Mechanical Analysis On Micro-nano Structure Based On Isogeometric Numerical Method

Miniature device/systems,micro-and nano-sized device/systems that depends on the deformation,motion and dynamic behavior of beams,plates and other structures to achieve specific functions,are considered to play an important role in many fields such as national production economy and military.However,micro-and nano-scaled experiments confirmed that when the size of the structure shrinks to the order of micrometers or even nanometers,microstructure and surface effects of the material cannot be ignored.These physical effects that occur at the microscopic scale cause the material to exhibit properties different from those at the macroscopic scale.The constitutive relationship in the classical continuous mechanics theory does not contain any scale-related characteristic parameters,and it cannot explain the microstructure and surface effects phenomenon.Therefore,classic continuous mechanics theory cannot be used to design and optimize miniature devices/systems.Recently,the development of non-classical continuous mechanics theories that can explain the phenomena of the microstructure and surface effects has attracted the attention of scholars all over the world.Among the many non-classical continuous mechanics theories,the modified couple stress theory contains only one material scale parameter,which greatly simplifies the calculation model and improves the calculation efficiency,so it is favored by scholars.Surface elasticity theo ry,which introduces three additional surface material parameters to describe surface effects,is currently the most widely used theory to explain surface effect phenomena.The isogeometric numerical method is an emerging finite element formulation,a numerical method for accurately characterizing geometric shapes.Compared with the conventional finite element method,the isogeometric numerical method has many advantages such as high continuity within elements and controllable continuity between elements.In this dissertation,based on the modified couple stress theory,surface elasticity theory and sorts of beam and plate theories,mechanical models that can explain the phenomenon of the microstructure and surface effects are established,and the geometrical numerical method is used to solve the control equation.The impacts of microstructure and surface effects on mechanical behavior of beams or plates are investigated,which provides theoretical support for the design and optimization of miniature devices/systems.The works of this dissertation are as follows:1.Based on modified couple stress theory,surface elasticity theory and several beam theories,models of micro-and nano-scaled beam bending and free vibration are established.The models simultaneously consider the impacts of the microstrecture and surface effects on the mechanical behavior of beam s,and can meet the C1 continuity requirement of the modified couple stress theory for the displacement function.Through the analysis of typical numerical examples,the effects of material scale parameters,surface elastic parameters,geometric parameters and boundary conditions on the bending deflection and natural frequency of nano-scaled beams are discussed in detail.2.Based on the modified couple stress theory and Kirchhoff plate theory,the thermal-mechanical coupled buckling model for functionally graded microplates is established.This model can describe the phenomenon of size effect and meet the C1 continuous requirement of the modified couple stre ss theory for displacement function.By analyzing typical numerical examples of plates,the effects of material scale parameters,material gradient index,boundary conditions,etc.on the stability of the microplates under the condition of thermal-mechanical coupled are discussed in detail.