Derivation of a model of nonlinear micropolar plate
Starting from the equilibrium problem for three-dimensional nonlinear micropolar elastic plate-like bodies with nonlinear strains and linear constitutive law, the authors derive a two-dimensional model of nonlinear micropolar plate. To this end they use asymptotic expansions for deformation and microrotation on the middle plane of the plate. The plate model is formulated in terms of the deformation field, macrorotation vector and a function related to the rotation of the transversal segment of the plate around its axis. This model allows to describe the change of metrics, and contains fourth-order terms capturing the flexure of the plate, a term measuring the rotation of the transversal segment of the plate around its axis, and a term measuring shearability of the transversal segment of the plate.
scientific article; zbMATH DE number 5641476