Pub Date : 2020-12-27DOI: 10.15625/0866-7136/14795
D. Pham
Our major new results and the previous ones on the bounds for elastic random polycrystals, and most advanced 3D finite element results for random 3D Voronoi polycrystals are resumed and analysed (together for the first time). Recently obtained numerical Dirichlet and Neumann simulation results for the effective elastic moduli of a large 10000-grain-size random Voronoi polycrystal representative volume element (RVE) for a number of triclinic and monoclinic base crystals (Mursheda and Ranganathan, 2017) are compared critically with the bounds on the moduli. Though major parts within the simulation results fall within the bounds of Pham (2011), some Dirichlet upper estimates still lie outside the bounds. Many more RVEs are needed to represent the Voronoi polycrystal on the same RVE-size-level, and larger RVEs are needed for checking the convergence and comparisons with the bounds.
{"title":"On the estimates for the elastic moduli of random Voronoi triclinic polycrystals","authors":"D. Pham","doi":"10.15625/0866-7136/14795","DOIUrl":"https://doi.org/10.15625/0866-7136/14795","url":null,"abstract":"Our major new results and the previous ones on the bounds for elastic random polycrystals, and most advanced 3D finite element results for random 3D Voronoi polycrystals are resumed and analysed (together for the first time). Recently obtained numerical Dirichlet and Neumann simulation results for the effective elastic moduli of a large 10000-grain-size random Voronoi polycrystal representative volume element (RVE) for a number of triclinic and monoclinic base crystals (Mursheda and Ranganathan, 2017) are compared critically with the bounds on the moduli. Though major parts within the simulation results fall within the bounds of Pham (2011), some Dirichlet upper estimates still lie outside the bounds. Many more RVEs are needed to represent the Voronoi polycrystal on the same RVE-size-level, and larger RVEs are needed for checking the convergence and comparisons with the bounds.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131122000","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}
Pub Date : 2020-12-27DOI: 10.15625/0866-7136/14765
C. Le, Phuc L. H. Ho
This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.
{"title":"Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method","authors":"C. Le, Phuc L. H. Ho","doi":"10.15625/0866-7136/14765","DOIUrl":"https://doi.org/10.15625/0866-7136/14765","url":null,"abstract":"This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116679578","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}
Pub Date : 2020-12-24DOI: 10.15625/0866-7136/15073
T. Huynh, B. Nguyen, A. Pradhan, Quang Pham
Vision-based inspection has received significant interests from structural health monitoring and maintenance academia. The vision-based approach has unique advantages over the traditional sensor-based inspection, including non-contact sensing, low cost, simple setup, and being immune to environmental effects. Despite that, the translation of the vision-based inspection to in-service structures in Viet Nam has been limited so far. Herein, the authors examine the field applicability of a vision-based approach for joints monitoring of a historical truss bridge in Vietnam. Firstly, a well-established vision-based bolt-loosening monitoring approach is briefly described. Secondly, a field test on the Nam O bridge (Da Nang City) is performed. A digital camera is used to capture the images of representative bolted joints of the bridge. Lastly, the vision-based approach is applied to monitor the bolted joints. The angle of bolts in the joints is estimated from the captured images, from which the accuracy of the approach is evaluated. This study is one of the first case applications, demonstrating the field applicability of the vision-based bolt-loosening approach for inspecting a real bridge in Vietnam.
{"title":"Vision-based inspection of bolted joints: Field evaluation on a historical truss bridge in Vietnam","authors":"T. Huynh, B. Nguyen, A. Pradhan, Quang Pham","doi":"10.15625/0866-7136/15073","DOIUrl":"https://doi.org/10.15625/0866-7136/15073","url":null,"abstract":"Vision-based inspection has received significant interests from structural health monitoring and maintenance academia. The vision-based approach has unique advantages over the traditional sensor-based inspection, including non-contact sensing, low cost, simple setup, and being immune to environmental effects. Despite that, the translation of the vision-based inspection to in-service structures in Viet Nam has been limited so far. Herein, the authors examine the field applicability of a vision-based approach for joints monitoring of a historical truss bridge in Vietnam. Firstly, a well-established vision-based bolt-loosening monitoring approach is briefly described. Secondly, a field test on the Nam O bridge (Da Nang City) is performed. A digital camera is used to capture the images of representative bolted joints of the bridge. Lastly, the vision-based approach is applied to monitor the bolted joints. The angle of bolts in the joints is estimated from the captured images, from which the accuracy of the approach is evaluated. This study is one of the first case applications, demonstrating the field applicability of the vision-based bolt-loosening approach for inspecting a real bridge in Vietnam.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125664482","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}
Pub Date : 2020-12-15DOI: 10.15625/0866-7136/15467
N. D. Anh, D. Hieu
The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler – Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution. The influences of the nonlocal parameter, material length scale parameter, aspect ratio, diameter ratio, Winkler parameter and longitudinal magnetic field on the nonlinear vibration responses of the nanotubes with pinned-pinned and clamped-clamped boundary conditions are investigated and discussed.
