Structural Mechanics Analysis Of Higher-order Shear Deformation Theory With Size Effect

Micro-Electro-Mechanical Systems(MEMS)and Nano-Electro-Mechanical Systems(NEMS)are microscale high-tech products that have developed rapidly in recent years,and micro-nano beams are simple and important key structures in these systems.When the size of the structure is in the micro-nano,the mechanical properties of the structure are no longer independent of the size,but vary with the size.The size-dependent behavior of this mechanical property is the size effect.In addition,for macrostructures,the surface layer is negligible,but for microstructures with large ratio of surface layer to bulk volume,the surface layer can not be ignored,and the surface effect also has a great influence on the mechanical properties of the microstructure.And this is all the classic mechanics theory can not explain.Therefore,based on the modified couple stress theory and surface elasticity theory,this paper proposes a higher-order shear deformation theory beam model at microscale.By modifying the symmetric rotation gradient in the couple stress theory,the material feature scale parameter is introduced,which predicts the size effect of microstructures,the total strain energy of microbeams,in addition to the strain energy based on classical elastic theory,also considers the strain energy caused by the rotation gradient and surface effects.By using the Hamilton variational principle,the equilibrium equations and boundary conditions of the microbeams are derived.The differential quadrature element method is used to study the static bending,free vibration and stability problems of the microbeams under different boundary conditions.The effects of micro-beam size and surface layer thickness on micro-beam bending deflection,free vibration frequency and buckling critical stress are analyzed.Based on the modified couple stress theory and the surface elasticity theory,the bending deflection,free vibration frequency and buckling critical stress of the microbeam are calculated respectively.The obtained results are significantly different from the results obtained by classical elastic theory,which verifies the existence of size effect.In addition,the surface effect also has a great influence on the mechanical properties of the microbeam.For functionally graded microbeams,the influence of volume fraction index on the mechanical response of microbeams is also analyzed.