analysis of the steel lattice telecommunication structure exposed to the wind pressure, whose average value is treated as the Gaussian random variable. The Least Squares Method is provided here for symbolic recovery of the polynomial responses of this structure in addition to the given uncertainty source and it serves to the twentieth order perturbation-based approximations for the first four probabilistic moments and coefficients. Static numerical analysis has been carried out by the use of the incremental BFGS (Broyden–Fletcher–Goldfarb–Shanno) procedure necessary for the so-called P-delta effect in steel structures, while the basic statistics of the ultimate limit state have been included into the formulas for the reliability indices of both first and second order. This study shows that the safety margin of such structures is definitely wider than it follows the basic Eurocodes statements, which means that designed durability period for these telecommunication structures is definitely longer.
{"title":"From full-scale testing of steel lattice towers to stochastic reliability analysis","authors":"J. Szafran, M. Kaminski","doi":"10.24423/AOM.2562","DOIUrl":"https://doi.org/10.24423/AOM.2562","url":null,"abstract":"analysis of the steel lattice telecommunication structure exposed to the wind pressure, whose average value is treated as the Gaussian random variable. The Least Squares Method is provided here for symbolic recovery of the polynomial responses of this structure in addition to the given uncertainty source and it serves to the twentieth order perturbation-based approximations for the first four probabilistic moments and coefficients. Static numerical analysis has been carried out by the use of the incremental BFGS (Broyden–Fletcher–Goldfarb–Shanno) procedure necessary for the so-called P-delta effect in steel structures, while the basic statistics of the ultimate limit state have been included into the formulas for the reliability indices of both first and second order. This study shows that the safety margin of such structures is definitely wider than it follows the basic Eurocodes statements, which means that designed durability period for these telecommunication structures is definitely longer.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41602727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of the present paper is to develop the classical potential method in the linear theory of thermoelasticity for materials with a double porosity structure based on the mechanics of materials with voids. The fundamental solution of the system of equations of steady vibrations is constructed explicitly by means of elementary functions and its basic properties are established. The Sommerfeld-Kupradze type radiation conditions are established. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method and the theory of singular integral equations.
{"title":"Boundary value problems of steady vibrations in the theory of thermoelasticity for materials with a double porosity structure","authors":"M. Svanadze","doi":"10.24423/AOM.2551","DOIUrl":"https://doi.org/10.24423/AOM.2551","url":null,"abstract":"The purpose of the present paper is to develop the classical potential method in the linear theory of thermoelasticity for materials with a double porosity structure based on the mechanics of materials with voids. The fundamental solution of the system of equations of steady vibrations is constructed explicitly by means of elementary functions and its basic properties are established. The Sommerfeld-Kupradze type radiation conditions are established. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method and the theory of singular integral equations.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42673459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Stupak, R. Kačianauskas, A. Kačeniauskas, V. Starikovičius, A. Maknickas, R. Pacevič, Migle Staskuniene, G. Davidavičius, A. Aidietis
This paper presents the patient-specific simulations of the aortic valve based on the proposed geometric model. A structural analysis is performed by using the finite element method to determine the stress-strain state of the aortic valve. The study is focused on the investigation of various turbulence models crucial for the appropriate description of the flow in the deceleration phase, following the peak systole. A comparative study of the flow solution without a turbulence model and the numerical results obtained by using various turbulence models is also performed. The results yielded by the shear-stress transport k - ω model supplemented with the intermittency transition equation most closely match those of numerical simulations without a turbulence model.
{"title":"The geometric model-based patient-specific simulations of turbulent aortic valve flows","authors":"E. Stupak, R. Kačianauskas, A. Kačeniauskas, V. Starikovičius, A. Maknickas, R. Pacevič, Migle Staskuniene, G. Davidavičius, A. Aidietis","doi":"10.24423/AOM.2543","DOIUrl":"https://doi.org/10.24423/AOM.2543","url":null,"abstract":"This paper presents the patient-specific simulations of the aortic valve based on the proposed geometric model. A structural analysis is performed by using the finite element method to determine the stress-strain state of the aortic valve. The study is focused on the investigation of various turbulence models crucial for the appropriate description of the flow in the deceleration phase, following the peak systole. A comparative study of the flow solution without a turbulence model and the numerical results obtained by using various turbulence models is also performed. The results yielded by the shear-stress transport k - ω model supplemented with the intermittency transition equation most closely match those of numerical simulations without a turbulence model.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46420744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A multilayered thin metal film subjected to an ultra-short laser pulse is considered. A mathematical description of the discussed process is based on the system of the dual-phase lag equations supplemented by appropriate boundary and initial conditions. Special attention is devoted to the ideal contact conditions at the interfaces between the layers, which in the case of the dual-phase lag model must be formulated in a different way than in the macroscopic Fourier model. To solve the problem the explicit scheme of the finite difference method is developed. In the final part of the paper the example of computations is shown.
