Formulation of a beam finite element for micro beams

Pehlivanoğlu, Yücel
This study presents an Euler Bernoulli type micro-beam finite element for analyzing the size-dependent static and dynamic behavior of micro beams. The new element is based on Modified Couple Stress Theory (MCST). The governing equations of motion and the boundary conditions for the beam are derived and the conventional Galerkin technique is employed to formulate the finite element. The new element can be reduced to Classical Euler-Bernoulli beam element if the size-effect parameter in the element matrices is taken as zero. Using this finite element, static and free vibration analyses are carried out for different boundary conditions. The results are compared with analytical, numerical and similar finite element method based results in the literature and it is found that they are in good agreement. Two case studies are done to demonstrate possible uses of this beam finite element. One of the case studies pertains to the calculation of mesh stiffness of micro gears. This case study shows that there is a strong size effect for the mesh stiffness.
Citation Formats
Y. Pehlivanoğlu, “Formulation of a beam finite element for micro beams,” M.S. - Master of Science, Middle East Technical University, 2018.