Structural Mechanics Analysis Of Theoretical Beams With Triangular Shear Deformation With Scale Effect

Small structural elements such as beams,plates and shells are commonly used as components for micro and nano-sized electromechanical systems(MEMS and NEMS),sensors,actuators and atomic force microscopes.Experiments show that this micro-scale structure has a scale effect on mechanical behavior.Due to the difficult performance of experimental research on microscale structures,we usually use numerical calculation methods or analytical methods to study the microscale effects.We propose a new triangular shear-deformation beam model using the modified couple stress theory and surface elasticity theory to describe the scale effect of micro-scale beams.In this paper,the scale effects of uniform microbeams and functionally graded microbeams are studied separately.The following are the research contents and conclusions of this paper:1.The research background and significance of microscale structure in recent years and the research status at home and abroad are introduced.The research results of microstructure scale effect in theory and experiment are expounded.The performance and research status of functionally graded materials are introduced.2.The theoretical basis of microbeam scale effect research is introduced,including modified couple stress theory,triangular shear deformation beam theory,surface energy theory,Hamilton variational principle,differential quadrature method based on Hermite interpolation,and functional gradient beam parameters.3.Based on the modified couple stress theory,surface energy theory and triangular shear deformation beam model,the Hamilton variational principle is used to derive the governing equations and boundary conditions of the functionally graded beams and uniform beams respectively,and the bending,buckling and vibration of the uniform beams and the functionally graded beams under different boundary conditions are carried out.The effects of functional gradient index,beam thickness,beam length-to-thickness ratio,surface energy constant on bending deflection,buckling load and vibration frequency were analyzed.4.It is found that the mechanical properties of micro-scale beams are quite different from those of classical mechanics after applying the new beam model,which verifies the existence of scale effects.