{"title":"Nonlinear vibration of nonlocal strain gradient nanotubes under longitudinal magnetic field","authors":"N. D. Anh, D. Hieu","doi":"10.15625/0866-7136/15467","DOIUrl":"https://doi.org/10.15625/0866-7136/15467","url":null,"abstract":"The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler – Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution. The influences of the nonlocal parameter, material length scale parameter, aspect ratio, diameter ratio, Winkler parameter and longitudinal magnetic field on the nonlinear vibration responses of the nanotubes with pinned-pinned and clamped-clamped boundary conditions are investigated and discussed.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123929368","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}
Pub Date : 2020-09-27DOI: 10.15625/0866-7136/15479
P. Kumar, A. Rajagopal, M. Pandey
In this work our objective is to understand the failure behaviour of unreinforced masonry under in-plane cyclic loading. For this purpose we proposed a plasticity based interface model consists of a single yield surface criteria which is a direct extension of Mohr-Coulomb criteria with a tension cut and compression cap and a back stress vector is introduced as a mixed hardening law variable in the adopted yield surface to capture the unloading/reloading behaviour of masonry under cyclic loading. A simplified micromechanical interface modelling approach is adopted to capture all the failure modes of masonry. The integration of the differential constitutive equation is done by using implicit Euler backward integration approach and the obtained non-linear set of equations are solved by a combined local/global Newton solver. The proposed constitutive model is implemented in ABAQUS by writing UMAT (user-defined subroutine) and the obtained numerical results are compared with experimental results available in the literature.
{"title":"Plasticity based interface model for failure modelling of unreinforced masonry under cyclic loading","authors":"P. Kumar, A. Rajagopal, M. Pandey","doi":"10.15625/0866-7136/15479","DOIUrl":"https://doi.org/10.15625/0866-7136/15479","url":null,"abstract":"In this work our objective is to understand the failure behaviour of unreinforced masonry under in-plane cyclic loading. For this purpose we proposed a plasticity based interface model consists of a single yield surface criteria which is a direct extension of Mohr-Coulomb criteria with a tension cut and compression cap and a back stress vector is introduced as a mixed hardening law variable in the adopted yield surface to capture the unloading/reloading behaviour of masonry under cyclic loading. A simplified micromechanical interface modelling approach is adopted to capture all the failure modes of masonry. The integration of the differential constitutive equation is done by using implicit Euler backward integration approach and the obtained non-linear set of equations are solved by a combined local/global Newton solver. The proposed constitutive model is implemented in ABAQUS by writing UMAT (user-defined subroutine) and the obtained numerical results are compared with experimental results available in the literature.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128919871","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}
Pub Date : 2020-09-27DOI: 10.15625/0866-7136/15512
A. Hassanirad, V. Vaziri, K. Woo, M. Wiercigroch
Initiation of cracks and their propagation in prescribed orientations on tubular specimens has been made possible on a dynamic fatigue testing rig developed at the University of Aberdeen. This rig was originally designed to perform experiments on single edge notched beams (SENB) [1,2]. Modifications have recently been made so as to accommodate experimental tests on tubular specimens with a range of sizes and other cross sections. Crack initiation at grooves on such specimens has been followed by crack growth. At the same time, lateral oscillations of cracked specimen have been measured, as well as accelerations of base excitation, masses above and below cracked specimen. Forces on these two masses have been observed by two load cells attached at positions close to specimen. These load cells facilitated the measurement of stresses in experiment. Crack length time histories have also been constructed by applying an alternating current potential difference (ACPD) method. Fatigue cracks were initiated at the pre-cut grooves in aluminium tubular specimens. Three specimens with different groove sizes were tested in fifteen individual experiments. A three-dimensional Finite Element model was established for each specimen so as to calculate the stress concentration factor (SCF). This formed the basis of determining the amplitude of forcing input made possible by an electromechanical shaker. The phase shifts of acquired time histories has provided some indication of energy transfer mechanism during fatigue and system dynamic response. Observations of cracked specimen displacement during experiments was compared against calculated displacement from elastic theory. Nonlinear responses were observed, suggesting nonlinear stiffness characteristics of the specimen due to discontinuities introduced by crack growth and plasticity effects. Comparison of damage combinations in experimental observation was made with predictions from BS EN 1999-1-3. All experimental observations of total damage combination were higher than predicted values by the latter code.
