On Nonlinearly Elastic Membranes under Compression

2006 ◽  
Vol 27 (4) ◽  
pp. 379-392 ◽  
Author(s):  
Karim Trabelsi
Keyword(s):  
Elastic Membranes ◽  
Nonlinearly Elastic

Shock loading of fixed flexible thread and orthotropic elastic membrane

2003 ◽  
Vol 3 ◽  
pp. 52-59
Author(s):  
S.S. Komarov ◽  
N.Yu. Tsvileneva ◽  
N.I. Miskaktin
Keyword(s):  
Numerical Methods ◽  
Dynamic Loading ◽  
Elastic Deformation ◽  
Numerical Algorithm ◽  
Shock Loading ◽  
Elastic Membrane ◽  
Wave Dynamics ◽  
Elastic Membranes ◽  
Pneumatic Structures

The main problems of the wave dynamics of flexible filaments and elastic membranes are solved. The reliability of the numerical algorithm proposed by the authors for calculating the elastic deformation of pneumatic structures under dynamic loading is confirmed when compared with the results of known studies obtained by analytical and numerical methods.

Elastic Membranes

2001 ◽  
pp. 233-267 ◽  
Author(s):  
D.M. Haughton
Keyword(s):  
Elastic Membranes

scholarly journals CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

2010 ◽  
Vol 52 (2) ◽  
pp. 160-178 ◽  
Author(s):  
A. MATEI ◽  
R. CIURCEA
Keyword(s):  
Lagrange Multipliers ◽  
Variational Equation ◽  
Small Deformation ◽  
Contact Problems ◽  
Point Theory ◽  
The Body ◽  
Elastic Materials ◽  
Weak Formulation ◽  
Nonlinearly Elastic ◽  
Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

Finite Deflections of a Nonlinearly Elastic Bar

1970 ◽  
Vol 37 (1) ◽  
pp. 48-52 ◽  
Author(s):  
J. T. Oden ◽  
S. B. Childs
Keyword(s):  
Differential Equations ◽  
Axial Force ◽  
Classical Theory ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Finite Deflections ◽  
Hyperbolic Tangent ◽  
Elastic Bar ◽  
Elastoplastic Materials ◽  
Nonlinearly Elastic

The problem of finite deflections of a nonlinearly elastic bar is investigated as an extension of the classical theory of the elastica to include material nonlinearities. A moment-curvature relation in the form of a hyperbolic tangent law is introduced to simulate that of a class of elastoplastic materials. The problem of finite deflections of a clamped-end bar subjected to an axial force is given special attention, and numerical solutions to the resulting system of nonlinear differential equations are obtained. Tables of results for various values of the parameters defining the material are provided and solutions are compared with those of the classical theory of the elastica.

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