Isogeometric Analysis Of The Size-dependent Micro-nanostructure

A great deal of experimental results have showed that the traditional continuum mechanics theory is no longer applicable to the micro/nano materials and structures of the study.After decades of exploration of predecessors,by making assumptions and modifications of traditional mechanical theory constantly,they developed a new continuum mechanics theory of micro/nano scale.In this paper,the new modified couple stress theory and the nonlocal elasticity theory in the new continuum mechanics theory are applied to the study of micro beams and plates,respectively.In this paper,the method of the isogeometric analysis(IGA)are adopted,which can not only meet the requirement of high order continuity of elements easily,but also eliminate phenomenon of the shear locking for plates.In this paper,the matlab tools box of isogeometric analysis are used to model the beam and plate structure by modular programming.According to the control equations of beam or plate models under different theories,the stiffness matrix and the mass matrix of the structure are obtained by the programming calculation.For the study of the micro beam,the model of a composite laminated beam with rotation motion was established by applying the isogeometric analysis based on the new modified coupling stress theory.Then we calculated the vibration frequencies of the beam model,and discussed the influences of scale parameter,rotating angular velocity,slenderness ratio and ply angles.At the same time,the reliability of the isogeometric analysis method is verified by the two degeneration models,which are the classical rotating beam and the ordinary beam of the modified couple stress respectively.For micro plates' research,based on the nonlocal elasticity theory,the isogeometric analysis was applied on the establishment of the two models of the classical plate theory model and the first-order shear deformation plate theory model.Then we computed the vibration frequencies of different types of the graphene sheets,and the effects of the nonlocal parameter,size length of the plate,material properties and boundary conditions are discussed.In addition,the results of single layered and double layered graphene sheets calculated by the isogeometric analysis are compared with the results of traditional finite element method or theoretical solutions,and the effect of van der Walls(vdW)interaction on the double layered graphene sheets have discussed.