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国际多尺度计算工程期刊

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ISSN 打印: 1543-1649

ISSN 在线: 1940-4352

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Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures

卷 8, 册 4, 2010, pp. 441-446
DOI: 10.1615/IntJMultCompEng.v8.i4.70
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摘要

Size-dependent effects can significantly be indicated in experimental deformation of microstructures. In accordance with statistic behavior of size-dependent parameters, it is predictable that finite deformation and nonlinear forms of equations may obtain more appropriate computational results for microstructures. In this paper, classic couple stress theory is used to explain size dependency in strain gradient theory. Based on results obtained from couple stress in strain gradient theory, the theory is extended in nonlinear form. In this case, a length scale parameter is used in this model as a Lagrangian coefficient and a strain gradient is attested in a classic constitutive equation as a constraint. Finally, a nonlinear form of equation is used for a cylinder in micron order subjected to torsion, and results are compared with a linear model, the model expressed by Yang et al. (Int. J. Solids Struct., 39, pp. 2731-2743, 2002), and the finite element model of bone.

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对本文的引用
  1. Kondrat V. F., Hrytsyna O. R., Relations of gradient thermomechanics taking into account the irreversibility and inertia of local mass displacement, Journal of Mathematical Sciences, 183, 1, 2012. Crossref

  2. Ahmadi Ali Reza, Farahmand Hamed, Static deflection analysis of flexural rectangular micro-plate using higher continuity finite-element method, Mechanics & Industry, 13, 4, 2012. Crossref

  3. Farahmand H., Ahmadi A.R., Arabnejad S., Thermal buckling analysis of rectangular microplates using higher continuity p-version finite element method, Thin-Walled Structures, 49, 12, 2011. Crossref

  4. FARAHMAND HAMED, AHMADI ALIREZA, ARABNEJAD SAID, A NOVEL APPLICATION OF HIGHER CONTINUITY FINITE ELEMENT IN VIBRATION ANALYSIS OF MICRO-PLATES, International Journal of Structural Stability and Dynamics, 13, 04, 2013. Crossref

  5. Mohammadi M., Fooladi Mahani M., An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories, Acta Mechanica, 226, 10, 2015. Crossref

  6. Farahmand H., Naseralavi S. S., Iranmanesh A., Mohammadi M., Navier Solution for Buckling Analysis of Size-Dependent Functionally Graded Micro-Plates, Latin American Journal of Solids and Structures, 13, 16, 2016. Crossref

  7. Mohammadi Meisam, Iranmanesh Afshin, Naseralavi Seyed Sadegh, Farahmand Hamed, Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory, Science and Engineering of Composite Materials, 25, 3, 2018. Crossref

  8. Farahmand H., Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42, 5, 2020. Crossref

  9. Farahmand H., A variational approach for analytical buckling solution of moderately thick microplate using strain gradient theory incorporating two-variable refined plate theory: a benchmark study, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 3, 2021. Crossref

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