Nonlocal isogeometric analysis for bidirectional functionally graded porous curved microbeams with arbitrary boundary conditions

This research aims to analyze the static bending and free vibration behaviors of bidirectional functionally graded porous (BFGP) curved microbeams with elastic boundary conditions resting on a Pasternak’s elastic foundation in a hygro-thermal environment. Isogeometric analysis based on non-uniform rational B-splines, first-order shear deformation theory, nonlocal elasticity theory combined with the modified strain gradient theories, modified Timoshenko beam theory are formulated to depict bending and shear deformations of BFGP curved microbeams. Especially, because using the modified Timoshenko beam theory, this study removes the requirement for a shear correction factor and describes shear stress by zero at the upper and lower cross-sectional sites of the BFGP curved microbeam. Different from traditional boundary conditions, where the beginning and end positions of a curved beam are connected by an elastic system of straight and torsion springs. This allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries. To assess the accuracy and convergence of the proposed approach, validation numerical examples were conducted in the various examples. (Figure presented.). © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2024.