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	1. Numerical and experimental study on the lateral contact model of a circular rod moving in a circular channel
	Wu Feng,Zhao Ke,Wu Xuanlong,Zhao Liliang,Zhao Yuelin
	Mechanics 27 February 2023
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	Abstract:When a rod moves in a circular channel, high-frequency collisions occur between the rod and the channel wall. Contact models are crucial for predicting the motion of the rod. This paper conducts experimental studies on the movement of a rod in a circular channel and compares four different contact models based on experimental data. To improve the computational efficiency of simulating high-frequency collisions between the rod and the pipe wall, a time-averaging method is used to establish a time-averaged collision equation. This equation uses time-averaged displacement as the basic variable and handles contact problems through time-averaged gap functions and time-averaged contact forces. Two time-averaged contact models are proposed through polishing methods and machine learning, and comparison with experimental data shows that these models can ensure the accuracy of rod motion analysis while improving computational efficiency.
	TO cite this article:Wu Feng,Zhao Ke,Wu Xuanlong, et al. Numerical and experimental study on the lateral contact model of a circular rod moving in a circular channel[OL].[27 February 2023] http://en.paper.edu.cn/en_releasepaper/content/4759296


	2. Feedforward neural network with Reformulated Levenberg-Marquardt optimization algorithm for solving ordinary differential equations
	Li Shangjie,Li Haibin,He Yun
	Mechanics 10 July 2018
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	Abstract:This paper reformulates Levenberg-Marquardt (RLM) training algorithm in neural networks for solving ordinary differential equations (ODEs), and multiple joint training LM (MJLM) algorithm is proposed for solving coupled ODEs. However, there are several new approaches in literature to solve ODEs, but the new approach has more advantages, such as fast convergence and also little error. The optimal values for the corresponding adjustable parameters are calculated, an accurate approximate solution is obtained, which works well for interior and exterior points of the original domain. We show how to apply this method to a specific example of ODEs, the accuracy of the method is illustrated by solving several problems.
	TO cite this article:Li Shangjie,Li Haibin,He Yun. Feedforward neural network with Reformulated Levenberg-Marquardt optimization algorithm for solving ordinary differential equations[OL].[10 July 2018] http://en.paper.edu.cn/en_releasepaper/content/4745699


	3. Nonlinear analysis for a rectangular plate subjected to low velocity impact considering the effect of the structural deformation
	HU Yaqing,DAI Hongliang,LIN Zhongyan
	Mechanics 23 March 2018
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	Abstract:In this paper, by applying the Hertz contact law and considering the effect of the structural deformation, the dynamic contact coefficient is proposed. On the base of the classical theory of thin plate, by using von Kaman equations the governing equations of the rectangular plate subjected to low velocity is built. Considering the effect of the structural deformation, the governing equations of contact force is coupled with that of the plate, thus the finite difference method is used and the displacement functions is discrete in space domains. Also, the Newmark method is used and the whole problem is solved by applying iterative method. The results shows the influence of boundary condition, material of the plate, impact speeds and other factors on the displacement, normal stress and contact force while considering the effect of the structural deformation.
	TO cite this article:HU Yaqing,DAI Hongliang,LIN Zhongyan. Nonlinear analysis for a rectangular plate subjected to low velocity impact considering the effect of the structural deformation[OL].[23 March 2018] http://en.paper.edu.cn/en_releasepaper/content/4744096


	4. Dual solutions in MHD stagnation-point flow and heat transfer of Williamson nanofluid over a nonlinear shrinking sheet
	TANG Shujiang,LI Mingjun
	Mechanics 19 December 2017
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	Abstract:A MHD stagnation-point flow and heat transfer of Williamson nanofluid over a nonlinear shrinking sheet is investigated. The boundary-layer governing equations with a variable induced magnetic field are formulated and reduced to ordinary differential equations. The similar equations are solved numerically using Bvp4c with Matlab, and the dual solutions are found. Interestingly, there exists mc as a critical power-law index for the special dual solutions, in fact, there exists no critical value for the general Williamson nanofluid model. And on the two sides of the critical value, the dimensionless physical quantity will show different trending with the increase of the power low index.
	TO cite this article:TANG Shujiang,LI Mingjun. Dual solutions in MHD stagnation-point flow and heat transfer of Williamson nanofluid over a nonlinear shrinking sheet[OL].[19 December 2017] http://en.paper.edu.cn/en_releasepaper/content/4742888


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