Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

Abstract In this study, an innovative procedure is presented for the analysis of static behavior plates at micro and nano scale, with arbitrary shape various boundary conditions. regard, well-known Eringen’s nonlocal elasticity theory used to appropriately model small length scale effects. The proposed mesh-free procedure, namely Line Element-Less Method (LEM), only requires evaluation simple line integrals along plate parametric equation. Further, variations introduced functionals eventually lead a linear system algebraic equations in terms expansion coefficients deflection function. Notably, yields approximate analytical solutions general shapes conditions, even exact some geometries. addition, several applications are discussed show simplicity applicability comparison pertinent data literature assesses accuracy approach.