scholarly journals EXISTENCE OF SOLUTIONS FOR FRACTIONAL EVOLUTION INCLUSION WITH APPLICATION TO MECHANICAL CONTACT PROBLEMS

Fractals ◽  
2021 ◽  
pp. 2140036
Author(s):  
JINXIA CEN ◽  
YONGJIAN LIU ◽  
VAN THIEN NGUYEN ◽  
SHENGDA ZENG
Keyword(s):  
Existence Of Solutions ◽  
Contact Problems ◽  
Constitutive Law ◽  
Discrete Approximation ◽  
Inclusion Problem ◽  
Elliptic Type ◽  
Evolution Inclusion ◽  
Gronwall’S Inequality ◽  
Priori Estimates ◽  
Backward Euler

The goal of this paper is to study an evolution inclusion problem with fractional derivative in the sense of Caputo, and Clarke’s subgradient. Using the temporally semi-discrete method based on the backward Euler difference scheme, we introduce a discrete approximation system of elliptic type corresponding to the fractional evolution inclusion problem. Then, we employ the surjectivity of multivalued pseudomonotone operators and discrete Gronwall’s inequality to prove the existence of solutions and its priori estimates for the discrete approximation system. Furthermore, through a limiting procedure for solutions of the discrete approximation system, an existence theorem for the fractional evolution inclusion problem is established. Finally, as an illustrative application, a complicated quasistatic viscoelastic contact problem with a generalized Kelvin–Voigt constitutive law with fractional relaxation term and friction effect is considered.

scholarly journals A generalized neutral-type inclusion problem in the frame of the generalized Caputo fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adel Lachouri ◽  
Mohammed S. Abdo ◽  
Abdelouaheb Ardjouni ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Neutral Type ◽  
Inclusion Problem ◽  
Integral Conditions ◽  
Caputo Fractional Derivatives ◽  
Generalized Kernel ◽  
Type Inclusion ◽  
Theoretical Results ◽  
Fixed Point Principles

AbstractIn this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of $( \vartheta (t)-\vartheta (s)) $ ( ϑ ( t ) − ϑ ( s ) ) along with differential operator $\frac{1}{\vartheta '(t)}\,\frac{\mathrm{d}}{\mathrm{d}t}$ 1 ϑ ′ ( t ) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results.

Numerical analysis of history-dependent variational–hemivariational inequalities with applications to contact problems

2015 ◽  
Vol 26 (4) ◽  
pp. 427-452 ◽  
Author(s):  
MIRCEA SOFONEA ◽  
WEIMIN HAN ◽  
STANISŁAW MIGÓRSKI
Keyword(s):  
Numerical Analysis ◽  
Real World ◽  
Viscoelastic Body ◽  
Contact Problems ◽  
Uniqueness Result ◽  
Constitutive Law ◽  
Hemivariational Inequalities ◽  
New Class ◽  
Nonlinear Anal ◽  
Dependence Result

A new class of history-dependent variational–hemivariational inequalities was recently studied in Migórski et al. (2015Nonlinear Anal. Ser. B: Real World Appl.22, 604–618). There, an existence and uniqueness result was proved and used in the study of a mathematical model which describes the contact between a viscoelastic body and an obstacle. The aim of this paper is to continue the analysis of the inequalities introduced in Migórski et al. (2015Nonlinear Anal. Ser. B: Real World Appl.22, 604–618) and to provide their numerical analysis. We start with a continuous dependence result. Then we introduce numerical schemes to solve the inequalities and derive error estimates. We apply the results to a quasistatic frictional contact problem in which the material is modelled with a viscoelastic constitutive law, the contact is given in the form of normal compliance, and friction is described with a total slip-dependent version of Coulomb's law.

Soil structure interaction analysis: modeling the interface

2002 ◽  
Vol 39 (3) ◽  
pp. 620-628 ◽  
Author(s):  
Morched Zeghal ◽  
Tuncer B Edil
Keyword(s):  
Soil Structure ◽  
Interaction Analysis ◽  
Laboratory Data ◽  
Contact Problems ◽  
Constitutive Law ◽  
Shear Stresses ◽  
Grain Crushing ◽  
Wide Range ◽  
Close Relationship ◽  
Element Technique

The sand–structure interface, developed under monotonic loading, was modeled based on physical observations. The model takes into account the macroscopic conditions to yield a general constitutive law applicable to a wide range of contact problems and the microstructural considerations constitute the specialization of the general equations to a specific problem. The surface of slippage was idealized to be sinusoidal based on an intensive numerical simulation program that made use of the discrete element technique. The model incorporates the effect of grain crushing found to play a major role in the behavior of the interface. Analysis of laboratory data revealed a close relationship between grain crushing and the work dissipated plastically during shear. The proposed elastoplastic model, requiring a limited number of parameters, predicts the shear stresses for the modified direct shear test and reproduces the shaft resistance of the shaft–sand interface pullout tests in a satisfactory manner.Key words: sand-structure interface, microstructure, grain crushing, plastic work.

scholarly journals Existence results of nonlinear generalized proportional fractional differential inclusions via the diagonalization technique

2021 ◽  
Vol 6 (11) ◽  
pp. 12832-12844
Author(s):  
Mohamed I. Abbas ◽  
◽  
Snezhana Hristova ◽  
Keyword(s):  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Inclusion Problem ◽  
Fractional Differential Inclusions ◽  
New Class ◽  
Nonlinear Alternative ◽  
Fractional Differential ◽  
Infinite Intervals ◽  
The Right

<abstract><p>The present paper is concerned with the existence of solutions of a new class of nonlinear generalized proportional fractional differential inclusions with the right-hand side contains a Carathèodory-type multi-valued nonlinearity on infinite intervals. The investigation of the proposed inclusion problem relies on the multi-valued form of Leray-Schauder nonlinear alternative incorporated with the diagonalization technique. By specializing the parameters involved in the problem at hand, an illustrated example is proposed.</p></abstract>

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