Professor
Research Interest
Nonlinear differential equations with industrial applications; Modeling, numerical simulations, finite element analysis, symbolic computation, application of simulation software; Stability and integrity of structures of advanced materials with applications in energy and bio-medical engineering, MEMS and NEMS; Non-Newtonian flows and polymer extrusion; Interdisciplinary research; Actuarial mathematics.
The nonlinear differential equations arise from nonlinear material constitutive equations and the continuum mechanics of solids and fluids. For numerical simulations and analysis, lumped parameter models; asymptotic and perturbation methods, finite element and finite difference methods, symbolic and numerical computation software (Matlab, Methamtica, Ansys, Comsol, Maple, and Abaqus) are developed and integrated with synergistic and interdisciplinary research collaborations. For industries, my research interests are in three application areas: 1) Developing novel optimal design methodology, design equations, and algorithms for design of polymer thin sheets and coating die interior geometric flow channels; 2) Optimal design of resonators for Microelectromechanical systems (MEMS) using advanced materials such as graphene and heat-treated metals; and 3) Stability of aerospace and energy structures made of advanced materials with built-in internal shear rate dependency damping, such as metal rubber and INVAR.
Dongming Wei is a full Professor in the Department of Mathematics of Nazarbayev University, he joined the Mathematics faculty in June of 2014. He obtained his BS Degree in Mathematics from Guangxi University in 1982 and his PhD in Applied Mathematics from Michigan State University in 1988. Prior to SST he held assistant, associate, and full professor positions at University of New Orleans from 1988 to 2014. His research portfolio includes nonlinear finite element analysis of engineering problems in solid and fluid mechanics, modeling of graphene based structural materials, modeling of human eye and cancer cells, modeling of soil foundations and landslides, modeling of porous medium flows at high Reynolds numbers, computational non-Newtonian thermal flows in extrusion dies, numerical solutions of nonlinear option price equations.
Research Grants
- D. Wei (PI) et al, Modeling and Simulation of Nonlinear Material Structures for Mechanical Pressure Sensing and Actuation Applications, ORAU grant- ID: 090118FD5347, 2017- 2020: US$150,000.00.
- D. Wei (PI) et al, Development and Prototyping of Extrusion Dies for Advanced Plastic Sheets and Thin Film Production, Kazakhstan Ministry of Education and Science (MES) Grant, AP05134166, 2018-2020: US$ 140,000.
- D. Wei (PI) et al, Design & Development of Multiphysics Algorithm for Polymer Sheet Processing Die Design, Faculty Development Grant, 021220FD4651, 2021-2023: US$150,000.00.
- D. Wei (PI) et al, Engineering design of high precision polymer sheet/film extrusion dies, Commercialization Grant, 2024-2026: US$ 140,000/Yr.
- Co-PI with Christa Spitas (PI) et al, Rapid Response Fixed Astronomical Telescope for Gamma Ray Bust Observation, Nazarbayev University Collaborative Research Grants Program, 2020-2023: US$449,820.00.
- Co-PI with Dichuan Zhang (PI) et al, Multi-layered Inertial Reactive Armour, MES Grant AP09259703, 2021-2023: US$140,000.
- Co-PI with Yong Zho (PI) et al, High-fidelity concurrent multidisciplinary design optimization based on arbitrary hybrid turbulence modelling and fully coupled FSI, Faculty Development Grant, 20122022FD4126, 2023-2026: US$150,000.00.
Capstone Research Projects
- Nonlinear Spring and Dynamics of Graphene in Micro-Electro-Mechanical Systems, Zhassulan Kazbek, 2015 (the results lead to a journal paper published in 2017).
- Application of Finite Element Analysis on Viscous non-Newtonian fluids, Narken Aimambet, 2016.
- Modeling of Ocular Lamina Cribrosa by Nonlinear Differential Equations, Alya Jangabylova and Aidana Zhalgas, Co-adviser Prof. M.W.L Ko (SENG), 2016.
- Finite Element Solutions of the RAPM Model in Option Pricing, Laila Zhexembay and Andrey Pak, 2016.
- Estimating Insurance Premiums for Alzheimer disease, Aitore Issadykova, 2017.
- Comparison of Advanced Logistic Model with Gompertz and Logistic Models, Rassulla Kari, 2017.
