Static and Dynamic Analyses of Multi-Directional Functionally Graded Porous Nanoplates with Variable Nonlocal Parameter Using MITC3 + Element

Purpose: In this paper, a new three-node triangular plate element is proposed to analyze static bending, free vibration and forced vibration analysis of multi-directional functionally graded porous (MFGP) nanoplates based on the improved first-order shear deformation theory (i-FSDT) and nonlocal elastic theory. Method: Originating from the MITC3 + shell finite elements, the displacement fields of the i-FSDT are interpolated by usual linear functions of the three-node triangular element and a cubic supplemented function associated with a node located at the centroid of the element. Material properties vary in three directions i.e., x-, y- and z-direction with different porosity distributions. The main advantages of the present work include: (1) using i-FSDT without any shear correction factor and having the transverse shear stress equal to zero at two free surfaces of the plates; (2) the transverse shear strain fields are separately approximated according to the MITC3 + shear-locking removal technique; (3) the nonlocal parameter and other material properties are assumed to be material-dependent and vary smoothly across the thickness of the nanoplates, which has not been reported in any literature yet. Results: The accuracy and effectiveness of the proposed method are shown by comparing the obtained numerical results with those of previously published findings. Furthermore, the influences of the nonlocal parameter, volume exponent, porosity parameter on the static, free vibration and transient behaviour of MFGP nanoplates are fully studied. © 2023, Springer Nature Singapore Pte Ltd.