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The Mesh-Free Method with Couple Stress Theory for Vibration Analysis of Micro-Structure

Author: SongFeng
Tutor: WangXiPing
School: Shandong University
Course: Solid Mechanics
Keywords: Size effect Couple stress theory Meshless method Microstructure Vibration
CLC: O327
Type: Master's thesis
Year: 2010
Downloads: 66
Quote: 0
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Abstract


In recent years, with the rapid development of modern science and technology , industrial components are increasingly miniaturized , especially micro - mechanical structure system is widely applied in practice . Theoretical prediction in the micron or nanoscale material behavior under the macro-scale is completely different, which requires to build the microscale under the laws of physics . Systematic exposition and summary of the couple stress theory , research and derive the equilibrium equations of general couple stress theory , strain-displacement relations and constitutive relation . Strain gradient theory to explain the material in the micron scale size effect phenomenon and developed a new theory, couple stress theory is to develop one of the first strain gradient theory is now widely used in the micro-scale stress and deformation analysis , but so far mainly depends on the numerical method , only a few analytical solution of the plane problem . Meshless method in recent years, the rise of a new numerical method has unique advantages in dealing with couple stress micromechanical structure vibration problems . Couple stress theory and meshless method developed meshless method based on the use of the couple stress theory the micro structural vibration analysis , meshless method for solving the problem of structural vibration constitutive model and control equation . Meshless method for couple stress theory to study the micro- structure vibration problems , reasonable selection affect the calculation accuracy and convergence speed of several important parameters of the meshless method , find the general micro- structure vibration response of the numerical solution obtained ideal results provide a theoretical basis for the design and analysis of the micro - mechanical structure . Finally, the couple stress theory meshless method further application in the field of micro - mechanical vibration prospect .

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CLC: > Mathematical sciences and chemical > Mechanics > Vibration theory > Structural vibration
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