Researcher ORCID Identifier

0009-0001-4201-967X

Graduation Year

2025

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Chiu-Yen Kao

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

Mark Z. Wang

Abstract

In this thesis we explore the geometric optimization among various cross-sectional shapes in order to maximize the shear stress of a cylindrical bar under torsion. We provide derivations of existing analytic methods by using various techniques including conformal mapping. Analytically, we found the optimal ellipse which maximizes shear stress when the domain is subjected to an area or arc length constraint. In addition, numerically, we use method of particular solutions and finite element methods to find the shear stress and then optimize it among different shapes. In particular, we consider the moduli space of triangles and shapes that can are presented by a particular complex formula. Our methods successfully find the optimal triangle and the optimal shapes among these complex-represented shapes.

Download

This thesis is restricted to the Claremont Colleges current faculty, students, and staff.

Share

COinS