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# Thin Shell Finite Element Formulations for Geometrically Non-Linear Analysis of Straight and Curved Pipes

• Author / Creator
Attia, Saher, S.
• Special finite element formulations were developed to accurately predict the structural response of straight and curved pipes. Although the ELBOW elements implemented in the ABAQUS library have been verified under in-plane and out-of-plane loading, the effect of internal pressure loading had not been well addressed. Therefore, a detailed assessment for the structural response of the ELBOW elements under internal pressure is introduced showing their limitations. One of these limitations is the inability of the ELBOW elements to model initial geometric imperfections associated with the manufacturing processes of pipes. The influence of these imperfections is tangible and cannot be ignored, particularly the initial ovality of the pipe. Thus, new finite element formulations are developed to model thin-walled straight and curved pipes with generic cross-sections to involve initial geometric imperfections. In order to develop these new formulations, the writer adopts the cumulative learning approach through developing three families of formulations: (1) a family for initially circular straight pipes, (2) a family for initially circular curved pipes, and (3) a family for straight and curved pipes with general cross-sections. Starting with the principle of virtual work, generalized expressions for the force vectors and the stiffness matrix are obtained in terms of a generic displacement field vector. These expressions are specialized for initially circular straight pipes in ‎Chapter 3 by employing a cylindrical coordinate system. The accuracy of the formulations developed in ‎Chapter 3 encouraged the writer to employ a toroidal coordinate system in conjunction with these generalized expressions to model initially circular curved pipes as introduced in ‎Chapter 4. An innovative idea is presented to capture initial geometric imperfections by introducing three configurations (e.g., un-deformed, deformed, reference) of the pipe under consideration. Strains and stresses induced due to the motion are formulated in the reference configuration. Although the numerical examples are focused on ovalized pipes, the mathematical approach proposed in ‎Chapter 5 is applicable to model straight and curved pipes with generic cross-sections. Comparisons with general shell models demonstrate the accuracy and versatility of the proposed formulations to predict the structural response of initially circular and ovalized straight and curved thin-walled pipes under various loading conditions. In addition, the effect of the follower pressure load (e.g., internal or external pressure) is properly included.

• Subjects / Keywords
• Graduation date
Fall 2021
• Type of Item
Thesis
• Degree
Doctor of Philosophy
• DOI
https://doi.org/10.7939/r3-5jn5-3907
• License
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
• Language
English
• Institution
University of Alberta
• Degree level
Doctoral
• Department
• Specialization
• Structural Engineering
• Supervisor / co-supervisor and their department(s)