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International Journal for Multiscale Computational Engineering

Erscheint 6 Ausgaben pro Jahr

ISSN Druckformat: 1543-1649

ISSN Online: 1940-4352

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Indexed in

A SIZE-DEPENDENT FINITE-ELEMENT MODEL FOR A MICRO/NANOSCALE TIMOSHENKO BEAM

Volumen 13, Ausgabe 6, 2015, pp. 491-506
DOI: 10.1615/IntJMultCompEng.2015014055
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ABSTRAKT

A size-dependent finite-element model for a micro/nanoscale Timoshenko beam is developed based on the strain gradient elasticity theory. The newly developed element contains three material length scale parameters that capture the size effect. This element is a new, comprehensive Timoshenko beam element that can reduce to the modified couple stress Timoshenko beam element or the classical Timoshenko beam element if two (l0 and l1) or three (l0, l1, and l2) material length scale parameters are set to zero. The element satisfies C0 continuity and C1 weak continuity and has two nodes, with four degrees of freedom at each node considering only bending deformation. The deflection and cross-sectional rotation of the element are interpolated independently. The finite-element formulations and the stiffness and mass matrices are derived using the corresponding weak-form equations. To verify the reliability and accuracy of the proposed element, the problems of convergence and shear locking are studied. Using the newly developed element, the static bending and free vibration problems of the clamped and simply supported Timoshenko microbeam are investigated. The results for a simply supported Timoshenko microbeam predicted by the new element model agree well with results from the literature. Moreover, the results illustrate that the size effect on the Timoshenko microbeam can be effectively predicted by using the proposed element.

REFERENZIERT VON
  1. Thai Huu-Tai, Vo Thuc P., Nguyen Trung-Kien, Kim Seung-Eock, A review of continuum mechanics models for size-dependent analysis of beams and plates, Composite Structures, 177, 2017. Crossref

  2. Kwon Young-Rok, Lee Byung-Chai, Numerical evaluation of beam models based on the modified couple stress theory, Mechanics of Advanced Materials and Structures, 29, 11, 2022. Crossref

  3. Trabelssi M., El-Borgi S., A novel formulation for the weak quadrature element method for solving vibration of strain gradient graded nonlinear nanobeams, Acta Mechanica, 2022. Crossref

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