Thin-shell finite element

Thin Shell Finite Element by the Mixed Method Formulation—2,3 Chan, A. S. L. 

In designing axi-symmetric shell structures such as large-type cooling towers, it is necessary to predict the vibration responses to various external forces. The authors describe the linear vibration response analysis of axi-symmetric shell structures by the finite element method. They also analyze geometric nonlinear (large deflection) vibration which poses a problem in thin shell structures causes dynamic buckling in cooling towers. They present examples of numerical calculation and study the validity of this method. 11 refs, cited. 

Of particular importance is the assumption of thin-walled geometry. From Eq. (7.3) we see that the pressure is independent of the z coordinate. Consequently, the finite element utilized for pressure calculation need have no thickness. That is, the element is a plane shell—generally a triangle or quadrilateral. This has great implications for users of plastics CAE. It means that a finite element model of the component is required that has no thickness. In the past this was not a problem. Almost all common CAD systems were using surface or wireframe modeling and thickness was never shown explicitly. The path from the CAD model to the FEA model was clear and direct. 

Ahmed S, Irons BM, Zienkiewicz OC (1970) Analysis of thick and thin shell structures by curved finite elements. Int J Numer Meth Eng 2 419-451 Akczurowski E, Mason SG (1968) Particle motions in sheared suspensions XXIV rotation of spheroids and cylinders. Trans Soc Rheol 12 209-215 Albert C, Femlund G (2002) Spring-in and warpage of angled composite laminates. Compos Sci Technol 62 1895-1912... 

The simulation of component parts exhibiting electromechanical coupling with the aid of commercial finite element packages is subject to some restrictions. Usually the piezoelectric effect is considered only in connection with volume elements, see Freed and Bahuska [76]. For complex structures, the modeling with volume elements often does not represent a viable procedure with respect to implementation and calculation expenditure. A prominent example for this are structures with thin walls made of multiple layers. Their mechanical behavior may be simulated efficiently with layered structural shell elements. 

As outlined in Section 4.2.5, the implementation of anisotropic thermal effects in commercial finite element codes may be utilized to simulate the implications of the piezoelectric effect. To capture the behavior of thin-walled beams with cross-sections as defined above, spatial shell elements may be employed. With this methodology, however, it is not possible to examine problems with dynamic actuation. The beams with rectangular and convex cross-sections have been discretized with 2200, respectively 2300, SHELL99 elements of ANSYS as exemplarily shown for the latter case in Figure 10.11. 

Karamanou et al. [65] have performed finite element analyses to large strains to simulate the thermoforming process, in which thin sheets of polymer are inflated using gas pressure. They adopted a model comprising hyperelastic components and a linear viscous element. Applying a thin shell analysis enabled them to produce realistic predictions of the inflating membrane. 

---