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The elastic theory of shells using geometric algebra
A L Gregory1, J Lasenby1, A Agarwal1
1Cambridge University Engineering Department , Trumpington Street, Cambridge CB2 1PZ, UK.
Royal Society Open Science
|April 14, 2017
Summary
This study introduces a new method for deriving the elastic theory of shells using geometric algebra. This approach simplifies physical interpretation and clarifies previous confusions in shell theory.
Area of Science:
- Mechanical Engineering
- Applied Mathematics
- Theoretical Physics
Background:
- The elastic theory of shells is fundamental in structural analysis.
- Previous derivations have faced challenges in physical interpretation and coordinate system application.
- Ambiguities in angular velocity and coordinate conventions have caused confusion.
Purpose of the Study:
- To present a novel derivation of the elastic theory of shells.
- To enhance physical interpretation and applicability of shell theory equations.
- To clarify existing confusions in linearized shell theory and introduce prior strain.
Main Methods:
- Utilizing geometric algebra for a component-free formulation.
- Employing bivector representation to clarify the role of moments and angular velocity.
- Revisiting and clarifying coordinate conventions in the linearized theory.
Main Results:
- A simplified and physically intuitive derivation of shell theory.
- Clearer understanding of moments and angular velocity, resolving prior ambiguities.
- Facilitation of incorporating prior strain into the linearized elastic shell theory.
Conclusions:
- Geometric algebra offers a powerful framework for advancing shell theory.
- The novel derivation enhances clarity and practical utility of shell mechanics.
- This work resolves longstanding issues and opens new avenues for research in shell analysis.
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