– the equations for the three-dimensional continuum. In contrast, the direct approach is based on the straight-forward introduction of the two-dimensional equations. This approach in combination with the effective properties concept allows the global analysis of all branches of plate theories (homogeneous, sandwich, laminated, etc.). The different possibilities of the formulation of plate theories are discussed in [10–12] among others. Fig. 2 Nonhomogeneous structure of the foam In this contribution, we present a new theory based on the direct approach combined with the effective properties concept. We consider plates made of polymer foams with a highly nonhomogeneous structure through the thickness (see Fig. 2) and apply the theory of plates and shells formulated in [13–17]. From the direct approach point of view, a plate or a shell is modeled as a material surface each particle of which has five degrees of freedom (three displacements and two rotations, the rotation about the normal to the plate is not considered). Such a model can be accepted in the case of plates with constant or slow changing thickness. For the linear elastic variant the identification of the elastic stiffness tensors was proposed in [18–20]. Using the techniques presented in these articles the static boundary-value problems for FGM plates made of metal foams which behave elastically are solved in . Here we extend this analysis to the case of viscoelastic polymer foams
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