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| A MULTI-SCALE MODEL FOR NONLOCAL EFFECTS AND ITS APPLICATION ON BENDING ANALYSIS OF MICRO-BEAMS |
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Abstract Exact nonlocal stress field is derived via a successive approximation approach based on Eringen’s nonlocal elasticity theory. The explicit solution of nonlocal stress is provided and it can be expressed as an infinite series. Subsequently, the transverse bending and pure bending deformations of micro-beams are taken as examples to exhibit the effect of nonlocal small scale parameter on static deflection. The equilibrium equations are solved and the results are analyzed and discussed in detail. It shows that with different nonlocal small scale parameters, nonlocal bending deflection is lower or higher than that predicted by the classical continuum mechanics, or nonlocal effect increases or decreases structural stiffness of micro-beams. Two opposite nonlocal models proposed respectively by Wang et al and Lim et al are both existence and acceptable. It is demonstrated firstly that deflection fluctuates up and down with increasing the scale parameters, and the existence of some discontinuity points is also observed. The deflection is a non-monotone function with respect to nonlocal small scale parameter. The present study also suggests a possible approach to determine the nonlocal material parameter.
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Received: 02 September 2013
Published: 28 June 2014
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2014, Vol. 35 
