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http://dx.doi.org/10.12989/sem.2020.76.6.765

On bending analysis of perforated microbeams including the microstructure effects  

Abdelrahman, Alaa A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University)
Abd-El-Mottaleb, Hanaa E. (Structural Engineering Department, Faculty of Engineering, Zagazig University)
Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University)
Publication Information
Structural Engineering and Mechanics / v.76, no.6, 2020 , pp. 765-779 More about this Journal
Abstract
This article presents a nonclassical size dependent model based on the modified couple stress theory to study and analyze the bending behavior of perforated microbeams under different loading patterns. Modified equivalent material and geometrical parameters for perforated beam are presented. The modified couple stress theory with one material length scale parameter is adopted to incorporate the microstructure effect into the governing equations of perforated beam structure. The governing equilibrium equations of the perforated Timoshenko as well as the perforated Euler Bernoulli are developed based on the potential energy minimization principle. The Poisson's effect is included in the governing equilibrium equations. Regular square perforation configuration is considered. Based on Fourier series expansion, closed forms for the bending deflection and the rotational displacements are obtained for simply supported perforated microbeams. The proposed methodology is validated and compared with the available results in the literature and an excellent agreement is detected. Numerical results demonstrated the applicability of the proposed methodology to investigate the bending behavior of regularly squared perforated beams incorporating microstructure effect under different excitation patterns. The obtained results are significantly important for the design and production of perforated microbeam structures.
Keywords
microstructure effect; modified couple stress; perforated microbeam; filling ratio; shear deformation; bending behavior; poisson's effect;
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Times Cited By KSCI : 48  (Citation Analysis)
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