Static analysis of thin-walled beams using two-phase local-nonlocal integral model

A mathematical model is developed for static analysis of small-scale thinwalled beams having arbitrary cross sections. Constitutive relations of the thin-walled beams are defined upon the two-phase local-nonlocal mixture model with integral formulation. The developed model includes flexural-torsional coupling and warping effects. Governing equations of the thin-walled beams having nonlocal property are derived by using the principle of minimum potential energy. The displacement based finite element method is used to solve both local and nonlocal part of the model. The effect of the nonlocal parameters on the static behavior of micro-scale thin-walled beams having closed and open cross-sections is examined and discussed for various nonlocal parameters and boundary conditions.