{"title":"Analysis of thermal processes occurring in heated multilayered metal films using the dual-phase lag model","authors":"E. Majchrzak, G. Kałuża","doi":"10.24423/AOM.2494","DOIUrl":"https://doi.org/10.24423/AOM.2494","url":null,"abstract":"A multilayered thin metal film subjected to an ultra-short laser pulse is considered. A mathematical description of the discussed process is based on the system of the dual-phase lag equations supplemented by appropriate boundary and initial conditions. Special attention is devoted to the ideal contact conditions at the interfaces between the layers, which in the case of the dual-phase lag model must be formulated in a different way than in the macroscopic Fourier model. To solve the problem the explicit scheme of the finite difference method is developed. In the final part of the paper the example of computations is shown.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46391470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The modeling of bioheat transfer process described by the dual-phase lag equation is considered. The basic equation is supplemented by the appropriate boundary-initial conditions. In the central part of the cylindrical domain the heated sub-domain is located. In this region the additional component determining the capacity of an internal heat source is taken into account. At the stage of numerical computations the generalized finite difference method (GFDM) is used. The GFDM nodes distribution is generated in a random way (with some limitations). The examples of computations for different nodes distribution and comparison with the classical finite difference method are presented. In the final part of the paper the conclusions are formulated.
{"title":"Solving the dual-phase lag bioheat transfer equation by the generalized finite difference method","authors":"Łukasz Turchan","doi":"10.24423/AOM.2567","DOIUrl":"https://doi.org/10.24423/AOM.2567","url":null,"abstract":"The modeling of bioheat transfer process described by the dual-phase lag equation is considered. The basic equation is supplemented by the appropriate boundary-initial conditions. In the central part of the cylindrical domain the heated sub-domain is located. In this region the additional component determining the capacity of an internal heat source is taken into account. At the stage of numerical computations the generalized finite difference method (GFDM) is used. The GFDM nodes distribution is generated in a random way (with some limitations). The examples of computations for different nodes distribution and comparison with the classical finite difference method are presented. In the final part of the paper the conclusions are formulated.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46730156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies are considered when the shear modulus depending on the body projection (i.e., on a domain lying in the plane of interest) variables may vanish either on a part or on the entire boundary of the projection. We study the dependence of the well-posedness of the boundary conditions (BCs) on the character of the vanishing of the shear modulus. The case of vibration is considered as well.
{"title":"Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies","authors":"N. Chinchaladze, G. Jaiani","doi":"10.24423/AOM.2533","DOIUrl":"https://doi.org/10.24423/AOM.2533","url":null,"abstract":"Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies are considered when the shear modulus depending on the body projection (i.e., on a domain lying in the plane of interest) variables may vanish either on a part or on the entire boundary of the projection. We study the dependence of the well-posedness of the boundary conditions (BCs) on the character of the vanishing of the shear modulus. The case of vibration is considered as well.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47415166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to develop the reciprocating rotary driving actuator with a simple mechanism using shape memory alloy (SMA) tapes, the graphical method to design the actuator was proposed based on the torsional deformation properties of SMA tapes. The torsional deformation properties of the SME tape showing the shape memory effect (SME) and the SE tape showing superelasticity (SE) were obtained. The bias-type reciprocating rotary actuator was composed of the pretwisted SME tape and the flat SE tape in series. The design chart expressed by the relationship between torque and twisting angle of the SME tape and the SE tape was proposed. The rotational angle and torque, which vary depending on temperature, can be estimated based on the design chart. The rotational angle is controlled by adjusting the mounting angle of the SME tape and the heating temperature. The automatically opening and closing blind driven by sunlight was demonstrated. The blind was controlled by using the reciprocating rotary element composed of the SME tape and the SE tape. The behavior of the blind can be achieved based on the proposed design method of the reciprocating rotary driving element.
{"title":"Torsional deformation properties of SMA tapes and their application to bias-type reciprocating rotary driving actuator","authors":"K. Takeda, R. Matsui, H. Tobushi, E. Pieczyska","doi":"10.24423/AOM.2504","DOIUrl":"https://doi.org/10.24423/AOM.2504","url":null,"abstract":"In order to develop the reciprocating rotary driving actuator with a simple mechanism using shape memory alloy (SMA) tapes, the graphical method to design the actuator was proposed based on the torsional deformation properties of SMA tapes. The torsional deformation properties of the SME tape showing the shape memory effect (SME) and the SE tape showing superelasticity (SE) were obtained. The bias-type reciprocating rotary actuator was composed of the pretwisted SME tape and the flat SE tape in series. The design chart expressed by the relationship between torque and twisting angle of the SME tape and the SE tape was proposed. The rotational angle and torque, which vary depending on temperature, can be estimated based on the design chart. The rotational angle is controlled by adjusting the mounting angle of the SME tape and the heating temperature. The automatically opening and closing blind driven by sunlight was demonstrated. The blind was controlled by using the reciprocating rotary element composed of the SME tape and the SE tape. The behavior of the blind can be achieved based on the proposed design method of the reciprocating rotary driving element.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45415850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper analyzes the frictionless double contact problem of a two-layer laminate pressed against a homogeneous half-plane substrate by a rigid punch. The laminate is composed of a homogeneous elastic strip and a functionally graded layer, perfectly bonded along their interface. The mechanical properties of the graded layer are modeled by an exponentially varying shear modulus and constant Poisson’s ratio. Both the governing equations and the boundary conditions of the double contact problem are converted into a pair of singular integral equations by Fourier integral transforms, which are numerically integrated by Chebyshev–Gauss quadrature. The contact pressure and the contact size at both the advancing and the receding contact interface are eventually obtained by an iterative algorithm, developed from the method of steepest descent. Extensive parametric studies suggest that it is possible to control contact stress and contact size by introducing functionally graded materials into multilayered elastic structures.
