scholarly journals Effective Properties of Nonlinear Laminated Composites With Perfect Adhesion

2005 ◽  
Vol 73 (1) ◽  
pp. 174-178 ◽  
Author(s):  
F. Lebon ◽  
R. Rodríguez-Ramos ◽  
J. C. Lopez-Realpozo ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Diaz ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Effective Properties ◽  
Laminated Composites ◽  
Laminated Composite ◽  
Nonlinear Problems ◽  
Dimensional Problem ◽  
Numerical Examples ◽  
One Dimensional ◽  
Theoretical Results ◽  
Perfect Adhesion

This paper is devoted to the homogenization of a nonlinear one-dimensional problem as a particular case of laminated composite and its solution by a Wavelet-Galerkin method. This approach is an extension of this method to nonlinear problems. Theoretical results are given and numerical examples are presented.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Error Bound ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Time Stepping ◽  
Theoretical Results

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

Analysis of Geometrically Consistent Schemes with Finite Range Interaction

2017 ◽  
Vol 22 (5) ◽  
pp. 1333-1361
Author(s):  
Hongliang Li ◽  
Pingbing Ming
Keyword(s):  
Error Estimate ◽  
Numerical Experiments ◽  
Optimal Error Estimate ◽  
Finite Range ◽  
Dimensional Problem ◽  
Optimal Error ◽  
Range Interaction ◽  
One Dimensional ◽  
Sharp Stability ◽  
Theoretical Results

AbstractWe analyze the geometrically consistent schemes proposed by E. Lu and Yang [6] for one-dimensional problem with finite range interaction. The existence of the reconstruction coefficients is proved, and optimal error estimate is derived under sharp stability condition. Numerical experiments are performed to confirm the theoretical results.

Theoretical and experimental investigations of the reflexion of normal shock waves with vibrational relaxation

1967 ◽  
Vol 30 (1) ◽  
pp. 51-64 ◽  
Author(s):  
N. H. Johannesen ◽  
G. A. Bird ◽  
H. K. Zienkiewicz
Keyword(s):  
Shock Wave ◽  
Vibrational Relaxation ◽  
Experimental Investigations ◽  
Rayleigh Line ◽  
Dimensional Problem ◽  
Density Measurements ◽  
Wave Characteristic ◽  
One Dimensional ◽  
The One ◽  
Theoretical Results

The one-dimensional problem of shock-wave reflexion with relaxation is treated numerically by combining the shock-wave, characteristic, and Rayleigh-line equations. The theoretical results are compared with pressure and density measurements in CO2, and the agreement is found to be excellent.

scholarly journals Positive Solutions for Discrete Boundary Value Problems to One-Dimensionalp-Laplacian with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Linjun Wang ◽  
Xumei Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Numerical Examples ◽  
One Dimensional ◽  
Existence Of Positive Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Theoretical Results

We study the existence of positive solutions for discrete boundary value problems to one-dimensionalp-Laplacian with delay. The proof is based on the Guo-Krasnoselskii fixed-point theorem in cones. Two numerical examples are also provided to illustrate the theoretical results.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

scholarly journals Comparative study of elastic properties and mode I fracture energy of carbon nanotube/epoxy and carbon fibre/epoxy laminated composites

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Jyotikalpa Bora ◽  
Sushen Kirtania
Keyword(s):  
Carbon Nanotube ◽  
Carbon Fibre ◽  
Fracture Energy ◽  
Elastic Properties ◽  
Volume Fraction ◽  
Laminated Composites ◽  
Laminated Composite ◽  
Fe Analysis ◽  
Mode I ◽  
Mode I Fracture

Abstract A comparative study of elastic properties and mode I fracture energy has been presented between conventional carbon fibre (CF)/epoxy and advanced carbon nanotube (CNT)/epoxy laminated composite materials. The volume fraction of CNT fibres has been considered as 15%, 30%, and 60% whereas; the volume fraction of CF has been kept constant at 60%. Three stacking sequences of the laminates viz.[0/0/0/0], [0/90/0/90] and [0/30/–30/90] have been considered in the present analysis. Periodic microstructure model has been used to calculate the elastic properties of the laminated composites. It has been observed analytically that the addition of only 15% CNT in epoxy will give almost the same value of longitudinal Young’s modulus as compared to the addition of 60% CF in epoxy. Finite element (FE) analysis of double cantilever beam specimens made from laminated composite has also been performed. It has been observed from FE analysis that the addition of 15% CNT in epoxy will also give almost the same value of mode I fracture energy as compared to the addition of 60% CF in epoxy. The value of mode I fracture energy for [0/0/0/0] laminated composite is two times higher than the other two types of laminated composites.

Effects of hostile solutions on the static and dynamic behavior of carbon/epoxy composites

2021 ◽  
pp. 002199832110200
Author(s):  
H Ersen Balcıoğlu ◽  
Raif Sakin ◽  
Halit Gün
Keyword(s):  
Bending Strength ◽  
Laminated Composites ◽  
Fatigue Behavior ◽  
Laminated Composite ◽  
Test Sample ◽  
Solution Concentration ◽  
Static Stability ◽  
Three Point Bending ◽  
Sem Image ◽  
Solution Type

Fiber-reinforced laminated composite is often used in harsh environments that may affect their static stability and long-term durability as well as residual strength. In this study, the effect of heavy chemical environments such as acid and alkaline and retaining time for these environments on flexural strength and flexural fatigue behavior of carbon/epoxy laminated composites were investigated. In this context, carbon/epoxy was retained into an acidic and alkaline solution having 5%, 15%, and 25% concentration by weight for 1–4 months. Fatigue behavior of carbon/epoxy was determined under dynamic flexural load, which corresponds to 80%, 70%, 60%, 50%, and 40% of static three-point bending strength of the test sample. SEM image of damaged specimens was taken to describe the failure mechanism of damage which occurs after fatigue. Also, to better understand environmental condition on the fatigue life, results were compared with results of carbon/epoxy laminated composites, which were not retained into any environments (unretained). The test results showed that the solution type, solution concentration, and retaining time caused noticeable changes in the static and dynamic strengths of carbon/epoxy laminated composites.

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