Publication Date
Fall 2010
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Advisor
Samih Obaid
Keywords
Conformal Mapping, Flexure, potential theory, Saint-Venant, Torsion
Subject Areas
Mathematics
Abstract
In this thesis, we solved the Saint-Venant's torsion problem for beams with different cross sections bounded by simple closed curves using various methods. In addition, we solved the flexure problem of beams with certain curvilinear cross sections. The first method was derived by Bassali and Obaid. We focused on cross sections bounded by hyperbolas, circular groves, lemniscate of Booth, and sectorial cross sections. The second method used Tchebycheff polynomials to solve the torsion problem corresponding to the circle and ellipse. The third method used conformal mapping to derive the solution of different cross sections bounded by curvilinear edges. The flexure problem has been reduced to six boundary value problems; three are Dirichlet and three are Neumann problems. We derived the flexure functions corresponding to a certain boundary.
Recommended Citation
Nguyen, Annie, "Applications of Boundary Value Problems" (2010). Master's Theses. 3881.
DOI: https://doi.org/10.31979/etd.hry9-khhs
https://scholarworks.sjsu.edu/etd_theses/3881
