Multilayered shell finite element with interlaminar continuous shear stresses: a refinement of the Reissner–Mindlin formulation
✍ Scribed by Boštjan Brank; Erasmo Carrera
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 307 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0029-5981
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✦ Synopsis
A ÿnite element formulation for reÿned linear analysis of multilayered shell structures of moderate thickness is presented. An underlying shell model is a direct extension of the ÿrst-order shear-deformation theory of Reissner-Mindlin type. A reÿned theory with seven unknown kinematic ÿelds is developed: (i) by introducing an assumption of a zig-zag (i.e. layer-wise linear) variation of displacement ÿeld through the thickness, and (ii) by assuming an independent transverse shear stress ÿelds in each layer in the framework of Reissner's mixed variational principle. The introduced transverse shear stress unknowns are eliminated on the cross-section level. At this process, the interlaminar equilibrium conditions (i.e. the interlaminar shear stress continuity conditions) are imposed. As a result, the weak form of constitutive equations (the so-called weak form of Hooke's law) is obtained for the transverse strains-transverse stress resultants relation. A ÿnite element approximation is based on the four-noded isoparametric element. To eliminate the shear locking e ect, the assumed strain variational concept is used. Performance of the derived ÿnite element is illustrated with some numerical examples. The results are compared with the exact three-dimensional solutions, as well as with the analytical and numerical solutions obtained by the classical, the ÿrst-order and some representative reÿned models.