PDF Index| SDT-visc
Contents
Functions
PDF Index |
Two main strategies have been considered to model sandwich structures: building higher order shell models [] or connecting multiple elements. The main problem with the higher order element approach is that developing good shell elements is very difficult so that most developments for sandwiches will not perform as well as state of the art shell elements. The multiple element strategy is also the only available for immediate implementation into industrial FEM software.
To properly account for shear effects in the viscoelastic layer, the offsets between the neutral fiber and the shell surface are most of the time essential. Rather than defining offsets for shell elements [], rigid links between the shell nodes and the volume element are used here as shown in figure ??. Although this generates additional nodes (4 node layers for a single constrained layer model), this strategy accommodates all possible layer configurations. During resolution, the model is smaller since all viscoelastic volume nodes are constrained.
Automated layer mesh generation from a selected area of a nominal shell model is a basic need (supported by the fevisco MakeSandwich commands). Figure ?? illustrates the fact that for curved shells, the use of flat elements generates a distinction between layer thicknesses along the element normal hie or along the normal at nodes hin. This distinction is important for relatively coarse meshes of press formed parts (as the floor panel of figure ??). Advanced options meshing options, let you preserve thickness either at element center or nodes and possibly control the normal map used as a meshing support.
For stiff layers, shells are preferred over volumes, because volume element formulations are sensitive to shear locking when considering high aspect ratio (dimensions of the element large compared to thickness).
For soft layers, the use of a volume element both necessary, because shell elements will typically not correctly represent high shear through the thickness, and acceptable, because almost all their energy is associated with shear so that they will not lock in bending []. Note that shear corrections used in some FEM codes to allow bending representation with volumes may have to be turned off to obtain appropriate results. Finally there are doubts on how to properly model the through the layer compression stiffness of a very thin viscoelastic layer (this can have significant effects on curved layers).
The demo basic_sandwich generates curves for the validation of shell/volume/shell model used to represent constrained layer treatments as first discussed in []. The idea is to vary the properties of a central volume layer between a very soft modulus and the skin modulus.
For a very soft value, figure ?? shows convergence to the asymptotic value of a single skin plate. For a modulus of the viscoelastic core equal to that of the skins, one should converge to the frequency of a plate model with thickness equal to the sum of skins + viscoelastic core. Figure ?? shows that the high modulus asymptote is slightly higher for the shell / volume / shell model. This is due to shear locking in the very thin volume layer (well known and documented problem that low order volumes cannot represent bending properly). This difficulty can be limited by using volume element with shear locking protection. The figure also shows that damping is optimal somewhere between the low and high modulus values.
Figure ?? illustrates the validity of a shell/volume model as compared to a single shell based on composite shell theory. Figure ?? illustrates that the results are nearly identical, provided that volume elements with proper shear locking protection are used. For a standard isoparametric volume, a shell/volume model tends to be be to stiff (shear locking associated with bending).
The element degree does not seem critical to obtain accurate predictions of the response. The use of multiple elements through the viscoelastic layers has also been considered by some authors but the motivation for doing so is not understood.
For press formed sandwiches, there are further unknowns in how the forming process affects the core thickness and material properties. In particular, most materials used for their high damping properties are also very sensitive to static pre-stress. For a simple folded plate, figure ?? illustrates how the modal frequencies and energy distribution in the viscoelastic layer are modified if the shear modulus is multiplied by 10 in the fold. Such behavior was found in tests and motivated the study in Ref. [], where the effect of static pre-stress is measured experimentally. Overall, predicting the effects press forming or folding sandwiches is still a very open issue.
A final difficulty is to deal properly with boundary conditions of the skin layers. Since differential motion of the skins plays a major role in the effectiveness of the core, the boundary conditions of each layer has to be considered separately. This is easily illustrated by the generation of cuts in constraining layers [] (and cut_optim demo).
As illustrated in figure ?? the dissipation if often localized on a fairly small sub-part of the structure. It is thus quite important to validate the accuracy of predictions obtained with various mesh refinements. Figure ?? illustrates a convergence study where a constrained layer damping treatment is refined and one compares the strain energy density maps for two levels of refinement. The strain energy maps, clearly indicate edge effects, which are typical of constrained layer treatments. In such studies the author's have usually found, that the distribution of constraints is well predicted and energy fractions (strain energy in the viscoelastic compared to total strain energy in the model) predicted with the fine and coarse meshes do not show significant differences.
When considering free placement of damping devices (see section ??), one is rapidly faced with the problem of incompatible meshes. For discrete connections, where loads are transmitted at isolated points with at most one point on a given element of the supporting structure, the problem is very much related to that of the representation of weld spots and strategies that use the underlying shape functions are most effective (see SDT feutilb MpcFromMatch command).
