Study On The Scale Effect Of Micro-sized Elastic Structure

With the development of modern micro-manufacturing and micro-integration technologies,micro-electromechanical systems(MEMS)play an extremely important role in the fields of biomedicine,aerospace,vehicle systems,engineering machinery,and home appliances.The MEMS contains various micro-beams and micro-plates and other elastic structures,and the mechanical properties of these micro-elastic structures have scale effects.Scale effect is the key problem to overcome in the design of MEMS.At present,the classical elasticity theory cannot measure the scale effect,while other non-classical elasticity theory still has a huge controversy to interpret the scale effect.Therefore,it is very important to study the scale effect of the mechanical properties of micro-elastic structures and reveal the cause of the scale effect for the design,manufacture and optimization of MEMS.Based on the idea of Mindlin's couple stress theory,combined with the geometric description of deformation and the understanding of the curvature tensor asymmetry,the content of the couple stress theory is enriched,and it is called generalized elasticity theory.In this study,the generalized elasticity theory is used as the basic theory to study the scale effect of the mechanical properties of micro-beams and micro-plates.The generalized elasticity theory is developed from the couple stress theory.The establishment of the constitutive equation of the couple stress theory involves the symmetry of the couple stress tensor and curvature tensor.In this paper,we prove that curvature tensor and couple stress tensor are asymmetric by simple shear problem.The outstanding characteristic of the generalized elasticity theory is that it can measure the scale effect.Although some non-classical elastic theories can also be used to calculate the scale effect of elastic body,the reasons for the scale effect have not yet been revealed.In the framework of generalized elasticity theory,the deformation of an elastic body is decomposed into translational deformation and rotational deformation.In this paper,the scale effect is analyzed from the perspective of deformation and the concept of the degree of influence of rotational deformation is proposed.According to the analytical solution of Euler-Bernoulli beam and Kirchhoff plate model based on the generalized elasticity theory and the results of its bending deformation,it is revealed that the scale effect is caused by the amplification of the effect of rotation deformation on the micro scale.The generalized elasticity theory has three material parameters,namely two Laméparameters and a rotational modulus.Whether this rotational modulus can be accurately measured is related to whether the generalized elasticity theory can implement engineering guidance.The significance of the rotational modulus measurement is extremely important for the generalized elasticity theory from theoretical analysis to practical guidance.Combining with the research for the problem of electrostatically driven pull-in,an experimental method for measuring the rotational modulus using the principle of electrostatically driven pull-in instability is proposed.According to the experimental data in the existing references,the rotation modulus of the silicon beam and the pull-in voltage curve of the experiment are obtained.The results show that the pull-in voltage considering the generalized elasticity theory can just make up the gap between the results of the classical elasticity theory and the experimental values.For the numerical analysis of some irregular beams and plates in MEMS,solid elements have the advantage of universality that other types of elements do not.Therefore,based on the generalized elasticity theory and the penalty function method in the constraint variational principle,the finite element equations of the solid element are established.The 8-node reduced integration element,8-node complete integration element and 20-node full integration element are constructed,and the performance of these three elements and the influence of penalty parameters on the calculation results are discussed.The results show that the performance of 8-node fully integrated element is poor,and this element should be avoided.In addition,the scale effect of the bending deformation of the micro-cantilever beam and the simply supported micro-circular plate and the normalized frequency of the corresponding mode of the pre-twisted plate are analyzed.The results show that the influence of rotational deformation on the macro scale is minimal and negligible,while the influence on the micro scale is very large,and the scale effect is caused by the magnification of the rotational deformation on the micro scale.The stress concentration of inclusions is of great significance to the study of the destruction of some composite materials containing particles.With reference to the finite element formulation of the three-dimensional solid element,the finite element equation of the two-dimensional planar quadrilateral isoparametric element is constructed.The performance of the element is verified by the stress concentration around the hole in the infinite tensile plate.Last,the quadrilateral isoparametric element is used to analyze the scale effect of the stress concentration around circular inclusion in an infinite tensile plate and the influence of material parameters on the stress concentration of inclusions.Abnormal operating conditions with large fluctuations in speed and sudden impacts from the external environment are detrimental to the normal operation of machinery and equipment and the health of operators.Hence it is very important for the normal operation of these mechanical equipment and the health of operators to monitor the excessive angular velocity and unsafe acceleration and send out alarm information or trigger emergency signals.Based on this,a micro-trigger sensor capable of emergency treatment of unsafe acceleration and alarm of excessive angular velocity is studied.The core problem of the micro-trigger sensor is a mechanical problem,the essence of which is the dynamics response of the triggering microstructure under angular velocity and acceleration.Based on the generalized elasticity theory,the Hamilton principle is used to establish the dynamics control equation of the triggering microstructure,and the modal superposition method is used to solve this equation.Last,the scale-dependent trigger characteristics of the micro-trigger sensor are analyzed.