General applied theory of micropolar thin elastic shells.

Local Symmetry Group in the General Theory of Elastic 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...

Theory of thin shells in general relativity: Equivalence of direct and Wheeler-DeWitt quantizations

We justify the way of the direct quantization which means immediate quantization of a conservation law. It is shown that this approach is equivalent to introducing the super Hamiltonian on a minisuperspace in spirit of the Wheeler-DeWitt’s approach. Then we will have: (i) all values are observable and have an obvious physical meaning and well-defined application domain; (ii) wave function is we...

Theory of thin shells in general relativity: Direct versus Dirac quantization

In this report we discuss the merits and demerits of the formal Hamiltonian approach for spherically symmetric thin shells and methods of quantization connected with it. The merits are: (1) we are using the approved way of quantization, which algorithm was filed earlier; (2) we do not know other ways. The demerits are: (1) we attempt to introduce a time into the of essence stationary theory, th...

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...