- Advanced Logistic Model Analysis, Rustam Bekishev, 2017.
- Life Insurance for Breast Cancer Patients, Anel Sotsialova, 2017.
- Actuarial Applications of a Two-parameter Generalized Logistic Model, Nargiz Alekberova, 2018
- Copulas and Correlation in Statistical Risk Theory, Sara Rat, 2018
- Estimation and Application of best ARIMA Model for Forecasting the Uranium Price, Medeu Amanngeldi, 2018
- Copula functions in Credit Metrics’ VaR estimation, Shynggys Magzanov 2019
- Finite Element Method for Retaining Walls Subjected to Swelling Pressure, Mansur Shakipov, 2020
- Modeling Dependencies Between Exchange Rates Using Time Invariant and Time-varying Copulas, Asem Adil, 2020
Textbook:
Introduction to Finite Element Analysis-A Computational Approach, Springer- Birkhäuser (http://www.springer.com/us/book/9780817643089)
Journal papers:
[1] D. Wei, Y. A. Erlangga, G. Zhumakhanova, A finite element approach to the numerical solutions of Leland’s model, International Review of Economics & Finance, available online, August (2023). Impact factor: 4.77, Q1.
[2] D. Wei, A. Aniyarov, D. Zhang, C. Spitas, D. Nurakhmetov, A. Amrin, Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams, Alexandria Engineering Journal, Vol. 78, (2023) 246-255. Impact factor: 6.626, Q1.
[3] S. Batay, B. Kamalov, D. Zhangaskanov, Y. Zhao, D. Wei, T. Zhou, and X. Su, Adjoint-Based High-Fidelity Concurrent Aerodynamic Design Optimization of Wind Turbine, Fluids, (2023) 8(3), 85. Impact Factor: 1.9, Q2.
[4] D. Wei, D. Nurakhmetov, A. Aniyarov, D. Zhang, C. Spitas, Lumped-parameter model for dynamic monolayer graphene sheets, Journal of Sound and Vibration, Vol. 534, 15 (2022) 117062. Impact factor: 4.71, Q1.
[5] A. Razeghiyadaki, D. Wei, A Perveen, D. Zhang, Y. Wang, Effects of Melt Temperature and Non-Isothermal Flow in Design of Coat Hanger Dies Based on Flow Network of Non-Newtonian Fluids, Polymers, 14 (2022) 3161. Impact factor: 4.967, Q1.
[6] M. Amengeldi, D. Wei, A. Perveen, D. Zhang, Y. Wang, An Iterative Approach for the Parameter Estimation of Shear-Rate and Temperature-Dependent Rheological Models for Polymeric Liquids, Polymers, 13 (2021) 4185. Impact factor: 4.967, Q1.
[7] D. Wei, D. Nurakhmetov, A. Aniyarov, D. Zhang, C. Spitas, Nonlinear Dynamical Analysis of Some MEMS Resonators with Internal Damping, Acta Mechanica Sinica, (2021) 1-10. Impact factor: 2.910, Q1.
[8] A Razeghiyadaki, D Zhang, D Wei, A Perveen, Optimization of Polymer Extrusion Die Based on Response Surface Method, Processes, Vol.8, 9, (2020) 1043-1055. Impact factor: 3.31, Q2.
[9] R. J. Giardina, D. Wei, Ramberg–Osgood material behavior expression and large deflections of Euler beams, Mathematics and Mechanics of Solids, 26 (2) (2020) 179-198. Impact factor: 2.74, Q2.
[10] P. Skrzypacz, D. Nurakhmetov, D. Wei, Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams, Acta Mechanica Sinica 36 (1), (2020) 160-175. Impact factor: 2.910, Q1.
[11] A. Razeghiyadaki, D. Zhang, D. Wei, A. Perveen, Optimization of polymer extrusion die based on response surface method, Processes, 8 ( 2020) 1043. Impact factor: 3.31, Q2.
[12] Dynamic pull-in for micro–electromechanical device with a current-carrying conductor J.H. He, D. Nurakhmetov, P. Skrzypacz, D. Wei, Journal of Low Frequency Noise, Vibration and Active Control, (2019) Impact factor: 2.368, Q1.
