The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.
{"title":"A mixed boundary value problem of a cracked elastic medium under torsion","authors":"B. Kebli, F. Madani","doi":"10.2298/tam200923010k","DOIUrl":"https://doi.org/10.2298/tam200923010k","url":null,"abstract":"The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84439216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.
{"title":"Longitudinal waves in an elastic rod caused by sudden damage to the foundation","authors":"I. Shatskyi, V. Perepichka, M. Vaskovskyi","doi":"10.2298/TAM200615001S","DOIUrl":"https://doi.org/10.2298/TAM200615001S","url":null,"abstract":"We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75824888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate a nonlinear viscoelastic equation. By assuming time-varying delay feedback acting on the boundary, under certain assumptions on the given data, the general decay estimates for the energy are established by introducing suitable Lyapunov functionals. This model improves earlier ones in the literature in which only the dissipative term in the feedback condition is considered.
{"title":"Asymptotic stability of a viscoelastic problem with time-varying delay in boundary feedback","authors":"Abita Rahmoune","doi":"10.2298/TAM200629003R","DOIUrl":"https://doi.org/10.2298/TAM200629003R","url":null,"abstract":"In this paper, we investigate a nonlinear viscoelastic equation. By assuming time-varying delay feedback acting on the boundary, under certain assumptions on the given data, the general decay estimates for the energy are established by introducing suitable Lyapunov functionals. This model improves earlier ones in the literature in which only the dissipative term in the feedback condition is considered.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75918134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Minh‐Quan Thai, Sy-Tuan Nguyen, Thanh-Sang Nguyen, Phu-Son Mai
This paper aims to model the effect of different shapes of inclusions on the homogenized viscoelastic properties of composite materials made of a viscoelastic matrix and inclusion particles. The viscoelastic behavior of the matrix phase is modeled by the Generalized Maxwell rheology. The effective properties are firstly derived by combining the homogenization theory of elasticity and the correspondence principle. Then, the effective rheological properties in time space are explicitly derived without using the complex inverse Laplace?Carson transformation (LC). Closed-form solutions for the effective bulk and shear rheological viscoelastic properties, the relaxation and creep moduli as well as the Poisson ratio are obtained for the isotropic case with random orientation distribution and different shapes of inclusions: spherical, oblate and elongate inclusions. The developed approach is validated against the exact solutions obtained by the classical inverse LC method. It is observed that the homogenized viscoelastic moduli are highly sensitive to different shapes of inclusions.
{"title":"Analytical solutions for the effective viscoelastic properties of composite materials with different shapes of inclusions","authors":"Minh‐Quan Thai, Sy-Tuan Nguyen, Thanh-Sang Nguyen, Phu-Son Mai","doi":"10.2298/TAM200806004T","DOIUrl":"https://doi.org/10.2298/TAM200806004T","url":null,"abstract":"This paper aims to model the effect of different shapes of inclusions on the homogenized viscoelastic properties of composite materials made of a viscoelastic matrix and inclusion particles. The viscoelastic behavior of the matrix phase is modeled by the Generalized Maxwell rheology. The effective properties are firstly derived by combining the homogenization theory of elasticity and the correspondence principle. Then, the effective rheological properties in time space are explicitly derived without using the complex inverse Laplace?Carson transformation (LC). Closed-form solutions for the effective bulk and shear rheological viscoelastic properties, the relaxation and creep moduli as well as the Poisson ratio are obtained for the isotropic case with random orientation distribution and different shapes of inclusions: spherical, oblate and elongate inclusions. The developed approach is validated against the exact solutions obtained by the classical inverse LC method. It is observed that the homogenized viscoelastic moduli are highly sensitive to different shapes of inclusions.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77410205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.
{"title":"Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays","authors":"M. Woldaregay, W. Aniley, G. Duressa","doi":"10.2298/tam201208006w","DOIUrl":"https://doi.org/10.2298/tam201208006w","url":null,"abstract":"This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79901838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1913 A. D. Bilimovich observed that rheonomic constraints which are linear and homogeneous in generalized velocities are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations whose scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovich system, equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.
{"title":"On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich","authors":"A. Borisov, A. Tsiganov","doi":"10.2298/TAM200120009B","DOIUrl":"https://doi.org/10.2298/TAM200120009B","url":null,"abstract":"In 1913 A. D. Bilimovich observed that rheonomic constraints which are linear and homogeneous in generalized velocities are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations whose scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovich system, equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83642041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fracture of welded joints has been an important research and industrial topic for a long time, having in mind the key role of welded joints in ensuring the safe operation and integrity of welded structures. This work contains an overview of application of micromechanical models to ductile fracture of welded joints. The main benefit of these models, in comparison with the classical fracture mechanics approach, is consideration of the local quantities (stress and strain) in prediction of damage development. The damage is quantified through the value of the damage parameter, which is typically related to the void nucleation, growth and coalescence for ductile fracture of metallic materials, i.e. the description of the material can be related to the actual material behaviour during fracture. Most of the presented studies, including those published by the present authors, are performed on steel as the base material, and the rest deal with aluminium alloys.
