A strain gradient functionally graded Euler–Bernoulli beam formulation

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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].”
Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories (2014, methodology): “[38] derived the equation of motion and boundary conditions of a micro - beam using strain gradient approach and functionally graded Euler – Bernoulli beam model considering the variation of material length scale parameter through the thickness.”
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].”