Pub Date : 2023-03-17DOI: 10.1177/03093247231159820
Jing Liu, Zhifeng Shi, Jin Xu, Yan Cheng, Hongwu Li
The roller profile shape can change the fatigue life and vibrations for planet roller bearing (PRB), as well as the impact between the rollers and cage. In this study, an analytical study of the dynamic forces and vibrations of a PRB considering the roller profile. To avoid the stress concentration at the roller ends, the roller modification method is proposed to improve the dynamic forces. The contact stiffness and load-deformation exponent of the roller-race interaction for four different roller modification types are achieved. A PRB dynamic model is established to discuss the effects of roller modification types on the dynamic forces and vibrations for PRB. Computation results of those four roller modification types are compared to the results of the PRB with the cylindrical roller type. It includes that the roller profile shape can greatly change the contact forces between the rollers and races, as well as the impact forces between the rollers and cage. The roller profile shapes can also influence the vibrations of PRBs.
{"title":"A simulation method for dynamic force and vibrations of a roller bearing in the planetary gears considering the roller profile","authors":"Jing Liu, Zhifeng Shi, Jin Xu, Yan Cheng, Hongwu Li","doi":"10.1177/03093247231159820","DOIUrl":"https://doi.org/10.1177/03093247231159820","url":null,"abstract":"The roller profile shape can change the fatigue life and vibrations for planet roller bearing (PRB), as well as the impact between the rollers and cage. In this study, an analytical study of the dynamic forces and vibrations of a PRB considering the roller profile. To avoid the stress concentration at the roller ends, the roller modification method is proposed to improve the dynamic forces. The contact stiffness and load-deformation exponent of the roller-race interaction for four different roller modification types are achieved. A PRB dynamic model is established to discuss the effects of roller modification types on the dynamic forces and vibrations for PRB. Computation results of those four roller modification types are compared to the results of the PRB with the cylindrical roller type. It includes that the roller profile shape can greatly change the contact forces between the rollers and races, as well as the impact forces between the rollers and cage. The roller profile shapes can also influence the vibrations of PRBs.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88841415","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}
Pub Date : 2023-03-13DOI: 10.1177/03093247231160414
Aman Garg, M. Belarbi, Li Li, Neha Sharma, A. Gupta, H. D. Chalak
Helicoidal schemes possessed by biological creatures possess high strength and stiffness. The adoption of the layup configurations possessed by these biological creatures is not fully explored. The present article aims to carry out the free vibration analysis of biological-inspired laminated composite (B-ILC) plates having helicoidal layup. The analysis is carried out using higher-order zigzag theory (HOZT) as due to the presence of several layers, the HOZT can predict the behavior accurately compared to the shear deformation theory. Based on Hamilton’s principle, the governing equations are worked out and analyzed using the finite element method. The influence of boundary conditions, geometric properties, number of layers, the skew angle of the plate, and material properties on the free vibration behavior are studied in detail.
{"title":"Free vibration analysis of bio-inspired helicoid laminated composite plates","authors":"Aman Garg, M. Belarbi, Li Li, Neha Sharma, A. Gupta, H. D. Chalak","doi":"10.1177/03093247231160414","DOIUrl":"https://doi.org/10.1177/03093247231160414","url":null,"abstract":"Helicoidal schemes possessed by biological creatures possess high strength and stiffness. The adoption of the layup configurations possessed by these biological creatures is not fully explored. The present article aims to carry out the free vibration analysis of biological-inspired laminated composite (B-ILC) plates having helicoidal layup. The analysis is carried out using higher-order zigzag theory (HOZT) as due to the presence of several layers, the HOZT can predict the behavior accurately compared to the shear deformation theory. Based on Hamilton’s principle, the governing equations are worked out and analyzed using the finite element method. The influence of boundary conditions, geometric properties, number of layers, the skew angle of the plate, and material properties on the free vibration behavior are studied in detail.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78808463","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}
Pub Date : 2023-02-07DOI: 10.1177/03093247231152288
Zahra Ramezani Anbaran, F. Rahimzadeh Lotfabad, R. Ebrahimi, H. Danesh Manesh
In this investigation, the previously proposed phenomenological model in the literature is generalized both in terms of the mathematical form of the model and the yield function used to describe the plasticity of the material. Al 1050 is chosen as the model material, where the sheets made from this material are first annealed and then subjected to a tensile test and Erichsen cupping test to obtain tensile properties as well as the FLC of the material. The constants of the generalized model are first obtained by curve fitting, whereby in this approach least overall error is expected as a single equation is used to predict the FLC of material. Further, it is shown that it would be possible to enhance the accuracy of the model at the cost of losing the applicability of a single mathematical expression for both branches of FLC. In this approach, the generalized model would be calibrated for the right branch based on Swift’s model and for the left branch based on Hill’s model. Finally, the effect of the yield criterion used to describe the plasticity of the material on the predictions of the generalized model is investigated, and it is shown that using the Hosford yield criterion yields better results compared to using the von Mises yield criterion.