[13] P. Skrzypacz, S. Kadyrov, D. Nurakhmetov, D. Wei, Analysis of dynamic pull-in voltage of a graphene MEMS model, Nonlinear Analysis: Real World Applications 45, (2019) pp.581-589.
Impact factor: 2.765, Q1.
[14] M. Ghazy, M.B. Elgindi, D. Wei, Analytical and numerical investigations of the collapse of blood vessels with nonlinear wall material embedded in nonlinear soft tissues, Alexandria engineering journal, 57 (4), (2018) 3437-3450. Impact factor: 6.626, Q1.
[15] M. B. M. Elgindi, D. Wei and Y. Liu, Buckling and Post-Buckling of Graphene Tubes, Mechanics of Advanced Materials and Structures, Vol. 23,Issue 4 (2016) 402-406. Impact factor: 3.338 Q1.
[16] M.B.M. Elgindi, D. Wei, Y. Liu, K. Kamran, and H.L. Xu, Buckling and Deformation of Hollomon’s Power-Law Tubes, Thin-Walled Structures, Vol. 74, (2014) 213 – 221. Impact factor: 5.881, Q1.
[17] D. Wei and P. Jordan, A note on acoustic propagation in power-law fluids: Compact kinks, mild discontinuities, and a connection to finite-scale theory, International Journal of Non-Linear Mechanics, 48 (2013) 72-77. Impact factor: 3.336, Q1
[18] D. Wei, M. B. M. Elgindi, and A. Sarria, Critical Buckling Loads of the Perfect Hollomon’s Power-law Columns, Mechanics Research Communications, Vol. 47 (2013) 69-76. Impact factor: 2.71, Q2.
[19] D. Wei and Y. Liu, Analytic and finite element solutions of the power-law Euler-Bernoulli beams, Finite Elements in Analysis & Design, 52 (2012), 31-40. Impact factor: 2.618, Q1.
[20] D. Wei and H.B. Luo, Finite element solutions of heat transfer in molten polymer flow in tubes with viscous dissipation, co-author H.B. Luo, International J. of Heat and Mass Transfer, Vol. 46, Issue 16, (2003), 3097-3708. Impact factor: 5.431 Q1.
[21] L. Lefton and D. Wei, Numerical approximation of the first eigenpair of the p-laplacian using finite elements and thepenalty method, Numerical Functional Analysis and Optimization, Vol. 18, 3-4 (1997) 389-399.
[22] D. Wei and L. Lefton, A priori Lp error estimates for Galerkin approximations to porous medium and fast diffusion equations, Mathematics of computation, Vol. 68, 227 (1999) 971-989.
[23] D. Wei, Existence, uniqueness, and numerical analysis of solutions of a quasilinear parabolic problem, SIAM journal on numerical analysis, Vol. 29, 2. 484-497.
Other Noticeable Items
[1] Two of my papers were chosen by the Target Selection Team of Advances in Engineering Ltd –A Canadian Establishment (https://advanceseng.com/?s=Dongming+Wei) which alerts the scientific community to breaking journal articles considered to be of importance to the progress in Engineering technologies.
[2] Republic of Kazakhstan Patent: No. 7631: D. Wei, P. Asma, D. Zhang, D. Igali, 2022.
TEACHING PORTFOLIO (Courses):
(BS):
- Math471 – Nonlinear Differential Equations,
- Math 477 – Applied Finite Element Method,
- Math 476-Numerical PDEs,
- Math 412-Nonlinear Optimization,
- Math 322-Actuarial Financial Math,
- Math 423-Actuarial Models of Life Contingency,
- Math 310-Introduction Applied Statistics,
- Math 481-Partial Differential Equations,
- Math 499-Graduation Project (Capstone),
(MS Applied Math)
- Math 571- Nonlinear Differential Equations,
- Math 517-Mathematical Modeling and Simulation,
- Math 518- Applied Finite Element Method,
- Math 576-Numerical Methods for PDEs,
- Math 512- Optimization Methods and Techniques,
- Math 551-Advanced Numerical Methods,
- Math 514 Operations Research
(Ph.D)
- Math 676-Partial Differential Equations,
- Math 771- Nonlinear Differential Equations,
- Math 776 Advanced Numerical PDES