysis based on an initial stress approach. Through variations in the potential energy a modified set of coupled homogeneous differential equations of GBT including initial stress is establish and solved. In this context instability solutions are found for simply supported columns and by solving the reduced order differential equations the crosssection displacement mode shapes and buckling load factor are given.
In order to handle arbitrary boundary conditions as well as the possibility to add concentrated loads as nodal loads the formulation of a generalized onedimensional semidiscretized thinwalled beam element including distortional contributions is developed. From the full assembled homogenous solution as well as the full assembled nonhomogeneous solution the generalized displacements of the exact full solution along the beam are found.
This new approach is a considerable theoretical development since the obtained GBT equations including distributed loading found by discretization of the cross section are now solved analytically and the formulation is valid without special attention and approximation also for closed single or multicell cross sections. Furthermore, the found eigenvalues have clear mechanical meaning, since they represent the attenuation of the distortional eigenmodes and may be used in the automatic meshing of approximate distortional beam elements. The magnitude of the eigenvalues thus also gives the natural ordering of the modes.
The results are compared to results found using other computational methods taking distortion of the cross section into account. Thus, the results are compared to results found using the commercial FE program Abaqus as well as the free available software GBTUL and CUFSM concerning conventional GBT and the finite strip method, respectively. Reasonable matches are obtained in all cases which confirm that this new approach to GBT provides reasonable results with a very small computational cost making it a good alternative to the classical FE calculations and other available methods.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  266 
ISBN (Print)  9788778773555 
Publication status  Published  2012 
Series  Byg Rapport 

ISSN  16012917 
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Dive into the research topics of 'Distortional Mechanics of ThinWalled Structural Elements'. Together they form a unique fingerprint.Projects
 1 Finished

Generaliseret bjælketeori med tværsnitsdeformation
Andreassen, M. J., Jönsson, J., Stang, H., Schneider, J., Silvestre, N. & Nielsen, L. O.
Technical University of Denmark
01/12/2008 → 28/09/2012
Project: PhD