Second order algorithm with convergence analysis for viscoelastic flow model by Chinedu Nwaigwe, Sanda Micula

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Mathematical modeling of two-phase compressible fluid filtration based on modified adaptive method of minimum amendments by Alexander I. Sukhinov, Lusine A. Grigoryan, Andrey A. Sukhinov

“…A two-layer iterative method of the variational type - a modified method of minimal amendments adapted for solving finite-difference equations of the two-phase compressible fluid with a non-selfadjoint operator under the most general assumptions on the properties of the grid-problem operator is built. …”
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Numerical schemes for 3D parabolic problem with non-local boundwy condition by Raimondas Čiegis, Mečislovas Meilūnas, Olga Subač

“… Two finite difference schemes are used to solve the 3D parabolic problem with a non-local boundary condition. …”
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Study on the Shear Lag Calculation Method for Damaged Box Girder by Yulong Zhang, Junguang Wang, Xiaoguang Wu, Jiahao Yin, Yuanxu Shi

“…Predicted upper-flange stresses differ from measured values by 5.7–13.6% and from finite element results by less than 10% for damage ratios up to 40%. …”
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A High Accuracy Local One-Dimensional Explicit Compact Scheme for the 2D Acoustic Wave Equation by Mengling Wu, Yunzhi Jiang, Yongbin Ge

“…Based on the local one-dimensional (LOD) method and Padé difference approximation, a fourth-order accuracy explicit compact difference scheme is proposed. …”
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Finite Element Simulation Analysis of Dynamic Contact Characteristic of Deep Groove Ball Bearing by Bai Guicai, Shentu Liufang

“…A multi-body dynamic contact finite element model of a deep groove ball bearings that be used in planetary gear is established in LS-DYNA,based on explicit dynamics finite element method,considering effect of rotational speed of bearing outer ring,radial load and rotational speed of carrier,the simulation analysis of dynamic contact characteristic（displacement,velocity,stress and contact force）under different working conditions are carried out,the dynamic contact response of the bearing is obtained.The study shows that the rolling exist revolution and rotation movement during operation,the maximum and the minimum line speed occurred at the contact point with the outer ring and the inner ring.The maximum stress occurred when the rolling contact with outer ring or inner ring,and the influence of the rotational speed to the maximum stress is little.It is proved reliable based on the simulation results compared with Hertz solution.The contacting force fluctuation between the rolling and cage is bigger than that and the inner or outer ring,but the value is the minimum,the contacting force value between the rolling and the outer ring or inner is almost same with the radial load.…”
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An exact implementation of the generalized Zhang-Zhu criterion for elasto-plastic finite element calculations by Lianjin Tao, Linkun Huang, Xu Zhao, Johan Clausen, Qi Zhang, Boyang Jiao, Hehua Zhu

“…The return mapping is employed to compute the updated stress and consistent stiffness matrix, facilitating calculations using both finite element implicit and explicit algorithms. Finally, the accuracy of the proposed method is validated using rock true triaxial test data and semi-analytical solutions for stresses and displacement around a circular opening under the GZZ criterion.…”
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Numerical Simulation of Finite Deformations of a Dynamically Loaded Elasto-Viscoplastic Circular Membrane by W. Dornowski

“…The theory is completed by an algorithm of the explicit finite difference method. With respect to the conditional stability of that method, the stability criterion is given. …”
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Finite mixtures of functional graphical models: Uncovering heterogeneous dependencies in high-dimensional data. by Qihai Liu, Kevin H Lee, Hyun Bin Kang

“…Graphical models have been widely used to explicitly capture the statistical relationships among the variables of interest in the form of a graph. …”
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The “Projection-by-Projection” (PbP) criterion for multiaxial random fatigue loadings by Denis Benasciutti, Davide Zanellati, Alessandro Cristofori

“…A first numerical example is then illustrated, in which various types of biaxial random stress are applied to three materials with different tension/torsion fatigue properties. Results of each analysis step are displayed explicitly to allow a plain understanding of how the PbP method works. …”
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Computational study of fluid forces over a cylinder attached with elastic beam: A finite element-based simulations by Yasir Arif, Rashid Mahmood, Mehdi Tlija, Afraz Hussain Majeed, Kamran Usman, Ehab Seif Ghith

“…The discrete systems are solved using a Newton method that employs split differences to explicitly generate the Jacobian matrices. …”
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Numerical study on the influence of material heterogeneity on mode III crack propagation using a phase-field model by Alfat S., Eso R., Barata L. O. A., Rianse M. S.

