Effect of scale parameter on the deflection of a nonlocal beam and application to energy release rate of a crack

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2015-12, Vol.95 (12), p.1428-1438
• Main Authors: Peng, X.-L., Li, X.-F., Tang, G.-J., Shen, Z.-B.
• Format: Article
• Language: English
• Subjects: crack; nanoscale beam; Nonlocal elasticity; Optimization; stress intensity factor
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201400132

This article studies the influence of the nonlocal scale parameter on the deflection of a nonlocal nanobeam and crack growth. Using the Timoshenko hypothesis, a single governing equation is derived and its exact solution can be determined through appropriate end‐support conditions. Numerical calculations are carried out for a cantilever microtubule in solution at a given flow speed. The effects of nonlocal scale parameter on the deflection are discussed. Based on the obtained solutions, the double cantilever beam model is utilized to determine energy release rate near a crack tip for an edge crack and a central crack, respectively. It is found that the scale parameter plays different roles in determining stress intensity factors and energy release rates, depending on crack constraints. When neglecting shear deformation, the results for nonlocal Euler‐Bernoulli beams can be directly obtained. This article studies the influence of the nonlocal scale parameter on the deflection of a nonlocal nanobeam and crack growth. Using the Timoshenko hypothesis, a single governing equation is derived and its exact solution can be determined through appropriate end‐support conditions. Numerical calculations are carried out for a cantilevermicrotubule in solution at a given flow speed. The effects of nonlocal scale parameter on the deflection are discussed.