Numerical Verification of Analytical Results for Statistical Description of Polymer Chains in Nematic Systems

2015 ◽  
Vol 24 (2) ◽  
pp. 133-140 ◽  
Author(s):  
Janusz Walasek ◽  
Radosław Jedynak
Keyword(s):  
Polymer Chains ◽  
Numerical Verification ◽  
Analytical Results

A Large Rotation Matrix for Nonlinear Framed Structures, Part 2: Numerical Verification

2014 ◽  
Vol 1065-1069 ◽  
pp. 2034-2039
Author(s):  
Jin Duan ◽  
Yun Gui Li
Keyword(s):  
Cantilever Beam ◽  
Numerical Results ◽  
Rotation Matrix ◽  
Numerical Verification ◽  
Structural Stiffness ◽  
Pure Bending ◽  
Large Rotation ◽  
Framed Structures ◽  
Analytical Results ◽  
Good Agreement

In this paper, some numerical verifications would be presented and discussed, mainly including the following three types: (1) the pure bending beam in which the structural stiffness would maintain the original value and not change along with the load; (2) the clamped arc-beam in which the structural stiffness would decrease gradually with the increment of load and the structure would be buckling at some certain load value; and (3) the cantilever beam in which the structural stiffness would increase significantly with the increment of load. For all of the above examples, the present results are in good agreement with the analytical results and numerical results in other literatures, testifying and illustrating the validity of the large rotation matrix for nonlinear framed structure, which is developed in the part 1 of this paper.

scholarly journals BOUND STATES IN WEAKLY DEFORMED WAVEGUIDES: NUMERICAL VERSUS ANALYTICAL RESULTS

2017 ◽  
Vol 59 (2) ◽  
pp. 200-214 ◽  
Author(s):  
PAOLO AMORE ◽  
JOHN P. BOYD ◽  
FRANCISCO M. FERNÁNDEZ ◽  
MARTIN JACOBO ◽  
PETR ZHEVANDROV
Keyword(s):  
Excellent Agreement ◽  
Bound States ◽  
Analytical Approach ◽  
Numerical Results ◽  
Numerical Verification ◽  
Analytical Results ◽  
Perturbative Method

We study bound states in weakly deformed and heterogeneous waveguides, and compare analytical predictions using a recently developed perturbative method with precise numerical results for three different configurations: a homogeneous asymmetric waveguide, a heterogenous asymmetric waveguide and a homogeneous broken strip. We have found excellent agreement between the analytical and numerical results in all the examples; this provides a numerical verification of the analytical approach.

scholarly journals Strain Localization of Orthotropic Elasto–Plastic Cohesive–Frictional Materials: Analytical Results and Numerical Verification

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2040
Author(s):  
Sungchul Kim ◽  
Miguel Cervera ◽  
Jian-Ying Wu ◽  
Michele Chiumenti
Keyword(s):  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Strain Localization ◽  
Numerical Results ◽  
Flow Rule ◽  
Numerical Verification ◽  
Applied Loading ◽  
Analytical Results ◽  
Frictional Materials

Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.

scholarly journals A deterministic model for (n = 2) competitive products in a market system

2011 ◽  
Vol 10 (2) ◽  
Author(s):  
M Kekana ◽  
O Makinde
Keyword(s):  
Deterministic Model ◽  
Numerical Verification ◽  
Market System ◽  
Personal Interaction ◽  
Analytical Results ◽  
Immigration And Emigration ◽  
The Stability ◽  
Competitive Products

We proposed a new deterministic model for the dynamics of two competitive products in a given market system. The model was analyzed qualitatively to determine the stability of its equilibrium under the influence of factors such as advertisement, personal interaction, immigration and emigration. Numerical verification of the analytical results is performed and presented graphically.

Shape of Confined Polymer Chains

1997 ◽  
Vol 7 (3) ◽  
pp. 433-447 ◽  
Author(s):  
C. E. Cordeiro ◽  
M. Molisana ◽  
D. Thirumalai
Keyword(s):  
Polymer Chains ◽  
Confined Polymer ◽  
Confined Polymer Chains

Dynamics of polymer chains trapped in a slit

1977 ◽  
Vol 38 (10) ◽  
pp. 1285-1291 ◽  
Author(s):  
F. Brochard
Keyword(s):  
Polymer Chains
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