Mechanical Modeling Of Anisotropic Functionally Graded Micro-beam And Plate

Based on the anisotropic modified Couple Stress Theory,a new model of orthotropic functionally graded micro-beams/plates and sandwich micro-plates were proposed.The two material length scale parameters included in the new model enables it to describe different scale effects in two orthogonal directions.The governing equations and related boundary conditions for static bending problem,free vibration and buckling problems were derived through the principle of minimum energy,virtual work and Hamilton's principle.The effects of the scale effect on the various mechanical behaviors were analyzed by various numerical examples with a variety of boundary conditions and loads for the micro-structures.Subsequently,the impacts of various kinds of structural dimension parameters and material parameters on the apparent degree of the scale effect are discussed.Precisely,the concrete work can be summarized as follows:1.Based on different beam/plate theories,several orthotropic functionally graded micro-beam/plate models were proposed.In view of static bending,free vibration and buckling behaviors,the influences of the scale effect on the deflections,stresses,natural frequencies and buckling loads of the structures were analyzed.The impacts of the ratio of material length scale parameters to structural thickness,geometric parameters and material parameters on the apparent degree of the scale effects are discussed2.Combining with the Refined Zigzag Theory,the functionally graded sandwich micro-plate models with accurate prediction ability on both global responses and local behaviors were proposed.The correctness and accuracy of macroscopic part of solutions in static bending,free vibration and buckling problems had been verified through comparing the results with the references.Based on the two kinds of grading laws,the scale effects in various mechanical behaviors of sandwich micro-plate were discussed.At the same time,the validity of using two material length scale parameters to describe the scale effects in different directions had been proved indirectly.Through concrete comparison of results and parameter investigations,the influences of various geometric parameters and material parameters on the apparent degree of the scale effect were discussed.Subsequently,the reasons of causing these influences were analyzed and explained.