The investigation of singular integro-differential equations relating to adhesive contact problems of the theory of viscoelasticity

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Nugzar Shavlakadze ◽  
Nana Odishelidze ◽  
Francisco Criado-Aldeanueva
Keyword(s):  
Differential Equations ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Theory Of Viscoelasticity

scholarly journals SOLUTION OF ADHESIVE CONTACT PROBLEM ON THE BASIS OF THE KNOWN SOLUTION FOR NON-ADHESIVE ONE

2018 ◽  
Vol 16 (1) ◽  
pp. 93 ◽  
Author(s):  
Valentin L. Popov
Keyword(s):  
Contact Problem ◽  
Material Properties ◽  
Present Method ◽  
Additional Assumption ◽  
Short Communication ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Contact Shape

The well-known procedure of reducing an adhesive contact problem to the corresponding non-adhesive one is generalized in this short communication to contacts with an arbitrary contact shape and arbitrary material properties (e.g. non homogeneous or gradient media). The only additional assumption is that the sequence of contact configurations in an adhesive contact should be exactly the same as that of contact configurations in a non-adhesive one. This assumption restricts the applicability of the present method. Nonetheless, the method can be applied to many classes of contact problems exactly and also be used for approximate analyses.

scholarly journals The JKR-type adhesive contact problems for transversely isotropic elastic solids

2014 ◽  
Vol 75 ◽  
pp. 34-44 ◽  
Author(s):  
Feodor M. Borodich ◽  
Boris A. Galanov ◽  
Leon M. Keer ◽  
Maria M. Suarez-Alvarez
Keyword(s):  
Transversely Isotropic ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Elastic Solids

scholarly journals The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

2014 ◽  
Vol 68 ◽  
pp. 14-32 ◽  
Author(s):  
Feodor M. Borodich ◽  
Boris A. Galanov ◽  
Maria M. Suarez-Alvarez
Keyword(s):  
Power Law ◽  
Contact Problems ◽  
Adhesive Contact

scholarly journals Studies on Static Frictional Contact Problems of Double Cantilever Beam Based on SBFEM

2017 ◽  
Vol 11 (1) ◽  
pp. 896-905
Author(s):  
Zhu Chaolei ◽  
Gao Qian ◽  
Hu Zhiqiang ◽  
Lin Gao ◽  
Lu Jingzhou
Keyword(s):  
Mathematical Programming ◽  
Differential Equations ◽  
Cantilever Beam ◽  
Frictional Contact ◽  
Double Cantilever Beam ◽  
Contact Problems ◽  
Contact Forces ◽  
Contact Conditions ◽  
Good Convergence ◽  
Practical Engineering

Introduction: The frictional contact problem is one of the most important and challenging topics in solids mechanics, and often encountered in the practical engineering. Method: The nonlinearity and non-smooth properties result in that the convergent solutions can't be obtained by the widely used trial-error iteration method. Mathematical Programming which has good convergence properties and rigorous mathematical foundation is an effective alternative solution method, in which, the frictional contact conditions can be expressed as Non-smooth Equations, B-differential equations, Nonlinear Complementary Problem, etc. Result: In this paper, static frictional contact problems of double cantilever beam are analyzed by Mathematical Programming in the framework of Scaled Boundary Finite Element Method (SBFEM), in which the contact conditions can be expressed as the B-differential Equations. Conclusion The contact forces and the deformation with different friction factors are solved and compared with those obtained by ANSYS, by which the accuracy of solving contact problems by SBFEM and B-differential Equations is validated.

scholarly journals Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories

2018 ◽  
pp. 15-33
Author(s):  
B. A. Khudayarov
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Aircraft Design ◽  
Panel Flutter ◽  
Scientific Problem ◽  
Wide Range ◽  
Hereditary Theory ◽  
Theory Of Viscoelasticity

Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.

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