{"title":"Generalized phenomenological model to analyze the forming limit curve of Al 1050","authors":"Zahra Ramezani Anbaran, F. Rahimzadeh Lotfabad, R. Ebrahimi, H. Danesh Manesh","doi":"10.1177/03093247231152288","DOIUrl":"https://doi.org/10.1177/03093247231152288","url":null,"abstract":"In this investigation, the previously proposed phenomenological model in the literature is generalized both in terms of the mathematical form of the model and the yield function used to describe the plasticity of the material. Al 1050 is chosen as the model material, where the sheets made from this material are first annealed and then subjected to a tensile test and Erichsen cupping test to obtain tensile properties as well as the FLC of the material. The constants of the generalized model are first obtained by curve fitting, whereby in this approach least overall error is expected as a single equation is used to predict the FLC of material. Further, it is shown that it would be possible to enhance the accuracy of the model at the cost of losing the applicability of a single mathematical expression for both branches of FLC. In this approach, the generalized model would be calibrated for the right branch based on Swift’s model and for the left branch based on Hill’s model. Finally, the effect of the yield criterion used to describe the plasticity of the material on the predictions of the generalized model is investigated, and it is shown that using the Hosford yield criterion yields better results compared to using the von Mises yield criterion.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83418801","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}
Pub Date : 2023-02-06DOI: 10.1177/03093247231152569
Peyman Talaie, Mahdi Shaban, Sanaz Khoshlesan
Corrugated cores with structural hierarchy are one types of advanced cores that inspired from nature. In this work, the bending behavior of a second order, hierarchical corrugated structure has been analyzed. Experimental tests are implied to sandwich panels with both first- and second-order corrugated core by means of three-point bending test. For trapezoidal core, finite element model is provided and numerical results are validated by experimental results. Then, the validated properties are used to model sandwich panel with first- and second-order corrugated cores. To make a correct comparison, out-of-plane shear modulus of mentioned cores is calculated. Further to classical approach of ASTM7250, based on the first-order shear deformation theory (FSDT), a closed-form solution is used to predict the out-of-plane core shear modulus and compared with ASTM procedure. Results reveal that including shear deformation effects, the determined shear modulus based on FSDT is larger than classical standard procedure. Furthermore, shear modulus of second-order corrugated core is smaller than first-order one of the same relative densities.
