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A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that includes only one material length scale parameter, while the Gurtin–Murdoch surface elasticity theory containing three surface elasticity constants is employed to approximate the nature of surface energy effects. A new effective computational approach is presented for the current nonclassical Timoshenko beam model based on isogeometric analysis with high-order continuity basis functions of non-uniform rational B-splines, which effectively fulfills the higher continuity requirements in MCST. To validate the new approach and quantitatively illustrate both the microstructure and surface energy effects, the numerical results obtained from the developed approach for static deflection and natural frequencies of beams are compared with the analytical results available in the literature. Numerical results reveal that both the microstructure effect and surface energy effect should be considered in very thin beams, which also explains the size-dependent behavior.

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In this paper, we acquire some sufficient and realistic conditions for the existence of positive periodic solution for a general neutral impulsive n-species competitive model with the effect of toxic substance and infinite delay, by applying some analysis techniques and a new existence theorem, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction. As an application, we also examine some special cases which have been studied extensively in the literature. Some known results are improved and generalized. JIE PENG et al. 62

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