Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory

2013 ◽  
Vol 103 ◽  
pp. 86-98 ◽  
Author(s):  
Jinseok Kim ◽  
J.N. Reddy
Keyword(s):  
Analytical Solutions ◽  
Couple Stress ◽  
Order Theory ◽  
Third Order ◽  
Bending Vibration

scholarly journals Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

2021 ◽  
Author(s):  
Ping-Cheng Hsieh ◽  
Tzu-Ting Huang
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Water Conservation ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Time Discretization ◽  
Third Order ◽  
Analytical And Numerical Solutions ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

Dynamic Analysis of a Functionally Greded Sandwich Beam Traversed by a Moving Mass Based on a Refined Third-Order Theory

2021 ◽  
pp. 301-315
Author(s):  
Le Thi Ngoc Anh ◽  
Tran Van Lang ◽  
Vu Thi An Ninh ◽  
Nguyen Dinh Kien
Keyword(s):  
Dynamic Analysis ◽  
Sandwich Beam ◽  
Order Theory ◽  
Moving Mass ◽  
Third Order

Asymptotic theory for third-order differential equations with extension to higher odd-order equations

1991 ◽  
Vol 117 (3-4) ◽  
pp. 215-223 ◽  
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Order Theory ◽  
Linear Differential Equations ◽  
Asymptotic Solutions ◽  
Third Order ◽  
Odd Order ◽  
Linear Differential ◽  
General Conditions

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. Theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.

Sign in / Sign up

Export Citation Format

Share Document