Algorithm of DRM with Kinetic Damping for Finite Element Static Solution of Strain-Softening Structures by Wei Wang, Xiaozu Su

“…In order to deal with the divergence and instability due to the ill-posedness of the nonlinear finite element (FE) model of strain-softening structure in implicit static analysis, the dynamic relaxation method (DRM) was used with kinetic damping to solve the static increments in the incremental solution procedure so that the problem becomes well-posed. …”
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Evaluation of Sustainability of Brazilian Ethanol Production: A model in System Dynamics by Arnoldo Jose de Hoyos Guevara, Orlando Roque da Silva, Haroldo Lhou Hasegawa, Délvio Venanzi

“…This approach is based on mathematical concepts of nonlinear processes developed in mathematics and physics and consolidated in engineering. …”
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DYNAMIC MODELING AND SIMULATION OF ROLLING BEARING WITH PITTING FAILURE by ZHANG HuiLing, LV FuLing

“…The five degree of freedom dynamic model of rolling bearing system with local fault is established by considering the nonlinear factors such as oil film and the sliding of rolling element. …”
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Efficient Neural Network Modeling for Flight and Space Dynamics Simulation by Ayman Hamdy Kassem

“…For linear flight/space dynamics systems, the technique can find the network weights and biases directly by solving a system of linear equations without the need for training. Nonlinear flight dynamic systems can be easily modeled by training its linearized models keeping the same network structure. …”
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Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces by Junaid Ahmad, Kifayat Ullah, Hüseyin Işik, Muhammad Arshad, Manuel de la Sen

“…We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. …”
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Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients by Dumitru Vieru, Constantin Fetecau, Nehad Ali Shah, Jae Dong Chung

“…The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. …”
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Slip Effect on MHD Chemically Reacting Convictive Boundary Layer Flow with Heat Absorption by Mekonnen Shifferaw Ayano, Negussie Tadege Demeke

“…The system of coupled nonlinear equations is solved numerically and the effects of various parameters on the velocity, the microrotation, the temperature, and the concentration field are calculated. …”
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Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

“…The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. …”
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Turing patterns in a networked vegetation model by Xiaomei Bao, Canrong Tian

“…The parameter space of Turing patterns for plant behavior is obtained based on the analysis of the eigenvalues of the Laplacian of weighted graph, while the amplitude equation determining the stability of Turing patterns is obtained by weakly nonlinear analysis. We also show that the optimal rainfall is only determined by the density of the water. …”
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Dynamic Analyses of Isolated Structures under Bi-Directional Excitations of Near-Field Ground Motions by Gokhan Ozdemir, Ugurhan Akyuz

“…Nonlinear response history analyses (NRHA) of a 3-story isolated reinforced concrete (RC) building are carried out under both uni- and bi-directional earthquake excitations of near-field records. …”
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The Exact Linearization and LQR Control of Semiactive Connected Hydropneumatic Suspension System by Xuyang Cao, Linlin Cao, Dianlong Wang

“…Based on differential geometry theory, the nonlinear system of connected hydropneumatic suspension was transformed to a linear one. …”
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Synchronization of Different Uncertain Fractional-Order Chaotic Systems with External Disturbances via T-S Fuzzy Model by Lin Wang, Jinbo Ni, Chunzhi Yang

“…T-S fuzzy models are employed to approximate the unknown nonlinear systems and tracking error signals are used to update the parametric estimates. …”
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BOLT COUPLING STRUCTURE OF CONTACT STRESS AND THE INFLUENCE FACTORS OF JOINT STIFFNESS by YANG Hui, HAN Jiang, CHU XiangQian

“…Considering the nonlinear factors,the contact and friction between plates as well as bolt and plates,bolt preload,etc,three-dimensional finite element model bolted structure was developed. …”
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Geometric Meshing Simulation Analysis of Zero Spiral Bevel Gear by Zhou Jiaojun

“…The contact path and transmission error curve are obtained by solving the nonlinear equations system. Then,the major axis of instantaneous contact ellipse is calculated based on differential geometry. …”
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THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION by A. Tarasenko, I. Egorova

“…The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. …”
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Chaos and Control in Coronary Artery System by Yanxiang Shi

“…Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. …”
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On the Definitions of Nabla Fractional Operators by Thabet Abdeljawad, Ferhan M. Atici

“…We formalize initial value problems for nonlinear fractional difference equations as an application of our findings. …”
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Finite-Time Synchronization for Complex-Valued Recurrent Neural Networks with Time Delays by Ziye Zhang, Xiaoping Liu, Chong Lin, Bing Chen

“…To achieve our aim, a nonlinear delayed controller with two independent parameters different from the existing ones is provided, which leads to great difficulty. …”
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A Novel System and Iterative Schemes for Generalized Variational Inclusion Problems and its Approximation Solvability by Mohd Sarfaraz, Md. Kalimuddin Ahmad

“…Here in this study, we investigate the approximation solvability of solutions for the system of generalized nonlinear ordered variational inclusions using an iterative algorithm under some apt conditions. …”
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Nanoscale nonlocal thermal transport and thermal field emission in high-current resonant tunnel structures by Michael V. Davidovich, Igor S. Nefedov, Olga E. Glukhova, J. Miguel Rubi

“…Abstract We present a nonlinear model of thermal field emission in resonant tunneling nanostructures with multiple barriers and potential wells, based on an accurate determination of the quantum potential shape and a rigorous solution of the Schrödinger equation, while considering thermal balance. …”
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