Theory of Elastic Thin Shells

A simplified model for elastic thin shells

We introduce a simplified model for the minimization of the elastic energy in thin shells. This model is not obtained by an asymptotic analysis. The thickness of the shell remains a parameter as in Reisner-Mindlin’s model for plates and Koiter’s model for shells in the linear case. The simplified model admits always minimizers by contrast with the original one. We show the relevance of our appr...

Local Symmetry Group in the General Theory of Elastic Shells

The elastic theory of shells using geometric algebra

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by p...

The Nonlinear Theory of Elastic Shells with Phase Transitions

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Free Vibration Analysis of Microtubules as Orthotropic Elastic Shells Using Stress and Strain Gradient Elasticity Theory

In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in con...