Degenerate similarity solutions in dynamic problems on the calculation of strains in nonlinearly elastic bodies

1988 ◽  
Vol 29 (1) ◽  
pp. 142-145 ◽  
Author(s):  
V. P. Yastrebov
Keyword(s):  
Similarity Solutions ◽  
Dynamic Problems ◽  
Elastic Bodies ◽  
Nonlinearly Elastic

The impact-contact problem of two nonlinearly elastic bodies

1979 ◽  
Vol 33 (1-2) ◽  
pp. 81-95 ◽  
Author(s):  
J. Aboudi
Keyword(s):  
Contact Problem ◽  
Elastic Bodies ◽  
The Impact ◽  
Nonlinearly Elastic

The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies

2001 ◽  
Vol 171 (1) ◽  
pp. 201-226 ◽  
Author(s):  
Dawn A. Lott ◽  
Stuart S. Antman ◽  
William G. Szymczak
Keyword(s):  
Wave Equation ◽  
Quasilinear Wave Equation ◽  
Elastic Bodies ◽  
Nonlinearly Elastic

scholarly journals BOUNDARY-ELEMENT PROCEDURE BASED ON MODIFIED CONVOCATIONQUADRATURE METHOD IN DYNAMIC PROBLEMS OF ELASTIC BODIES

2008 ◽  
Vol 70 (1) ◽  
pp. 155-161
Author(s):  
A. A. Belov ◽  
◽  
L. A. Igumnov ◽  
S. Yu. Litvinchuk ◽  
◽  
...  
Keyword(s):  
Boundary Element ◽  
Dynamic Problems ◽  
Elastic Bodies

Large shearing oscillations of incompressible nonlinearly elastic bodies

1984 ◽  
Vol 14 (3) ◽  
pp. 249-262 ◽  
Author(s):  
Stuart S. Antman ◽  
Guo Zhong-Heng
Keyword(s):  
Elastic Bodies ◽  
Nonlinearly Elastic

Contact between nonlinearly elastic bodies

2006 ◽  
Vol 136 (6) ◽  
pp. 1239-1266 ◽  
Author(s):  
Daniel Habeck ◽  
Friedemann Schuricht
Keyword(s):  
Variational Methods ◽  
Lagrange Equation ◽  
Existence Results ◽  
Necessary Condition ◽  
Generalized Gradients ◽  
Mechanical Problem ◽  
Elastic Bodies ◽  
Essential Tool ◽  
Nonlinearly Elastic

We study the contact between nonlinearly elastic bodies by variational methods. After the formulation of the mechanical problem, we provide existence results based on polyconvexity and on quasiconvexity. We then derive the Euler—Lagrange equation as a necessary condition for minimizers. Here Clarke's generalized gradients are an essential tool for treating the nonsmooth obstacle condi

Osculation of two nonlinearly elastic bodies

1991 ◽  
Vol 31 (5) ◽  
pp. 758-762
Author(s):  
L. G. Dobordzhginidze
Keyword(s):  
Elastic Bodies ◽  
Nonlinearly Elastic

Contact Problems for Elastic Bodies With Initial Stresses: Focus on Ukrainian Research

1998 ◽  
Vol 51 (5) ◽  
pp. 343-371 ◽  
Author(s):  
A. N. Guz’ ◽  
S. Yu. Babich ◽  
V. B. Rudnitsky
Keyword(s):  
Contact Problems ◽  
Elastic Potential ◽  
Initial Stresses ◽  
Dynamic Problems ◽  
Integral Transformations ◽  
Elastic Bodies ◽  
Incompressible Materials ◽  
Modern Classification ◽  
Initial Strains

In the present review article general results concerning problems of contact interaction (contact problems) of pre-stressed bodies with rigid, and elastic punches (facings) are presented. The modern classification of investigations on contact problems for bodies with initial stresses is based on two approaches. The first approach is applicable to bodies with a specific type of elastic potential. The second approach is developed in parallel with the first one. It describes investigations on contact problems for pre-stressed bodies with an arbitrary structure of an elastic potential in a general form for compressible and incompressible materials. In the last case, investigations were carried out in a common form for the theory of large (finite) initial strains and various variants of the theory of small initial strains. The formulation of the problems is given, and methods of solving planar and spatial contact problems for bodies with initial stresses are developed. Procedures of the theory of complex variables and methods of Riemann-Hilbert are used. For planar problems, the authors introduce planar potentials of the linearized static and dynamic problems for elastic compressible and incompressible bodies with initial stresses. In the case of spatial contact problems, various procedures are used: general solutions of spatial static problems for elastic bodies with initial stresses, methods of harmonic potential theory, integral transformations, and integral equations using numerical methods of investigation. The essential numerical results in the form of graphs and tables are presented. These give the quantitative and qualitative analysis of the influence of initial stresses on the main characteristics of contact problems. This review contains 98 references.

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