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Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress-driven nonlocal elasticity

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Abstract

In this work, the size-dependent buckling of functionally graded (FG) Bernoulli-Euler beams under non-uniform temperature is analyzed based on the stress-driven nonlocal elasticity and nonlocal heat conduction. By utilizing the variational principle of virtual work, the governing equations and the associated standard boundary conditions are systematically extracted, and the thermal effect, equivalent to the induced thermal load, is explicitly assessed by using the nonlocal heat conduction law. The stress-driven constitutive integral equation is equivalently transformed into a differential form with two non-standard constitutive boundary conditions. By employing the eigenvalue method, the critical buckling loads of the beams with different boundary conditions are obtained. The numerically predicted results reveal that the growth of the nonlocal parameter leads to a consistently strengthening effect on the dimensionless critical buckling loads for all boundary cases. Additionally, the effects of the influential factors pertinent to the nonlocal heat conduction on the buckling behavior are carefully examined.

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Chi Xu, Yang Li & Zhendong Dai

  2. Jiangsu Provincial Key Laboratory of Bionic Functional Materials, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Chi Xu, Yang Li, Mingyue Lu & Zhendong Dai

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  1. Chi Xu
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  2. Yang Li
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Correspondence to Zhendong Dai.

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Citation: XU, C., LI, Y., LU, M. Y., and DAI, Z. D. Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress-driven nonlocal elasticity. Applied Mathematics and Mechanics (English Edition), 43(3), 355–370 (2022) https://doi.org/10.1007/s10483-022-2828-5

Project supported by the National Natural Science Foundation of China (Nos. 51435008 and 51705247) and the China Postdoctoral Science Foundation (No. 2020M671474)

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Xu, C., Li, Y., Lu, M. et al. Buckling analysis of functionally graded nanobeams under non-uniform temperature using stress-driven nonlocal elasticity. Appl. Math. Mech.-Engl. Ed. 43, 355–370 (2022). https://doi.org/10.1007/s10483-022-2828-5

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  • DOI: https://doi.org/10.1007/s10483-022-2828-5

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