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Physical Sciences and Mathematics Commons™
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- Critical buckling load, Hollomon’s law, Axial plastic columns, High strength metals, Work-hardening (1)
- Finite element method (1)
- Finite element solution, Ritz-Galerkin method, Nonlinear Euler-Bernoulli beam, Power-law, Work hardening material, Hollomon's equation, Convergence, Error estimate, Hermite elements (1)
- Galerkin, Cauchy-Dirichlet (1)
- Generalized sine, Hamilton system, nonlinear spring, vibration, analytic solution (1)
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- Global solvability, fourth-order, nonlinear boundary value problems, monotone operator, Leray-Schauder fixed point theorem, coercivity (1)
- Heat transfer, Finite element solutions, Tubes, Power-law flows, Polymer flows, Viscous dissipation, Graetz-Nusselt (1)
- L2 estimates (1)
- Method of lines (1)
- Nonlinear acoustics, power-law fluids, traveling wave solutions, finite-scale Navier–Stokes equations (1)
- Power-law (1)
- Power-law, Stokes (1)
- Quasilinear parabolic problem (1)
- Traveling wave, Burgers' equation, Newtonian flows (1)
Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei
A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei
Dongming Wei
We study approximations of the steady state Stokes problem governed by the power-law model for viscous incompressible non-Newtonian flow using the penalty formulation. We establish convergence and find error estimates
Critical Buckling Loads Of The Perfect Hollomon’S Power-Law Columns, Dongming Wei, Alejandro Sarria, Mohamed Elgindi
Critical Buckling Loads Of The Perfect Hollomon’S Power-Law Columns, Dongming Wei, Alejandro Sarria, Mohamed Elgindi
Dongming Wei
In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Holloman’s power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and …
On The Global Solvability Of A Class Of Fourth-Order Nonlinear Boundary Value Problems, M.B.M. Elgindi, Dongming Wei
On The Global Solvability Of A Class Of Fourth-Order Nonlinear Boundary Value Problems, M.B.M. Elgindi, Dongming Wei
Dongming Wei
In this paper we prove the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of a Hollomon’s power-law plastic beam subject to an axial compression and nonlinear lateral constrains. For certain ranges of the acting axial compression force, the solvability of the equations follows from the monotonicity of the fourth order nonlinear differential operator. Beyond these ranges the monotonicity of the operator is lost. It is shown that, in this case, the global solvability may be generated by the lower order nonlinear terms of the equations for a certain type of constrains.
A Priori Lρ Error Estimates For Galerkin Approximations To Porous Medium And Fast Diffusion Equations, Dongming Wei, Lew Lefton
A Priori Lρ Error Estimates For Galerkin Approximations To Porous Medium And Fast Diffusion Equations, Dongming Wei, Lew Lefton
Dongming Wei
Galerkin approximations to solutions of a Cauchy-Dirichlet prob- lem governed by a generalized porous medium equation.
A Note On Acoustic Propagation In Power-Law Fluids: Compact Kinks, Mild Discontinuities, And A Connection To Finite-Scale Theory, Dongming Wei
Dongming Wei
Acoustic traveling waves in a class of viscous, power-lawfluids are investigated. Both bi-directional and unidirectional versions of the one-dimensional (1D), weakly-nonlinear equation of motion are derived; traveling wave solutions (TWS)s, special cases of which take the form of compact and algebraic kinks, are determined; and the impact of the bulk viscosity on the structure/nature of the kinks is examined. Most significantly, we point out a connection that exists between the power-law model considered here and the recently introduced theory of finite-scale equations.
Travelling Wave Solutions Of Burgers' Equation For Gee-Lyon Fluid Flows, Dongming Wei, Ken Holladay
Travelling Wave Solutions Of Burgers' Equation For Gee-Lyon Fluid Flows, Dongming Wei, Ken Holladay
Dongming Wei
In this work we present some analytic and semi-analytic traveling wave solutions of generalized Burger' equation for isothermal unidirectional flow of viscous non-Newtonian fluids obeying Gee-Lyon nonlinear rheological equation. The solution of Burgers' equation for Newtonian flow as a special case. We also derive estimates of shock thickness for non-Newtonian flows.
Traveling Wave Solutions Of Burgers’ Equation For Power-Law Non- Newtonian Flows, Dongming Wei, Harry Borden
Traveling Wave Solutions Of Burgers’ Equation For Power-Law Non- Newtonian Flows, Dongming Wei, Harry Borden
Dongming Wei
In this work we present some analytic and semi-analytic traveling wave solutions of a generalized Burgers' equation for unidirectional flow of power-law non-Newtonian fluids. The solutions include the corresponding well-known traveling wave solution of the Burgers' equation for Newtonian flows. We also derive estimates of shock thickness for the power-law flows.
Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu
Analytic And Finite Element Solutions Of The Power-Law Euler-Bernoulli Beams, Dongming Wei, Yu Liu
Dongming Wei
In this paper, we use Hermite cubic finite elements to approximate the solutions of a nonlinear Euler-Bernoulli beam equation. The equation is derived from Hollomon’s generalized Hooke’s law for work hardening materials with the assumptions of the Euler-Bernoulli beam theory. The Ritz-Galerkin finite element procedure is used to form a finite dimensional nonlinear program problem, and a nonlinear conjugate gradient scheme is implemented to find the minimizer of the Lagrangian. Convergence of the finite element approximations is analyzed and some error estimates are presented. A Matlab finite element code is developed to provide numerical solutions to the beam equation. Some …
Some Generalized Trigonometric Sine Functions And Their Applications, Dongming Wei, Yu Liu, Mohamed B. Elgindi
Some Generalized Trigonometric Sine Functions And Their Applications, Dongming Wei, Yu Liu, Mohamed B. Elgindi
Dongming Wei
In this paper, it is shown that D. Shelupsky's generalized sine function, and various general sine functions developed by P. Drabek, R. Manasevich and M. Otani, P. Lindqvist, including the generalized Jacobi elliptic sine function of S. Takeuchi can be defined by systems of first order nonlinear ordinary differential equations with initial conditions. The structure of the system of differential equations is shown to be related to the Hamilton System in Lagrangian Mechanics. Numerical solutions of the ODE systems are solved to demonstrate the sine functions graphically. It is also demonstrated that the some of the generalized sine functions can …
Existence, Uniqueness, And Numerical Analysis Of Solutions Of A Quasilinear Parabolic Problem, Dongming Wei
Existence, Uniqueness, And Numerical Analysis Of Solutions Of A Quasilinear Parabolic Problem, Dongming Wei
Dongming Wei
A quasilinear parabolic problem is studied. By using the method of lines, the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown. Also given are L2 error estimates for the error between the extended fully discrete finite element solutions and the exact solution.
Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo
Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo
Dongming Wei
This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. Aviscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.
Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang
Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang
Dongming Wei
In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.