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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 |
5. A Hermite differential quadrature finite element method and its application to free vibration of thin plates | |||
XING Yufeng,WU Yang | |||
Mechanics 09 May 2017 | |||
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Abstract:A Hermitedifferential quadraturefinite element method (Hermite DQFEM) is proposed and elaborated in this paper.Hermite differential quadrature (HDQ) rules based on the Hermite interpolation on two end points and Lagrange interpolation at other nodes are formulated. The optimized sampling points for the HDQ rules that provide the best interpolation accuracy were shown to be roots Jacobi polynomials with weights(3, 3). The HDQ rules together with the Gauss-Lobatto-Legendre integration rules were used to discretize the potential functional of thin plates in curvilinear domainto obtained HermiteDQFEM or weak form HDQ matrices. In comparison with Lagrange DQFEM results or available exact andother numerical results, high accuracy and rapid convergence were achieved without numerical stability even with a large number of sampling points, which indicates that the Hermite DQFEM has attractive potential as a novel numerical technique. | |||
TO cite this article:XING Yufeng,WU Yang. A Hermite differential quadrature finite element method and its application to free vibration of thin plates[OL].[ 9 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4732449 |
6. Application of multiscale asymptotic expansion method to three dimensional periodical composite structures | |||
GAO Yahe,XING Yufeng,LI Min | |||
Mechanics 04 May 2017 | |||
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Abstract:The decoupled Multiscale Asymptotic Expansion Method (MsAEM) is applied to the static analyses of three-dimensional (3D) periodical composite structures. The effects of perturbation orders, boundary conditions of unit cell problems and the derivatives of homogenized displacements on the accuracy are studied, the physical interpretation of the petrubation terms is revealed. By comprehensive results and comparisons, it is concluded that, 1) MsAEM can be viewed as the superposition method of different orders of admissible deformation modes represented by influence functions; 2) the second expansion term is leading in theoretical sense; 3) super unit cell approach and highly accurate differential quadrature method can improve the computational accuracy of influence functions and macro displacement derivatives; 4) the total potential energy functional is an effective method to evaluate the computational accuracy of displacements. | |||
TO cite this article:GAO Yahe,XING Yufeng,LI Min. Application of multiscale asymptotic expansion method to three dimensional periodical composite structures[OL].[ 4 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4732461 |
7. Fatigue physically short crack growth from a notch by plasticity-corrected stress intensity factor | |||
Li Meng,Menghao Yang,Zhonghua Li,Miaolin Feng | |||
Mechanics 02 May 2017 | |||
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Abstract:When a physically short crack propagates from a notch root, the crack growth rate shows a "V-shape" behavior, the rate firstly decreases and then increases with the crack growth. In this study, a plasticity-corrected stress intensity factor (PC-SIF) is applied to describe the effects of notch plastic zone and crack-tip plastic zone on the short crack growth in ductile materials under cyclic tensile load. Compact tension (CT) 1070 steel specimens with different notch sizes and loading ratios are examined. The "V-shape" curves of fatigue crack growth (FCG) data can be condensed into straight lines if the PC-SIF range was used due to the consideration of the influence of plastic zone near the notch root. The ratio between PC-SIF range and stress intensity factor (SIF) range can be fitted by exponential equations, and the expressions before and after the turning point of the "V-shape" curves are distinguish difference. | |||
TO cite this article:Li Meng,Menghao Yang,Zhonghua Li, et al. Fatigue physically short crack growth from a notch by plasticity-corrected stress intensity factor[OL].[ 2 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4729794 |
8. Vibration analysis of axially functionally graded beams with the composite element model | |||
LIU Jike,LV Zhongrong | |||
Mechanics 29 December 2016 | |||
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Abstract:This paper presents a simple yet accurate approach to analyze the free and forced vibrations of axially functionally graded (AFG) beams. The governing equations of the beam is derived by Lagrange's equations and then discretized by the composite element method. Numerical simulations are presented to show the effects of Young's modulus variation, mass density variation, and slenderness ratios, on the dynamic characteristics of the AFG beams. The natural frequencies obtained from the proposed method are found to be in close agreement with those from finite element and other methods. The forced vibration responses of the AFG beam are also calculated from the proposed method and compared with those obtained from the finite element method (FEM). Time histories from both methods are found to match very well. This further indicates the correctness of the present method for forced vibration analysis of the AFG beam. | |||
TO cite this article:LIU Jike,LV Zhongrong. Vibration analysis of axially functionally graded beams with the composite element model[OL].[29 December 2016] http://en.paper.edu.cn/en_releasepaper/content/4715329 |
9. A Two-step Approach for Damage Identification in Axially Functionally Graded Beams | |||
LIU Jike,LV Zhongrong | |||
Mechanics 29 December 2016 | |||
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Abstract:This study presents a two-stage approach based on residual force vector and response sensitivity analysis for structural damage identification in axially functionally graded (AFG) beams. The local damage is simulated by a reduction in the elemental Young's modulus of the beam. The residual force vector is used to find the possible damaged elements in the beam at first. Then, a hybrid objective function is established and a sensitivity-based model updating method is adopted to identify the perturbation of the stiffness parameter from the measured dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Damage identification results from measured natural frequencies and the dynamic responses from different excitation forces are compared. The effects of measurement noise on the identification results are investigated. Studies in this paper indicate that the proposed method is efficient and robust for identifying damages in the axially functionally graded beams. Good identified results can be obtained from the short time histories of a few number of measurement points and the first several natural frequencies. | |||
TO cite this article:LIU Jike,LV Zhongrong. A Two-step Approach for Damage Identification in Axially Functionally Graded Beams[OL].[29 December 2016] http://en.paper.edu.cn/en_releasepaper/content/4715444 |
10. A Globally Convergent and Closed Analytical Solution of Blasius Equation with its Approximation in Application | |||
ZHENG JUN | |||
Mechanics 16 November 2016 | |||
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Abstract:In this paper, a closed and globally convergent Analytical Solution (AS) was finally found for Blasius Equation (BE). The AS is concisely expressed by two power series. We found the inner boundary value of the $2^mathrm{nd}$ order derivative of the unknown function could also be exactly revealed by the convergence criterion, which is about $0.3320554$. Calculation directly based on the truncated AS shew a sound accordance with prior results. A method for approximately using the AS was also provided, even the $2^mathrm{nd}$ order approximation was found sufficiently accurate. Based on the AS, other problems coupled with laminar boundary layer, e.g. heat transfer on a semi-infinite plate with constant temperature could be analytically formulated subsequently. Besides, some higher order features on the wall of the boundary layer could be exactly found by the AS. Surely, positive significance could be also found in the area of differential equations, i.e. a class of nonlinear Ordinary Differential Equations (ODE) similar as BE could be analytically solved and analyzed. | |||
TO cite this article:ZHENG JUN. A Globally Convergent and Closed Analytical Solution of Blasius Equation with its Approximation in Application[OL].[16 November 2016] http://en.paper.edu.cn/en_releasepaper/content/4710204 |
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