Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Deformations Compatibility Equations in the General Shell Theory into the Relative Coordinate System with Projected Deformations

Version 1 : Received: 28 November 2020 / Approved: 30 November 2020 / Online: 30 November 2020 (11:33:52 CET)

How to cite: Álvarez-Pérez, J.; Mesa-Lavista, M. Deformations Compatibility Equations in the General Shell Theory into the Relative Coordinate System with Projected Deformations. Preprints 2020, 2020110719 (doi: 10.20944/preprints202011.0719.v1). Álvarez-Pérez, J.; Mesa-Lavista, M. Deformations Compatibility Equations in the General Shell Theory into the Relative Coordinate System with Projected Deformations. Preprints 2020, 2020110719 (doi: 10.20944/preprints202011.0719.v1).

Abstract

This paper presents a new analytical method for obtaining new deformations compatibility equations or, new Saint-Venant’s identities, into the relative coordinate system with projected deformations by applying the hypothesis of the lineal shell theory in general flexion state. The method proposed generalizes the compatibility conditions established by A.L. Goldenveizer for the shell theory. On the other hand, the new equations include the deformations compatibility equations by other authors: Flügge, Saint-Venant, Love-Kirchhoff, Timoshenko, Goldenveizer, and Reissner-Mindlin. The results showed an increase of knowledge in general shell theory, and provide inverse and semi-inverse solutions, whose systems solution correspond to the hyper-statics degrees of the physical model, and not to their degrees of freedom.

Subject Areas

Saint-Venant’s identities; compatibility equations; relative coordinate system; general shell theory.

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