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Structural Engineering and Mechanics Volume 7, Number 2, February 1999 , pages 159-180 DOI: https://doi.org/10.12989/sem.1999.7.2.159 |
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Fundamental theory of curved structures from a non-tensorial point of view |
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Paavola J, Salonen EM
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| Abstract | ||
| The present paper shows a new non-tensorial approach to derive basic equations for various structural analyses. It can be used directly in numerical computation procedures. The aim of the paper is, however, to show that the approach serves as an excellent tool for analytical purposes also, working as a link between analytical and numerical techniques. The paper gives a method to derive, at first, expressions for strains in general beam and shell analyses, and secondly, the governing equilibrium equations. The approach is based on the utilization of local fixed Cartesian coordinate systems. Applying these, all the definitions required are the simple basic ones, well-known from the analyses in common global coordinates. In addition, the familiar principle of virtual work has been adopted. The method will be, apparently, most powerful in teaching the theories of curved beam and shell structures for students not familiar with tensor analysis. The final results obtained have no novelty value in themselves, but the procedure developed opens through its systematic and graphic progress a new standpoint to theoretical considerations. | ||
| Key Words | ||
| fundamental structural mechanics, curved structures, local coordinate systems, equilibrium equations, principle of virtual work | ||
| Address | ||
| Paavola J, Helsinki Univ Technol, Lab Struct Mech, POB 2100, FIN-02015 HUT, Finland Helsinki Univ Technol, Lab Struct Mech, FIN-02015 HUT, Finland | ||