Contact problems for elastic bodies with initial stresses (rigid punches)

1989 ◽  
Vol 25 (8) ◽  
pp. 735-748
Author(s):  
S. Yu. Babich ◽  
A. N. Guz' ◽  
V. B. Rudnitskii
Keyword(s):  
Contact Problems ◽  
Initial Stresses ◽  
Elastic Bodies

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.

Plane contact problems for elastic bodies with initial stresses

1989 ◽  
Vol 25 (1) ◽  
pp. 79-85
Author(s):  
S. Yu. Babich ◽  
V. B. Rudnitskii
Keyword(s):  
Contact Problems ◽  
Initial Stresses ◽  
Plane Contact ◽  
Elastic Bodies

The method of caustics for the determination of normal loads acting on surfaces of elastic bodies

1980 ◽  
Vol 15 (1) ◽  
pp. 37-41 ◽  
Author(s):  
P S Theocaris ◽  
N I Ioakimidis
Keyword(s):  
Three Dimensional ◽  
Contact Problems ◽  
Two Dimensional ◽  
Concentrated Force ◽  
Elastic Bodies ◽  
Plate And Shell ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Quantities Of Interest

The optical method of caustics constitutes an efficient experimental technique for the determination of quantities of interest in elasticity problems. Up to now, this method has been applied only to two-dimensional elasticity problems (including plate and shell problems). In this paper, the method of caustics is extended to the case of three-dimensional elasticity problems. The particular problems of a concentrated force and a uniformly distributed loading acting normally on a half-space (on a circular region) are treated in detail. Experimentally obtained caustics for the first of these problems were seen to be in satisfactory agreement with the corresponding theoretical forms. The treatment of various, more complicated, three-dimensional elasticity problems, including contact problems, by the method of caustics is also possible.

A Modified Conjugate Gradient Method for Frictionless Contact Problems

1983 ◽  
Vol 105 (2) ◽  
pp. 242-246 ◽  
Author(s):  
W. R. Marks ◽  
N. J. Salamon
Keyword(s):  
Finite Element ◽  
Conjugate Gradient ◽  
Solution Method ◽  
Contact Region ◽  
Contact Problems ◽  
Computer Code ◽  
Frictionless Contact ◽  
Elastic Bodies ◽  
Gradient Technique ◽  
Modified Conjugate Gradient Method

The solution of elastic bodies in contact through the application of a conjugate gradient technique integrated with a finite element computer code is discussed. This approach is general, easily applied, and reasonably efficient. Furthermore the solution method is compatible with existing finite element computer programs. The necessary algorithm for use of the technique is described in detail. Numerical examples of two-dimensional frictionless contact problems are presented. It is found that the extent of the contact region and the displacements and stresses throughout the contacting bodies can be economically computed with precision.

scholarly journals Unilateral Contact of Elastic Bodies (Moment Theory)

2001 ◽  
Vol 8 (4) ◽  
pp. 753-766
Author(s):  
R. Gachechiladze
Keyword(s):  
Contact Zone ◽  
Couple Stress Theory ◽  
Contact Problems ◽  
Theory Of Elasticity ◽  
Unilateral Contact ◽  
Stress Theory ◽  
Nonhomogeneous Media ◽  
Elastic Bodies ◽  
The Moment ◽  
Boundary Contact

Abstract Boundary contact problems of statics of the moment (couple-stress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable for numerical realizations are considered.

Contact between a curved viscoelastic beam and a rigid plane

1973 ◽  
Vol 8 (1) ◽  
pp. 58-64 ◽  
Author(s):  
I Granstam
Keyword(s):  
Horizontal Plane ◽  
Contact Point ◽  
Critical Time ◽  
Contact Problems ◽  
Critical Value ◽  
Curved Beam ◽  
Viscoelastic Beam ◽  
Elastic Bodies ◽  
Concentrated Forces ◽  
Rigid Plane

The following problem has been analysed by the theory of small deflections of bending. A circularly curved beam of Maxwell material is pressed against a rigid horizontal plane by two constant and concentrated forces P, each acting on one end of the beam. Before loading there is contact only at the mid-point of the beam. As load is applied the Maxwellian beam behaves like a Hookean beam. If the load P is below a critical value Pc, there is contact only at the mid-point, but if the load exceeds this value, linear contact is formed along a certain length 2λ° of the beam. At the time t the beam will rise from the support over a distance of 2λ° ( t) if the load P exceeds Pc, while if P is less than Pc there will be a similar deflection only after a critical time tc. The contact pressure is two concentrated forces, acting on each contact point. Expressions for the deflections w(O, t) and w( L, t) of the centre and the ends of the beam are also derived and are compared with corresponding expressions for a Hookean beam. The paper shows that essential differences can exist between contact problems with similar viscoelastic or elastic bodies.

The Incremental Variational Principles for Frictional Contact Problems of Linear Elasticity

1993 ◽  
Vol 60 (4) ◽  
pp. 982-985 ◽  
Author(s):  
G. Zboinski
Keyword(s):  
Variational Principles ◽  
Contact Problems ◽  
Complementary Energy ◽  
Energy Functionals ◽  
Variational Functional ◽  
Elastic Bodies ◽  
Static Contact ◽  
Special Cases ◽  
The Common ◽  
Type Potential

Four types of the most frequently used variational functional are employed in order to form the inequality principles of the kineto-static contact problem of two elastic bodies in the common relative motion. As the general case, the principle based on the Hu- Washizu functional is proposed. The principles formed with the Reissner type, potential energy, and complementary energy functionals are derived as the special cases.

Contact Problems of Two Dissimilar Anisotropic Elastic Bodies

1998 ◽  
Vol 65 (3) ◽  
pp. 580-587 ◽  
Author(s):  
Chyanbin Hwu ◽  
C. W. Fan
Keyword(s):  
Boundary Conditions ◽  
Contact Region ◽  
Complex Function ◽  
Contact Problems ◽  
Anisotropic Elasticity ◽  
Analytical Continuation ◽  
Two Dimensional ◽  
Different Boundary Conditions ◽  
Elastic Bodies ◽  
Anisotropic Elastic

In this paper, a two-dimensional contact problem of two dissimilar anisotropic elastic bodies is studied. The shapes of the boundaries of these two elastic bodies have been assumed to be approximately straight, but the contact region is not necessary to be small and the contact surface can be nonsmooth. Base upon these assumptions, three different boundary conditions are considered and solved. They are: the contact in the presence of friction, the contact in the absence of friction, and the contact in complete adhesion. By applying the Stroh’s formalism for anisotropic elasticity and the method of analytical continuation for complex function manipulation, general solutions satisfying these different boundary conditions are obtained in analytical forms. When one of the elastic bodies is rigid and the boundary shape of the other elastic body is considered to be fiat, the reduced solutions can be proved to be identical to those presented in the literature for the problems of rigid punches indenting into (or sliding along) the anisotropic elastic halfplane. For the purpose of illustration, examples are also given when the shapes of the boundaries of the elastic bodies are approximated by the parabolic curves.

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