“…In this study, we investigate the influence of material heterogeneity on mode III crack growth using a phase-field model. The phase-field method offers a powerful computational framework for simulating crack initiation, propagation, and branching without explicitly tracking the crack surface. …”
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Finite-Time Synchronization and Practical Synchronization for Caputo Fractional-Order Fuzzy Cellular Neural Networks with Transmission Delays and Uncertainties via Information Feed... by Hongguang Fan, Hui Wen, Kaibo Shi, Anran Zhou

“…Namely, changing one of the feedback terms from positive to negative can cause PFT synchronization to switch to FT synchronization via adjusted control parameters, making our control methods applicable to different scenarios. The settling time depends explicitly on feedback coefficients, initial conditions, and fractional order.…”
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Bio-Inspired Thin-Walled Straight and Tapered Tubes with Variable Designs Subjected to Multiple Impact Angles for Building Constructions by Quanjin Ma, Nor Hazwani Mohd Yusof, Santosh Kumar Sahu, Yiheng Song, Nabilah Afiqah Mohd Radzuan, Bo Sun, Ahmad Yunus Nasution, Alagesan Praveen Kumar, Mohd Ruzaimi Mat Rejab

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Analysis of Fatigue Performance of Metallic Components with Gradient Microstructures by Pandi Zhao, Liheng Tuo, Hongrui Zhang, Zhiyan Sun, Shuai Ren, Gaihuan Yuan, Zebang Zheng

“…Based on this method, a macroscopic finite element model was developed to simulate the plastic strain accumulation and springback of the sealing ring in service. …”
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DYNAMIC CHARACTERISTICS OF INTERNAL CONTACT OF ROLLING BEARINGS UNDER DIFFERENT DEGREES OF FAILURE by TU WenBing, YANG JinWen, LUO Ya, REN JiWen

“…The effectiveness of the model was verified by the experiment on the outer ring fault of the rolling bearing. Based on the explicit dynamics method,the dynamic contact force between the rolling element and each component and the contact strain of the fault area was analyzed,then the influence law of different fault degrees on the internal dynamic characteristics of the bearing and the change law of the contact deformation under the fault condition were revealed. …”
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Akhmediev Breathers and Kuznetsov–Ma Solitons in the Cubic-Quintic Nonlinear Schrödinger Equation by Changchang Pan, Gangzhou Wu, Lei Zhang, Huicong Zhang

“…We used the Darboux transformation method to obtain explicit analytical solutions for the Akhmediev breather, the Kuznetsov-Ma soliton, and the Peregrine soliton of the cubic-quintic nonlinear Schrödinger equation. …”
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Modeling of Unsteady Flow through the Canals by Semiexact Method by Farshad Ehsani, Seyed Ghorban Hosseini, Hossein Soury

“…In this paper the Saint Venant equations and continuity equation are solved with homotopy perturbation method (HPM) and comparison by explicit forward finite difference method (FDM). …”
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Size-dependent nonlinear bending of microbeams based on a third-order shear deformation theory by Ngoc Duyen Dang, Dinh Kien Nguyen, Cong Ich Le

“…Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. …”
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Application of Homogenization Method in Free Vibration of Multi-Material Auxetic Metamaterials by Kadir Gunaydin, Orhan Gülcan, Aykut Tamer

“…However, due to the higher computational time spent on the modelling of lattice structures, different methods have been investigated to accurately predict mechanical properties. …”
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