Numerical Analysis On Rigid-Flexible Coupling And Scale Effects Of Generalized Linear Elastic Body

With development of modern high-tech fields, especially of micro-electro-mechanical systems (MEMS) which have strong scale effects, the research and analysison rigid-flexible coupling of micro-structure becomes increasingly important. In theframework of the continuum mechanics theory, finding a way to reflect the scale effectsof micro-structure and to be convenient to establish the dynamics model ofrigid-flexible coupling is an important basis for research and analysis. The combinationof generalized elastic model and rigid-flexible coupling theory brought the most directway to solve this problem.This article focused on the micro-structure under the framework of the generalizedelasticity, which is of scale effects and rigid-flexible coupling dynamics. The focus ofthe micro-structure of the scale effects and rigid-flexible coupling of the static anddynamic characteristics in micro-cantilever beam was to be the research object. Throughtheoretical modeling and numerical calculation quantitative analysis of the dynamicbehavior of micro-beam structure, having an analysis on micro-cantilever beam of scaleeffects and the fixed axis rotating in centrifugal environmental conditions, whichstanded up. The main study contents and conclusions in this thesis are as follows:①Based the introduction of the rotational deformation and Mindlin couple stresstheory of elasticity, the paper amended the constitutive relationship between the couplestress and the curvature tensor by the principle of virtual work and the isotropic tensorfunction linear representation theorem. The generalized linear elastic model containsthree material parameters. Establishing the total stress symmetry concept under thegeneralized elasticity, and defining an indicator of the size in the symmetry formeasuring stress-stress symmetry. The generalized elastic model can consider therotational deformation of the mechanical properties and be more complete comparedwith the classical elasticity. The generalized elastic model is able to reflect the scaleeffects of micro-structure, so is more suitable for the mechanical properties ofmacroscopic and microscopic structure analysis.②The static and dynamic finite element formulations of the generalized elasticbody were built by the constrained variational principle and the principle of virtual work.Using the way which the displacements and rotations of node independent interpolation,penalty method introduces forming constraints to construct4-nodes and12-dofs quadrilateral isoparametric element and hexahedral isoparametric element whichcontains8-node and48-dofs. Plane simple shearing and the static and dynamiccharacteristics analysis of cantilever beam showed that the generalized elastic modelcan be simplified as classic elastic model at the macro scale, the stress tensor as asymmetric tensor with sufficient accuracy. However, for micro-size of the structure,considering the rotational deformation makes the couple stress on the mechanicalproperties of a significant impact, mainly to destory stress symmetry and increase thestiffness and natural frequency of the structure.③The kinetic formulation of generalized elastic body for the fixed-axis rotation inthe centrifugal field was established by analytical methods based on continuummechanics. And it was discreted by use of constrained variational principle and8-nodesand48-dofs hexahedral isoparametric element, and then the finite element format wasgot to resolve the structural motion and deformation mechanism of rigid-flexiblecoupling. Finally, the finite element governing formulation of the classical elastic bodyrotated about fixed axis in the centrifugal field was got by Lagrange method.④Numerical analysison the dynamic characteristics, dynamic response and scaleeffects of micro-cantilever beam rotating about the fixed axis in different centrifugalconditions was made, which was put into upright position. The analysis showed that therotating micro-cantilever beam in the centrifugal field received by the forces whichcontain the initial centrifugal force and the initial cut to the combined effect of theinertial force, motion and deformation of the rigid-flexible coupling centrifugal forceand the Coriolis force, which together affect the dynamic response of the structure. Thedynamic characteristics of the structure have significant difference at different speeds,scale effects significantly improve the micro-structure of the static stiffness and naturalfrequency of the structure for increased maximum speed, dynamic response in advance.The centrifugal force has softening effect on the structure, and the Coriolis force, has afirst-order damping form different from the general structural damping effect. Responseto the micro-beam power the initial centrifugal force and the initial tangential inertiaforce plays a key role, but the deformation and motion of rigid-flexible coupling effectof the Coriolis force can not be ignored, precisely because of its role in the trajectory ofthe free end of the cantilever showing petals in the form of dynamic characteristics.