Bending solutions of Reddy beams based on modified couple stress theory in terms of Euler-Bernoulli beams

doi:10.1007/s10483-026-3382-8

Abstract

Abstract:

The bending behavior of microbeams in micro-nano devices exhibits significant size effects, making accurate prediction of their mechanical behaviors crucial for device reliability. This paper employs the modified couple stress theory (MCST) and derives the governing equations for the Reddy beam theory (RBT) via the principle of virtual work. By considering the load equivalence, the analytical solutions for the bending problem are derived and expressed as the functional relations based on the Euler-Bernoulli beam model. Once the Euler-Bernoulli beam solution is obtained, the exact solution for the corresponding Reddy beam can be directly determined through these functional relations and boundary conditions. Analytical solutions for the doubly simply-supported (S-S), clamped-free (C-F), and clamped-clamped (C-C) boundary conditions are derived and validated through comparison with the results of previous studies. This study clarifies the analytical relationship between the two beam theories at the micro-scale, enabling exact mechanical solutions for higher-order shear deformation beams without solving complex higher-order governing equations.

Key words: Reddy beam theory (RBT), Euler-Bernoulli beam theory (EBT), modified couple stress theory (MCST), bending solution

2010 MSC Number:

O342

Shenao ZHAO, Lei LI, Pengpeng SHI. Bending solutions of Reddy beams based on modified couple stress theory in terms of Euler-Bernoulli beams. Applied Mathematics and Mechanics (English Edition), 2026, 47(5): 1085-1104.

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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-026-3382-8

https://www.amm.shu.edu.cn/EN/Y2026/V47/I5/1085

Figures/Tables 9

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l/h	EBT		RBT
l/h	Ref. [31]	Present	Ref. [31]	Present
0	1.302 1	1.302 0	1.310 8	1.310 7
0.2	1.109 2	1.109 1	1.116 3	1.115 7
0.4	0.767 9	0.767 9	0.772 9	0.771 4
0.6	0.507 6	0.507 6	0.511 3	0.509 5
0.8	0.344 2	0.344 2	0.347 3	0.345 3
1	0.243 5	0.243 5	0.246 1	0.244 2