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Mathematical Theory of Shells on Elastic Foundations: An Analysis of Boundary Forms, Constraints, and Applications to Friction and Skin Abrasion

Jayawardana, Kavinda; (2016) Mathematical Theory of Shells on Elastic Foundations: An Analysis of Boundary Forms, Constraints, and Applications to Friction and Skin Abrasion. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

In this thesis we examine the behaviour of shells supported by elastic foundations. We begin by critically analysing the existing literature on the study of thin objects such as films, plates, membranes and shells, and we highlight their limitations, validity and present correct formulations when possible. We also do the same for various frictional laws, in particular, Coulomb's law of static friction. Then, we extend the capstan equation to noncircular geometries by modelling membranes supported by rigid foundations in presence of friction. We provide closed-form solutions and compare them to other similar existing models in the literature. Then, we begin the study of shells supported by elastic foundations. We treat the bonded case as a boundary form and prove the existence and the uniqueness of solutions, and thus, prove it is a mathematical theory and not merely a mathematical model. To conclude this case we conduct numerical experiments and compare the results against existing models in the literature. Finally, we introduce a constraint and assert that this condition is analogous to classical frictional laws. This constraint is then used to model shells supported by elastic foundations with friction. As with the previous case, we again prove the existence and the uniqueness of solutions, and conclude by conducting numerical experiments and comparing the results against existing models in the literature. Applications for our work can be found in cable drive electronic systems, curvilinear stretchable electronics and modelling skin abrasion.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Mathematical Theory of Shells on Elastic Foundations: An Analysis of Boundary Forms, Constraints, and Applications to Friction and Skin Abrasion
Event: University College London
Open access status: An open access version is available from UCL Discovery
Language: English
Keywords: Capstan Equation, Elastic Foundations, Elliptic Equations, Free Boundary Problems, Friction, Mathematical Elasticity, Membrane Theory, Nonlinear Partial Differential Equations, Shell Theory, Skin Abrasion
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1532145
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