Quasi-3D large deflection nonlinear analysis of isogeometric FGM microplates with variable thickness via nonlocal stress–strain gradient elasticity

Abstract

Via the nonlocal stress–strain gradient continuum mechanics, the microscale-dependent linear and nonlinear large deflections of transversely loaded composite sector microplates with different thickness variation schemes are investigated. Microplates are assumed to be prepared from functionally graded materials (FGMs) the characteristics of which are changed along the thickness direction. A quasi-3D plate theory with a sinusoidal transverse shear function in conjunction with a trigonometric normal function was employed for the establishment of size-dependent modelling of FGM microplates with different thickness variation schemes. Then, to solve the nonlocal stress–strain gradient flexural problem, the non-uniform rational B-spline type of isogeometric solution methodology was applied for an accurate integration of geometric discerptions. It was found that the gap between load–deflection curves drawn for linear, concave and convex thickness variation patterns became greater by changing FGM composite microplate boundary conditions from clamped to simply supported. In addition, it was found that by considering only the nonlocal size effect, the plate deflection obtained by the nonlocal strain gradient quasi-3D plate model was greater than that extracted by the classical continuum elasticity because of the softening character of nonlocal size effect, while the strain gradient microstructural size dependency acted in opposite way and represented a stiffening character.