___

• [1] Behera, L., Chakraverty, S., Recent researches on nonlocal elasticity theory in the vibration of carbon nanotubes using beam models: A review. Archives of Computational Methods in Engineering. 24(3), 481-494, 2017.
• [2] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54 (9), 4703-4710, 1983.
• [3] Civalek, O., Demir, C., A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method. Applied Mathematics and Computation, 289, 335-352, 2016.
• [4] Demir, C., Civalek, O., A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Composite Structures, 168, 872-884, 2017.
• [5] Civalek, O., Demir, C., Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Applied Mathematical Modeling, 35, 2053-2067, 2011.
• [6] Mercan, K., Civalek, O., Comparison of small scale effect theories for buckling analysis of nanobeams. International Journal of Engineering & Applied Sciences, 9(3), 87-97, 2017.
• [7] Mindlin, R.D., Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, 16 (1), 51-78, 1964.
• [8] Akgöz, B., Civalek, O., Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams. International Journal of Engineering Sciences, 49, 1268-1280, 2011.
• [9] Xu, W., Wang, L.F., Jiang, J.N., Strain gradient finite element analysis on the vibration of double-layered graphene sheets. International Journal of Computational Methods, 13, 1650011, 2016.
• [10] Lim, C.W., Zhang, G., Reddy, J.N.. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, 78, 298-313, 2015.
• [11] Wei, G.W., Discrete singular convolution for the solution of the Fokker-Planck equations. Journal of Chemical Physics, 110, 8930-8942, 1999.
• [12] Wei, G.W., A new algorithm for solving some mechanical problems. Computer Methods in Applied Mechanics and Engineering, 190, 2017-2030, 2001.
• [13] Wang, X., Duan, G., Discrete singular convolution element method for static，buckling and free vibration analysis of beam structures. Applied Mathematics and Computation, 234, 36-51, 2014.
• [14] Wang, X., Yuan, Z., Discrete singular convolution and Taylor series expansion method for free vibration analysis of beams and rectangular plates with free boundaries. International Journal of Mechanical Sciences, 122, 184-191, 2017.
• [15] Ng, C.H.W., Zhao, Y.B., Xiang, Y., Wei, G.W., On the accuracy and stability of a variety of differential quadrature formulations for the vibration analysis of beams. International Journal of Engineering & Applied Sciences, 1(4), 1-25, 2009.
• [16] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E., Strong formulation finite element method: A survey. Applied Mechanics Reviews, 67, 020801,2015.
• [17] Wang, X., Novel differential quadrature element method for vibration analysis of hybrid nonlocal Euler-Bernoulli beams. Applied Mathematics Letters, 77, 94-100, 2018.
• [18] Wang X. Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications. Oxford: Butterworth-Heinemann, 2015.
• [19] Jin, C., Wang, X., Ge, L., Novel weak form quadrature element method with expanded Chebyshev nodes. Applied Mathematics Letters, 34, 51-59, 2014.
• [20] Wang, X., Yuan, Z., Jin, C., Weak form quadrature element method and its applications in science and engineering: A state-of-the-art review. Applied Mechanics Reviews, 69, 030801, 2017.
• [21] Jin, C., Wang, X., Accurate free vibration of functionally graded skew plates. Transactions of Nanjing University of Aeronautics & Astronautics, 34(2), 188-194, 2017.
• [22] Jin, C., Wang, X., Weak form quadrature element method for accurate free vibration analysis of thin skew plates. Computers and Mathematics with Applications, 70, 2074-2086, 2015.