{"title":"Flexural analysis of second-order corrugated composite cores: Experimental, numerical, and theoretical studies","authors":"Peyman Talaie, Mahdi Shaban, Sanaz Khoshlesan","doi":"10.1177/03093247231152569","DOIUrl":"https://doi.org/10.1177/03093247231152569","url":null,"abstract":"Corrugated cores with structural hierarchy are one types of advanced cores that inspired from nature. In this work, the bending behavior of a second order, hierarchical corrugated structure has been analyzed. Experimental tests are implied to sandwich panels with both first- and second-order corrugated core by means of three-point bending test. For trapezoidal core, finite element model is provided and numerical results are validated by experimental results. Then, the validated properties are used to model sandwich panel with first- and second-order corrugated cores. To make a correct comparison, out-of-plane shear modulus of mentioned cores is calculated. Further to classical approach of ASTM7250, based on the first-order shear deformation theory (FSDT), a closed-form solution is used to predict the out-of-plane core shear modulus and compared with ASTM procedure. Results reveal that including shear deformation effects, the determined shear modulus based on FSDT is larger than classical standard procedure. Furthermore, shear modulus of second-order corrugated core is smaller than first-order one of the same relative densities.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90512677","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}
Pub Date : 2023-01-29DOI: 10.1177/03093247231152501
S. Mirshafiee, M. Ashrafi, E. Mousavi
The split Hopkinson pressure bar (SHPB) is a commonly used technique to measure the stress-strain of materials at high strain rate. Using the strain records in the input and output bars, the average stress-strain and strain rate in the sample can be calculated by SHPB formulas based on the one-dimensional wave propagation theory. The accuracy of a SHPB test is based on this assumption. In this paper, first a laser measuring system is designed, implemented, and calibrated in order to obtain the dynamic properties of different materials using split Hopkinson pressure bar test. In this method which is a non-contact one, the displacements of bar/sample interfaces are measured directly using a laser extensometer technique, by using the provided equations, in addition to the strain, the stress of the tested sample can be calculated. Moreover, the operation of the method is evaluated using numerical simulation. Aluminum 7075 and copper C10200 samples were studied to evaluate the implemented measurement method. The comparison with other measurement methods shows good agreement of numerical and experimental results. Moreover, since the one-dimensional wave propagation is not used directly in this method, we show the proposed method can be used even with shorter pressure bars which can reduce the cost of manufacturing and maintenance of the SHPB apparatus.
{"title":"Determination of dynamic material properties using laser measurement technique in split Hopkinson pressure bar","authors":"S. Mirshafiee, M. Ashrafi, E. Mousavi","doi":"10.1177/03093247231152501","DOIUrl":"https://doi.org/10.1177/03093247231152501","url":null,"abstract":"The split Hopkinson pressure bar (SHPB) is a commonly used technique to measure the stress-strain of materials at high strain rate. Using the strain records in the input and output bars, the average stress-strain and strain rate in the sample can be calculated by SHPB formulas based on the one-dimensional wave propagation theory. The accuracy of a SHPB test is based on this assumption. In this paper, first a laser measuring system is designed, implemented, and calibrated in order to obtain the dynamic properties of different materials using split Hopkinson pressure bar test. In this method which is a non-contact one, the displacements of bar/sample interfaces are measured directly using a laser extensometer technique, by using the provided equations, in addition to the strain, the stress of the tested sample can be calculated. Moreover, the operation of the method is evaluated using numerical simulation. Aluminum 7075 and copper C10200 samples were studied to evaluate the implemented measurement method. The comparison with other measurement methods shows good agreement of numerical and experimental results. Moreover, since the one-dimensional wave propagation is not used directly in this method, we show the proposed method can be used even with shorter pressure bars which can reduce the cost of manufacturing and maintenance of the SHPB apparatus.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78937548","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}
Pub Date : 2023-01-26DOI: 10.1177/03093247221150043
Arash Karimi Pour, E. Noroozinejad Farsangi
Two novel plate-bending elements are developed and investigated in this study. Elements with 13 and 15 degree-of-freedoms are named AT13 and AT15, respectively. These triangular elements are formulated in a semi-analytic way. For this aim, the basic elasticity function is employed with unknown parameters. Subsequently, the trial-and-error procedure is used to determine the unidentified constants. Besides, the achieved results are compared with those obtained by displacement-based triangular elements with the same degrees-of-freedom (TUBA13 and TUBA15). In this research, both stress and displacement responses of diverse structures are assessed. After performing extensive numerical studies, the findings clearly demonstrate the superiorities of the proposed elements.
{"title":"Representing capabilities of novel semi-analytical triangular plate elements","authors":"Arash Karimi Pour, E. Noroozinejad Farsangi","doi":"10.1177/03093247221150043","DOIUrl":"https://doi.org/10.1177/03093247221150043","url":null,"abstract":"Two novel plate-bending elements are developed and investigated in this study. Elements with 13 and 15 degree-of-freedoms are named AT13 and AT15, respectively. These triangular elements are formulated in a semi-analytic way. For this aim, the basic elasticity function is employed with unknown parameters. Subsequently, the trial-and-error procedure is used to determine the unidentified constants. Besides, the achieved results are compared with those obtained by displacement-based triangular elements with the same degrees-of-freedom (TUBA13 and TUBA15). In this research, both stress and displacement responses of diverse structures are assessed. After performing extensive numerical studies, the findings clearly demonstrate the superiorities of the proposed elements.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89896937","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}
Pub Date : 2023-01-26DOI: 10.1177/03093247221150666
C. Imediegwu, U. Grimm, R. Moat, I. Jowers
This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.
