This paper presents an extension of mathematical static model to dynamic problems of micropolar elastic plates, recently developed by the authors. The dynamic model is based on the generalization of Hellinger-Prange-R...This paper presents an extension of mathematical static model to dynamic problems of micropolar elastic plates, recently developed by the authors. The dynamic model is based on the generalization of Hellinger-Prange-Reissner (HPR) variational principle for the linearized micropolar (Cosserat) elastodynamics. The vibration model incorporates high accuracy assumptions of the micropolar plate deformation. The computations predict additional natural frequencies, related with the material microstructure. These results are consistent with the size-effect principle known from the micropolar plate deformation. The classic Mindlin-Reissner plate resonance frequencies appear as a limiting case for homogeneous materials with no microstructure.展开更多
This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed by the authors. The dislocation is modeled by a sequence of domains that co...This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed by the authors. The dislocation is modeled by a sequence of domains that converge to the point of the dislocation and by a residual force distributed around that point. The plate deformation caused by the dislocation is calculated using the Finite Element Method. We also discuss the effect of the dislocation on the cavities present in the Cosserat plates.展开更多
文摘This paper presents an extension of mathematical static model to dynamic problems of micropolar elastic plates, recently developed by the authors. The dynamic model is based on the generalization of Hellinger-Prange-Reissner (HPR) variational principle for the linearized micropolar (Cosserat) elastodynamics. The vibration model incorporates high accuracy assumptions of the micropolar plate deformation. The computations predict additional natural frequencies, related with the material microstructure. These results are consistent with the size-effect principle known from the micropolar plate deformation. The classic Mindlin-Reissner plate resonance frequencies appear as a limiting case for homogeneous materials with no microstructure.
文摘This article provides the numerical modeling of the dislocations in the Cosserat elastic plates based on the Cosserat Plates Theory developed by the authors. The dislocation is modeled by a sequence of domains that converge to the point of the dislocation and by a residual force distributed around that point. The plate deformation caused by the dislocation is calculated using the Finite Element Method. We also discuss the effect of the dislocation on the cavities present in the Cosserat plates.
