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Related Experiment Video

Updated: Jul 15, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

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Published on: April 16, 2017

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.

Keywords:

elasticity geometric algebra shells

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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.