A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory

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Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory (2015, methodology): “[29] used strain gradient theory to develop a geometrically nonlinear elastic size-dependent Timoshenko beam formulation.”
Buckling analysis of functionally graded microbeams based on the strain gradient theory (2013, methodology): “[52] developed nonlinear strain gradient microbeam models based on Bernoulli–Euler and Timoshenko beam theory, respectively.”
Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory (2013, methodology): “Recently, some new applications have been performed using the strain gradient elasticity and couple stress theory [26–32].”
Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics (2018, background): “, strain gradient and couple-stress theories, have been actively developed during the past years [15, 16, 17, 18, 19, 20, 21, 22, 23, 24].”
A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory (2015, background): “In the last five years, modified strain gradient theory has been extensively employed to investigate the mechanical responses of one-dimensional small-sized structures such as microbars [18–23] and microbeams [24–35].”