Size-dependent couple stress Timoshenko beam theory

Abstract

In this paper, a new size-dependent Timoshenko beam model is developed based on the consistent couple stress theory. In the present formulation, the governing equations and corresponding boundary conditions are obtained. Afterwards, this formulation is used to investigate size-dependency for several elementary beam problems. Analytical solutions are obtained for pure bending of a beam and for a cantilever beam with partially and fully clamped boundary conditions. These analytical results are then compared to the numerical results from a two-dimensional finite element formulation for the corresponding couple stress continuum problem.

arXiv comment48 pages, 12 figures, 60 references

References in corpus (4)

• Evolution of generalized couple-stress continuum theories: a critical analysis
• Foundations of consistent couple stress theory
• Couple stress theories: Theoretical underpinnings and practical aspects from a new energy perspective
• Comparison of theoretical elastic couple stress predictions with physical experiments for pure torsion