Phenomenon of sharp change and concise solutions for Timoshenko beam based on modified couple stress theory.

The functional relations between the modified couple stress theory (MCST) and the classical theory (CT) are derived and analyzed in detail for closed-form solutions of Timoshenko micro-beam. The results show that phenomenon of sharp change exists in the internal force fields at two ends of the micro-beam. This phenomenon is related to dimensionless material scale parameter l/h. The phenomenon at fixed end is different from that at free end because the shear force Q at fixed end cannot be degenerated from the MCST to the CT, which is proved from a mathematical point of view. What's more, the exponential functions in the closed-form solutions of the MCST are higher-order terms and can be ignored for the deflection and rotation when Poisson's ratio ν = 0–0.45, h/L = 1/100–1/8 and the l/h = 0–1. After exponential functions are omitted, except rotation of cantilever beam under bending moment M₀, the concise solutions are acquired and error is very small. The size effects of the deflection and rotation can be calculated quickly without additional computing tools by the concise solutions. Some results obtained in this paper are compared with the published data in literatures, which prove the correctness of the results in this paper. [ABSTRACT FROM AUTHOR]