{"title":"An overview of application of micromechanical models in ductile fracture analysis of welded joints","authors":"M. Rakin, B. Medjo, N. Gubeljak, A. Sedmak","doi":"10.2298/tam200117004r","DOIUrl":"https://doi.org/10.2298/tam200117004r","url":null,"abstract":"Fracture of welded joints has been an important research and industrial topic for a long time, having in mind the key role of welded joints in ensuring the safe operation and integrity of welded structures. This work contains an overview of application of micromechanical models to ductile fracture of welded joints. The main benefit of these models, in comparison with the classical fracture mechanics approach, is consideration of the local quantities (stress and strain) in prediction of damage development. The damage is quantified through the value of the damage parameter, which is typically related to the void nucleation, growth and coalescence for ductile fracture of metallic materials, i.e. the description of the material can be related to the actual material behaviour during fracture. Most of the presented studies, including those published by the present authors, are performed on steel as the base material, and the rest deal with aluminium alloys.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91253100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Being a common phenomenon in failure mechanism, fretting fatigue has emerged as one of the major concerns in recent years both in research and industrial applications. In the present study, the effect of notch and fretting on bending fatigue has been examined by FEM analysis. Based on the available and validated FEM model, analyses have been carried out on single point fretting with a double notch and double point fretting with a single notch respectively. Along the predefined paths through the edge, thickness and notch, fatigue behavior and stress-strain distribution have been studied. It has been found that stress and strain distribution is uniformly spaced for constant fretting loads with a variable concentric load whereas variable fretting loads yield almost two times results. Stress and strain singularity is found for transverse loading when highly stressed. Peak stress was found on the stress distribution path for fretting action for the combined fretting and notch pres-ence. Fatigue life was influenced more drastically by variable fretting loads than variable concentric loadings only in case of tension. Dual action of fretting with notches was found more detrimental than the single action of double fretting/notching.
{"title":"Investigation of the combined effect of notch and fretting on bending fatigue","authors":"Quazi Md. Zobaer Shah, A. Kowser, M. Chowdhury","doi":"10.2298/tam191019002z","DOIUrl":"https://doi.org/10.2298/tam191019002z","url":null,"abstract":". Being a common phenomenon in failure mechanism, fretting fatigue has emerged as one of the major concerns in recent years both in research and industrial applications. In the present study, the effect of notch and fretting on bending fatigue has been examined by FEM analysis. Based on the available and validated FEM model, analyses have been carried out on single point fretting with a double notch and double point fretting with a single notch respectively. Along the predefined paths through the edge, thickness and notch, fatigue behavior and stress-strain distribution have been studied. It has been found that stress and strain distribution is uniformly spaced for constant fretting loads with a variable concentric load whereas variable fretting loads yield almost two times results. Stress and strain singularity is found for transverse loading when highly stressed. Peak stress was found on the stress distribution path for fretting action for the combined fretting and notch pres-ence. Fatigue life was influenced more drastically by variable fretting loads than variable concentric loadings only in case of tension. Dual action of fretting with notches was found more detrimental than the single action of double fretting/notching.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82796320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through the distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. The microlocal approach in analyzing singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.
{"title":"Hereditariness and non-locality in wave propagation modeling","authors":"D. Zorica","doi":"10.2298/tam200116005z","DOIUrl":"https://doi.org/10.2298/tam200116005z","url":null,"abstract":"The classical wave equation is generalized within the framework of fractional calculus in order to account for the memory and non-local effects that might be material features. Both effects are included in the constitutive equation, while the equation of motion of the deformable body and strain are left unchanged. Memory effects in viscoelastic materials are modeled through the distributed-order fractional constitutive equation that generalizes all linear models having differentiation orders up to order one. The microlocal approach in analyzing singularity propagation is utilized in the case of viscoelastic material described by the fractional Zener model, as well as in the case of two non-local models: non-local Hookean and fractional Eringen.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83590059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions 𝜛 𝑖 , ( 𝑖 = 1 , 2), we prove local existence and unique- ness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [ 6 , 23 , 25 ].
{"title":"Local existence and blow-up of solutions for coupled viscoelastic wave equations with degenerate damping terms","authors":"E. Pişkin, F. Ekinci, K. Zennir","doi":"10.2298/tam200428008p","DOIUrl":"https://doi.org/10.2298/tam200428008p","url":null,"abstract":". In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions 𝜛 𝑖 , ( 𝑖 = 1 , 2), we prove local existence and unique- ness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [ 6 , 23 , 25 ].","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75711605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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