{"title":"A computational method for determining the linear elastic properties of 2D aperiodic lattice structures","authors":"C. Imediegwu, U. Grimm, R. Moat, I. Jowers","doi":"10.1177/03093247221150666","DOIUrl":"https://doi.org/10.1177/03093247221150666","url":null,"abstract":"This paper develops a framework for determining the linear elastic properties of non-periodic lattice structures. An element-based material assignment methodology is implemented that facilitates the generation and analyses of arbitrary patterns on a structured mesh. An adapted numerical homogenization strategy features the inclusion of a homogenized region in the neighbourhood of the domain boundary that validates the implementation of periodic boundary conditions for an arbitrary finite patch of a periodic or non-periodic lattice structure. To demonstrate the method, the linear elastic properties of an aperiodic lattice pattern based on the Penrose (P3) pattern is evaluated. Such a structure exhibits order without translational symmetry and consequently lacks a repeating unit cell. The isotropic performance of the aperiodic lattice structure is investigated and compared to that of the well-known square periodic lattice. The framework opens the door to the investigation and analyses of other novel cellular structures which are not based on a repeating unit cell. Additive manufacturing facilitates the physical realization of such lattice structures, presenting them as viable alternatives to conventional periodic structures in the aerospace and bio-engineering industries.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88683120","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}
Pub Date : 2023-01-12DOI: 10.1177/03093247221142661
Behrooz Ariannezhad, S. Shahrooi, M. Shishehsaz
In this research, in order to estimate 3D-Stress Intensity Factors in mode I–III, fatigue crack growth and fatigue life prediction of a cracked shaft under various cyclic loading, meshless methods are evaluated and the most appropriate method is selected. For better results, the Base Functions (BFs) are first identified and their performance and efficiency are compared with each other. In addition, while enriching the BFs in all methods and study the effect of increasing the number of sentences of Polynomial-BFs (m = 4, 7,10) and their Linearity or Quadraticity in the accuracy of calculations, two sets of Extend-Enriched-RBFs including the Multi-Quadrics and Gaussian RBFs are used in MQ-RPIM and EXP-RPIM methods. To optimize the shape parameters in the RPIM method and determine the Penalty Factor in the MLPG method, Uni and Multi-objective PSO algorithm was used. Then, a shaft with an initial semi-elliptic surface crack as a 3D-meshless domain for discretizing the weak differential equations was selected and modeled under a fixed latitude tensile, bending, and torsional cyclic loads. Changing the standard values of the shape parameters and estimating their optimal values by the PSO algorithm and comparison of findings with the results of Experimental, MLPG, PIM, FEM, and XFEM methods, has led to the best answer from the applied methods for calculation of; displacement, strain and stress fields, and the SIFs in Mode I–III. Finally, based on the results of uniaxial cyclic load analysis and selection of the MQ-RPIM method, the Multi-axial Cyclic load analysis has been performed on 3D-domain. During this analysis, the Paris Parametric equation along with the Elliptic equation and Liu’s Virtual Strain Energy (VSE) model was used to estimate the fatigue crack growth and fatigue life prediction of a submersible cracked shaft of a pump used in water pumping stations.
