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Multilayered shell finite element with interlaminar continuous shear stresses: A refinement of the Reissner-Mindlin formulation. (English) Zbl 0991.74066

Summary: We present a finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness. An underlying shell model is a direct extension of the first-order shear-deformation theory of Reissner-Mindlin type. A refined theory with seven unknown kinematic fields is developed: (i) by introducing an assumption of a zig-zag (i.e. layer-wise linear) variation of displacement field through the thickness, and (ii) by assuming an independent transverse shear stress fields 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. On this process, the interlaminar equilibrium conditions (i.e. the interlaminar shear stress continuity conditions) are imposed. As a result, we obtain the weak form of constitutive equations (the so-called weak form of Hooke’s law) for the transverse strain-transverse stress resultant relation. A finite element approximation is based on a four-noded isoparametric element. To eliminate the shear locking effect, we use the assumed strain variational concept. Performance of the derived finite element is illustrated with some numerical examples. The results are compared with the exact three-dimensional solutions, as well as with analytical and numerical solutions obtained by classical, first-order and some representative refined models.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
74E30 Composite and mixture properties
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