Shubham Desai, Sai Sidhardh^*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 1271-1334, 2025, DOI:10.32604/cmes.2025.068141 - 31 August 2025

Abstract The increasing integration of small-scale structures in engineering, particularly in Micro-Electro-Mechanical Systems (MEMS), necessitates advanced modeling approaches to accurately capture their complex mechanical behavior. Classical continuum theories are inadequate at micro- and nanoscales, particularly concerning size effects, singularities, and phenomena like strain softening or phase transitions. This limitation follows from their lack of intrinsic length scale parameters, crucial for representing microstructural features. Theoretical and experimental findings emphasize the critical role of these parameters on small scales. This review thoroughly examines various strain gradient elasticity (SGE) theories commonly employed in literature to capture these size-dependent effects… More >

Ömer Ekim Genel^*, Hilal Koç, Ekrem Tüfekci

CMC-Computers, Materials & Continua, Vol.82, No.2, pp. 2043-2059, 2025, DOI:10.32604/cmc.2025.060111 - 17 February 2025

Abstract Due to their superior properties, the interest in nanostructures is increasing today in engineering. This study presents a new two-noded curved finite element for analyzing the in-plane static behaviors of curved nanobeams. Opposite to traditional curved finite elements developed by using approximate interpolation functions, the proposed curved finite element is developed by using exact analytical solutions. Although this approach was first introduced for analyzing the mechanical behaviors of macro-scale curved beams by adopting the local theory of elasticity, the exact analytical expressions used in this study were obtained from the solutions of governing equations that… More >

Chih-Ping Wu^1,2, Wei-Chen Li¹

CMC-Computers, Materials & Continua, Vol.52, No.2, pp. 73-103, 2016, DOI:10.3970/cmc.2016.052.073

Abstract A three-dimensional (3D) asymptotic theory is reformulated for the static analysis of simply-supported, isotropic and orthotropic single-layered nanoplates and graphene sheets (GSs), in which Eringen's nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these. The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional (2D) nonlocal plate problems, the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory (CST), although with different nonhomogeneous terms. Expanding the primary More >

Farzad Ebrahimi^1,2, Erfan Salari¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 151-181, 2015, DOI:10.3970/cmes.2015.105.151

Abstract In this paper, a semi-analytical method is presented for free vibration and buckling analysis of functionally graded (FG) size-dependent nanobeams based on the physical neutral axis position. It is the first time that a semi-analytical differential transform method (DTM) solution is developed for the FG nanobeams vibration and buckling analysis. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form. The physical neutral axis position for mentioned FG nanobeams is determined. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The… More >

P.H. Wen¹, X.J. Huang¹, M.H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 199-225, 2013, DOI:10.3970/cmes.2013.096.199

Abstract In this paper, a Local Integral Equation Method (LIEM) is presented for solving two-dimensional nonlocal elasticity problems . The approach is based on the Eringen’s model with LIEM and the interpolation using the radial basis functions to obtain the numerical solutions for 2D problems. A weak form for the set of governing equations with a unit test function is transformed into the local integral equations. The meshless approximation technique with radial basis functions is employed for the implementation of displacements. A set of the local domain integrals is obtained in analytical form for the local More >