Evolution model of linear micropolar plate
First, the authors derive a three-dimensional evolution equation for linearized micropolar thin plate-like bodies, using the thickness of the plate as small parameter. Under suitable assumptions on the asymptotic behavior of the loads and initial conditions, the authors show that a family of approximate solutions converges to a function independent of the cross-sectional variable, that is the unique solution of the three-dimensional problem. Then, to justify mathematically a two-dimensional evolution model of linear micropolar plates, the authors apply the asymptotic analysis, as in classical elasticity. The weak formulation of the limit problem is given in terms of the limit microrotation and limit displacement. Using a correction result for the displacement, the authors interpret the displacement as the translation of the middle plane, and examine the radial stretch and the infinitesimal rotation of the cross-section.
scientific article; zbMATH DE number 5646392