scholarly journals Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations

Wave Motion ◽  
2019 ◽  
Vol 84 ◽  
pp. 110-124 ◽  
Author(s):  
Christian G. Böhmer ◽  
Yongjo Lee ◽  
Patrizio Neff
Keyword(s):  
Large Deformations ◽  
Soliton Solutions ◽  
Geometrically Nonlinear ◽  
Micropolar Elasticity

scholarly journals Regularity of Weak Solution of Variational Problems Modeling the Cosserat Micropolar Elasticity

2020 ◽  
Author(s):  
Yimei Li ◽  
Changyou Wang
Keyword(s):  
Weak Solution ◽  
Harmonic Maps ◽  
Lagrange Equation ◽  
Variational Problems ◽  
Energy Functional ◽  
Geometrically Nonlinear ◽  
Micropolar Elasticity ◽  
One Dimensional ◽  
The Poisson Equation ◽  
System Coupling

Abstract In this paper, we consider weak solutions of the Euler–Lagrange equation to a variational energy functional modeling the geometrically nonlinear Cosserat micropolar elasticity of continua in dimension three, which is a system coupling between the Poisson equation and the equation of $p$-harmonic maps ($2\le p\le 3$). We show that if a weak solution is stationary, then its singular set is discrete for $2<p<3$ and has zero one-dimensional Hausdorff measure for $p=2$. If, in addition, it is a stable-stationary weak solution, then it is regular everywhere when $p\in [2, \frac{32}{15}]$.

scholarly journals Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity

Wave Motion ◽  
2016 ◽  
Vol 60 ◽  
pp. 158-165 ◽  
Author(s):  
Christian G. Böhmer ◽  
Patrizio Neff ◽  
Belgin Seymenoğlu
Keyword(s):  
Geometrically Nonlinear ◽  
Micropolar Elasticity

Nonsymmetric Buckling of Plate-End Pressure Vessels

1989 ◽  
Vol 111 (3) ◽  
pp. 304-311 ◽  
Author(s):  
J. G. Teng ◽  
J. M. Rotter
Keyword(s):  
Flat Plate ◽  
Large Deformations ◽  
Deformation Mode ◽  
Pressure Vessels ◽  
Plastic Behavior ◽  
Geometrically Nonlinear ◽  
End Plate ◽  
Local Stresses ◽  
Nonlinear Elastic ◽  
Nonsymmetric Deformation

Small cylindrical pressure vessels are often constructed with a circular flat plate end closure. The end-plate undergoes large deformations under working loads. High local stresses develop at the junction between the cylinder and end-plate, causing yield under proof loading. The compressive circumferential stresses at the junction may lead to bifurcation into a nonsymmetric deformation mode. This study explores the geometrically nonlinear elastic-plastic behavior of plate-end pressure vessels. The form of the axisymmetric prebuckling path is investigated, showing the strongly stiffening nature of the response. Bifurcation of the closure into a nonsymmetric mode is then studied.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Static Geometrically Nonlinear Aeroelastic Framework for Multi-Fidelity Analysis

2020 ◽  
Vol 68 (4) ◽  
pp. 142-147
Author(s):  
Natsuki Tsushima ◽  
Masato Tamayama ◽  
Tomohiro Yokozeki
Keyword(s):  
Geometrically Nonlinear

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

THE SUPPORT BONDS RIGIDITY INFLUENCES ON THE CARRYING CAPACITY REDUCTION OF THE SHALLOW SHELLS ON A RECTANGULAR PLAN

2020 ◽  
Vol 92 (6) ◽  
pp. 3-12
Author(s):  
A.G. KOLESNIKOV ◽  
Keyword(s):  
Variable Thickness ◽  
Carrying Capacity ◽  
Geometric Nonlinearity ◽  
Progressive Collapse ◽  
Geometrically Nonlinear ◽  
Loss Of Stability ◽  
Shallow Shells ◽  
Capacity Reduction ◽  
Internal Forces ◽  
Hinged Support

Geometric nonlinearity shallow shells on a square and rectangular plan with constant and variable thickness are considered. Loss of stability of a structure due to a decrease in the rigidity of one of the support (transition from fixed support to hinged support) is considered. The Bubnov-Galerkin method is used to solve differential equations of shallow geometrically nonlinear shells. The Vlasov's beam functions are used for approximating. The use of dimensionless quantities makes it possible to repeat the calculations and obtain similar dependences. The graphs are given that make it possible to assess the reduction in the critical load in the shell at each stage of reducing the rigidity of the support and to predict the further behavior of the structure. Regularities of changes in internal forces for various types of structure support are shown. Conclusions are made about the necessary design solutions to prevent the progressive collapse of the shell due to a decrease in the rigidity of one of the supports.

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