{"title":"Double contact analysis of multilayered elastic structures involving functionally graded materials","authors":"J. Yan, C. Mi","doi":"10.24423/AOM.2544","DOIUrl":"https://doi.org/10.24423/AOM.2544","url":null,"abstract":"This paper analyzes the frictionless double contact problem of a two-layer laminate pressed against a homogeneous half-plane substrate by a rigid punch. The laminate is composed of a homogeneous elastic strip and a functionally graded layer, perfectly bonded along their interface. The mechanical properties of the graded layer are modeled by an exponentially varying shear modulus and constant Poisson’s ratio. Both the governing equations and the boundary conditions of the double contact problem are converted into a pair of singular integral equations by Fourier integral transforms, which are numerically integrated by Chebyshev–Gauss quadrature. The contact pressure and the contact size at both the advancing and the receding contact interface are eventually obtained by an iterative algorithm, developed from the method of steepest descent. Extensive parametric studies suggest that it is possible to control contact stress and contact size by introducing functionally graded materials into multilayered elastic structures.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45390411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many titanium alloys and even materials such as concrete exhibit a nonlinear relationship between strain and stress, when the strain is small enough that the square of the norm of the displacement gradient can be ignored in comparison to the norm of the displacement gradient. Such response cannot be described within the classical theory of Cauchy elasticity wherein a linearization of the nonlinear strain leads to the classical linearized elastic response. A new framework for elasticity has been put into place in which one can justify rigorously a nonlinear relationship between the linearized strain and stress. Here, we consider one such model based on a power-law relationship. Previous attempts at describing such response have been either limited to the response of one particular material, e.g. Gum Metal, or involved a model with more material moduli, than the model considered in this work. For the uniaxial response of several metallic alloys, the model that is being considered fits experimental data exceedingly well.
{"title":"Modeling Gum Metal and other newly developed titanium alloys within a new class of constitutive relations for elastic bodies","authors":"V. Kulvait, J. Málek, K. Rajagopal","doi":"10.24423/AOM.2659","DOIUrl":"https://doi.org/10.24423/AOM.2659","url":null,"abstract":"Many titanium alloys and even materials such as concrete exhibit a nonlinear relationship between strain and stress, when the strain is small enough that the square of the norm of the displacement gradient can be ignored in comparison to the norm of the displacement gradient. Such response cannot be described within the classical theory of Cauchy elasticity wherein a linearization of the nonlinear strain leads to the classical linearized elastic response. A new framework for elasticity has been put into place in which one can justify rigorously a nonlinear relationship between the linearized strain and stress. Here, we consider one such model based on a power-law relationship. Previous attempts at describing such response have been either limited to the response of one particular material, e.g. Gum Metal, or involved a model with more material moduli, than the model considered in this work. For the uniaxial response of several metallic alloys, the model that is being considered fits experimental data exceedingly well.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42846422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By means of the theory of elasticity, we investigate the structural instability of a parallel array of identical simply-supported plates. One plate interacts with the neighboring plates through surface attractive forces. The proposed method is based on the 2 × 2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array. Analytical expressions of the critical interaction coefficients for two, three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored. The influence of the end-effect and surface energy on the critical interaction coefficient is also numerically studied. Our solution is valid whether the plates are thin or extremely thick.
{"title":"Exact solution to the structural instability of a parallel array of mutually attracting identical simply-supported plates","authors":"X. Wang, L. Liu","doi":"10.24423/AOM.2699","DOIUrl":"https://doi.org/10.24423/AOM.2699","url":null,"abstract":"By means of the theory of elasticity, we investigate the structural instability of a parallel array of identical simply-supported plates. One plate interacts with the neighboring plates through surface attractive forces. The proposed method is based on the 2 × 2 transfer matrix for a plate and on the solution of the generalized eigenvalue problem for the plate array. Analytical expressions of the critical interaction coefficients for two, three and four interacting plates are obtained when the end-effect of the plates at the ends of the parallel array and the surface energy of the plates are ignored. The influence of the end-effect and surface energy on the critical interaction coefficient is also numerically studied. Our solution is valid whether the plates are thin or extremely thick.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2017-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47196571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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