Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions

Bending and vibration analysis of delaminated Bernoulli–Euler micro-beams using the modified couple stress theory

“…Similar to the aforementioned linear models, the nonlinear static and dynamic analyses of microbeams were investigated using the numerical and theoretical methods by many researchers based on the modi ed couple stress theory [19][20][21][22][23]. Dai et al developed a new nonlinear theoretical model for cantilever microbeams [19] to explore the nonlinear dynamic behavior.…”

“…Dai et al developed a new nonlinear theoretical model for cantilever microbeams [19] to explore the nonlinear dynamic behavior. Mohammad-Abadi and Daneshmehr [20] reported on the buckling analysis of microbeams based on the Bernoulli-Euler beam, Timoshenko beam, and Reddy beam theories. By employing the principle of minimum total potential energy, they derived the governing differential equations and corresponding boundary conditions.…”

Electromechanical buckling of functionally graded electrostatic nanobridges using strain gradient theory

“…The first significant phenomenon is electromechanical buckling (EMB) which consists of mechanical buckling and electromechanical bifurcation. Mechanical buckling is a known phenomenon such that many researches have been done in this field with different theories such as: size dependent buckling analysis [4,5], thermal and size effect on buckling of microbeams [6], buckling of beams and columns under combined axial and horizontal loading [7] and also buckling analysis of carbon nanotubes (CNTs) and nanobeams using nonlocal elasticity theory [8,9]. Also, the electromechanical bifurcation is a kind of instability results from the inherent nature of electrostatic forces in symmetric actuators [10,11].…”

“…The application of this method covers almost all the areas of structural and vibration analysis of beams, arches, shafts, plates and shells [5,[35][36][37][38]. In this study, the EMB of beam-type NEMSs made of TFGM and AFGM based on modified strain gradient theory is investigated.…”

Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory

“…A nonlinear Timoshenko beam formulation by Asghari et al [16], the size-dependent vibration analysis of microplates by Jomezadeh et al [17], free vibration analysis for single-layered graphene sheets by Akgoz and Civalek [18], a study of a microstructure-dependent composite laminated Timoshenko beam by Roque et al [19], and buckling analysis of micro-composite laminated beams by MohammadAbadi and Daneshmehr [20] were presented based on modified couple stress theory. Also, Mohammad-Abadi [21] investigated size-dependent buckling analysis of microbeam models containing the classical and high-order shear deformation theories and evaluated the influence of the shear deformation. Moreover, Shaat et al [22] studied the effect of the transverse shear strain on the bending behavior of FG plates by comparing the plate behaviors based on Kirchhoff and Mindlin assumptions.…”