scholarly journals One-Dimensional and Two-Dimensional Analytical Solutions for Functionally Graded Beams with Different Moduli in Tension and Compression

Materials ◽  
2018 ◽  
Vol 11 (5) ◽  
pp. 830 ◽  
Author(s):  
Xue Li ◽  
Jun-yi Sun ◽  
Jiao Dong ◽  
Xiao-ting He
Keyword(s):  
Analytical Solutions ◽  
Functionally Graded ◽  
Two Dimensional ◽  
One Dimensional ◽  
Tension And Compression

scholarly journals One-Dimensional Theoretical Solution and Two-Dimensional Numerical Simulation for Functionally-Graded Piezoelectric Cantilever Beams with Different Properties in Tension and Compression

Polymers ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1728 ◽  
Author(s):  
Xiao-Ting ◽  
Zhi-Xin ◽  
Hong-Xia ◽  
Jun-Yi
Keyword(s):  
Numerical Simulation ◽  
Cantilever Beam ◽  
Functionally Graded ◽  
Theoretical Solution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Analysis And Design ◽  
Piezoelectric Cantilever ◽  
Tension And Compression ◽  
Functionally Graded Piezoelectric

The existing studies indicate polymers will present obviously different properties in tension and compression (bimodular effect) which is generally ignored because of the complexity of the analysis. In this study, a functionally graded piezoelectric cantilever beam with bimodular effect was investigated via analytical and numerical methods, respectively, in which a one-dimensional theoretical solution was derived by neglecting some unimportant factors and a two-dimensional numerical simulation was performed based on the model of tension-compression subarea. A full comparison was made to show the rationality of one-dimensional theoretical solution and two-dimensional numerical simulation. The result indicates that the layered model of tension-compression subarea also makes it possible to use numerical technique to simulate the problem of functionally graded piezoelectric cantilever beam with bimodular effect. Besides, the modulus of elasticity E* and the bending stiffness D* proposed in the one-dimensional problem may succinctly describe the piezoelectric effect on the classical mechanical problem without electromechanical coupling, which shows the advantages of one-dimensional solution in engineering applications, especially in the analysis and design of energy harvesting/sensing/actuating devices made of piezoelectric polymers whose bimodular effect is relatively obvious.

scholarly journals Analytical solutions for the neutron transport using the spectral methods

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Abdelouahab Kadem
Keyword(s):  
Analytical Solutions ◽  
Spectral Methods ◽  
Chebyshev Polynomials ◽  
Neutron Transport ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Multidimensional Problems ◽  
Dimensional Equation ◽  
Transport Problems

We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independant variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems.

scholarly journals Peristatic solutions for finite one- and two-dimensional systems

2016 ◽  
Vol 22 (8) ◽  
pp. 1639-1653 ◽  
Author(s):  
Vinesh V Nishawala ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Numerical Method ◽  
Continuum Mechanics ◽  
Analytical Solutions ◽  
Differential Form ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Nonlocal Continuum ◽  
One Dimensional ◽  
Static Version ◽  
Special Case

Peridynamics is a nonlocal continuum mechanics theory where its governing equation has an integro-differential form. This paper specifically uses bond-based peridynamics. Typically, peridynamic problems are solved via numerical means, and analytical solutions are not as common. This paper analytically evaluates peristatics, the static version of peridynamics, for a finite one-dimensional rod as well as a special case for two dimensions. A numerical method is also implemented to confirm the analytical results.

scholarly journals Performance analysis and optimization of rectangular fin arrays used in plate-fin heat exchangers

2020 ◽  
pp. 213-213
Author(s):  
Weicheng Wu ◽  
Hassan Soliman
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Performance Analysis ◽  
Aspect Ratio ◽  
Analytical Solutions ◽  
Heat Exchangers ◽  
Two Dimensional ◽  
One Dimensional ◽  
Independent Parameters

This paper deals with longitudinal rectangular fin arrays used in plate-fin heat exchangers. The temperature distribution and rate of heat transfer were obtained using one dimensional (1-D) and two-dimensional (2-D) solutions. The ranges of independent parameters within which the 1-D solution was within 1% from the 2-D solution were determined. Simple analytical solutions were determined for the rate of heat transfer, fin effectiveness, and augmentation factor. The aspect ratio at which the rate of heat transfer reached a maximum was determined, as well as the corresponding effectiveness and augmentation factor.

Effect of Viscosity on Gaseous Flow in a Micro-Nozzle

2004 ◽  
Author(s):  
Shintaro Murakami ◽  
Yutaka Asako
Keyword(s):  
Heat Conduction ◽  
Analytical Solutions ◽  
Two Dimensional ◽  
Arbitrary Lagrangian Eulerian ◽  
Numerical Computations ◽  
Gaseous Flow ◽  
One Dimensional ◽  
Micro Nozzle ◽  
Wide Range ◽  
Energy Equations

Two-dimensional compressible momentum and energy equations are solved numerically to obtain the effect of viscosity on gaseous flow in a micro converging-diverging nozzle. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The numerical computations were performed for a wide range of the diverging angle and throat height and for no-heat conduction flow. The results are compared with one-dimensional analytical solutions for flow in a conventional sized nozzle and the effects of the viscosity on gaseous flow in the micro-nozzle are discussed.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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