{"title":"Evaluation and optimization of meshless methods to estimation of the 3D-stress intensity factors in mode I–III for fatigue life prediction cracked shaft under uni and multi-axial cyclic loading","authors":"Behrooz Ariannezhad, S. Shahrooi, M. Shishehsaz","doi":"10.1177/03093247221142661","DOIUrl":"https://doi.org/10.1177/03093247221142661","url":null,"abstract":"In this research, in order to estimate 3D-Stress Intensity Factors in mode I–III, fatigue crack growth and fatigue life prediction of a cracked shaft under various cyclic loading, meshless methods are evaluated and the most appropriate method is selected. For better results, the Base Functions (BFs) are first identified and their performance and efficiency are compared with each other. In addition, while enriching the BFs in all methods and study the effect of increasing the number of sentences of Polynomial-BFs (m = 4, 7,10) and their Linearity or Quadraticity in the accuracy of calculations, two sets of Extend-Enriched-RBFs including the Multi-Quadrics and Gaussian RBFs are used in MQ-RPIM and EXP-RPIM methods. To optimize the shape parameters in the RPIM method and determine the Penalty Factor in the MLPG method, Uni and Multi-objective PSO algorithm was used. Then, a shaft with an initial semi-elliptic surface crack as a 3D-meshless domain for discretizing the weak differential equations was selected and modeled under a fixed latitude tensile, bending, and torsional cyclic loads. Changing the standard values of the shape parameters and estimating their optimal values by the PSO algorithm and comparison of findings with the results of Experimental, MLPG, PIM, FEM, and XFEM methods, has led to the best answer from the applied methods for calculation of; displacement, strain and stress fields, and the SIFs in Mode I–III. Finally, based on the results of uniaxial cyclic load analysis and selection of the MQ-RPIM method, the Multi-axial Cyclic load analysis has been performed on 3D-domain. During this analysis, the Paris Parametric equation along with the Elliptic equation and Liu’s Virtual Strain Energy (VSE) model was used to estimate the fatigue crack growth and fatigue life prediction of a submersible cracked shaft of a pump used in water pumping stations.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81884224","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}
Pub Date : 2023-01-12DOI: 10.1177/03093247221145793
M. Faraji Oskouie, R. Ansari, H. Rouhi
Several non-classical elasticity theories are used for considering the size-dependent behavior of structures at small scales. The nonlocal theory is widely used to reflect the softening behavior of material at small scales, and theories like the strain gradient theory are employed to reflect the hardening behavior. In this article, the most general form of integral strain- and stress-driven nonlocal models with two nonlocal parameters is developed which is able to consider both hardening and softening influences simultaneously. To this end, it is considered that the stress field at the entire points of the domain is a function of strain field of the entire points of the domain. The free vibration problem of first-order shear deformable beams is solved herein. The integral form of governing equations and associated boundary conditions are obtained first, and then directly solved in a numerical approach. Through developing an efficient matrix formulation and using differential and integral matrix operators, the discretized governing equations are obtained. The simultaneous effects of strain- and stress-driven nonlocal parameters on the natural frequencies of fully clamped, fully simply-supported, and clamped-free nanobeams are investigated. The results indicate that the paradox related to the behavior of clamped-free nanobeams is resolved using the presented integral nonlocal formulation. Also, it is revealed that it is possible to find some specific values of nonlocal parameters at which the prediction of hybrid nonlocal model coincides with that of classical elasticity theory.
{"title":"Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain- and stress-driven nonlocal model","authors":"M. Faraji Oskouie, R. Ansari, H. Rouhi","doi":"10.1177/03093247221145793","DOIUrl":"https://doi.org/10.1177/03093247221145793","url":null,"abstract":"Several non-classical elasticity theories are used for considering the size-dependent behavior of structures at small scales. The nonlocal theory is widely used to reflect the softening behavior of material at small scales, and theories like the strain gradient theory are employed to reflect the hardening behavior. In this article, the most general form of integral strain- and stress-driven nonlocal models with two nonlocal parameters is developed which is able to consider both hardening and softening influences simultaneously. To this end, it is considered that the stress field at the entire points of the domain is a function of strain field of the entire points of the domain. The free vibration problem of first-order shear deformable beams is solved herein. The integral form of governing equations and associated boundary conditions are obtained first, and then directly solved in a numerical approach. Through developing an efficient matrix formulation and using differential and integral matrix operators, the discretized governing equations are obtained. The simultaneous effects of strain- and stress-driven nonlocal parameters on the natural frequencies of fully clamped, fully simply-supported, and clamped-free nanobeams are investigated. The results indicate that the paradox related to the behavior of clamped-free nanobeams is resolved using the presented integral nonlocal formulation. Also, it is revealed that it is possible to find some specific values of nonlocal parameters at which the prediction of hybrid nonlocal model coincides with that of classical elasticity theory.","PeriodicalId":50038,"journal":{"name":"Journal of Strain Analysis for Engineering Design","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87903378","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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