{"title":"Dynamic crack propagation in specimens with a surface irregularity","authors":"A. Hassanirad, V. Vaziri, K. Woo, M. Wiercigroch","doi":"10.15625/0866-7136/15512","DOIUrl":"https://doi.org/10.15625/0866-7136/15512","url":null,"abstract":"Initiation of cracks and their propagation in prescribed orientations on tubular specimens has been made possible on a dynamic fatigue testing rig developed at the University of Aberdeen. This rig was originally designed to perform experiments on single edge notched beams (SENB) [1,2]. Modifications have recently been made so as to accommodate experimental tests on tubular specimens with a range of sizes and other cross sections. Crack initiation at grooves on such specimens has been followed by crack growth. At the same time, lateral oscillations of cracked specimen have been measured, as well as accelerations of base excitation, masses above and below cracked specimen. Forces on these two masses have been observed by two load cells attached at positions close to specimen. These load cells facilitated the measurement of stresses in experiment. Crack length time histories have also been constructed by applying an alternating current potential difference (ACPD) method. Fatigue cracks were initiated at the pre-cut grooves in aluminium tubular specimens. Three specimens with different groove sizes were tested in fifteen individual experiments. A three-dimensional Finite Element model was established for each specimen so as to calculate the stress concentration factor (SCF). This formed the basis of determining the amplitude of forcing input made possible by an electromechanical shaker. The phase shifts of acquired time histories has provided some indication of energy transfer mechanism during fatigue and system dynamic response. Observations of cracked specimen displacement during experiments was compared against calculated displacement from elastic theory. Nonlinear responses were observed, suggesting nonlinear stiffness characteristics of the specimen due to discontinuities introduced by crack growth and plasticity effects. Comparison of damage combinations in experimental observation was made with predictions from BS EN 1999-1-3. All experimental observations of total damage combination were higher than predicted values by the latter code.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121660781","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}
Pub Date : 2020-09-27DOI: 10.15625/0866-7136/15356
A. Nguyen, N. D. Anh
The paper presents a new approach to the conventional averaging in which the role of boundary values is considered in a more detailed way. It results in a new weighted local averaging operator (WLAO) taking into account the particular role of boundary values. A remarkable feature of WLAO is that this operator contains a parameter of boundary regulation p and depends on a local value h of the integration domain. By varying these two parameters one can regulate the obtained approximate solutions in order to get more accurate ones. It has been shown that the combination of WLAO with Galerkin method can lead to an effective approximate tool for the buckling problem of columns and for the frequency analysis of free vibration of strongly nonlinear systems.
{"title":"A modified averaging operator with some applications","authors":"A. Nguyen, N. D. Anh","doi":"10.15625/0866-7136/15356","DOIUrl":"https://doi.org/10.15625/0866-7136/15356","url":null,"abstract":"The paper presents a new approach to the conventional averaging in which the role of boundary values is considered in a more detailed way. It results in a new weighted local averaging operator (WLAO) taking into account the particular role of boundary values. A remarkable feature of WLAO is that this operator contains a parameter of boundary regulation p and depends on a local value h of the integration domain. By varying these two parameters one can regulate the obtained approximate solutions in order to get more accurate ones. It has been shown that the combination of WLAO with Galerkin method can lead to an effective approximate tool for the buckling problem of columns and for the frequency analysis of free vibration of strongly nonlinear systems.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114285920","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}
Pub Date : 2020-09-27DOI: 10.15625/0866-7136/15309
H. Tung, N. D. Kien, L. N. Trang
For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.
{"title":"Thermal postbuckling analysis of FG-CNTRC doubly curved panels with elastically restrained edges using Reddy's higher order shear deformation theory","authors":"H. Tung, N. D. Kien, L. N. Trang","doi":"10.15625/0866-7136/15309","DOIUrl":"https://doi.org/10.15625/0866-7136/15309","url":null,"abstract":"For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123630192","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}
Pub Date : 2020-09-27DOI: 10.15625/0866-7136/15042
A. Pagani, R. Azzara, R. Augello, E. Carrera, B. Wu
The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second PiolaKirchhoff (PK2) stress distributions are evaluated, and lowerto higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.
{"title":"Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations","authors":"A. Pagani, R. Azzara, R. Augello, E. Carrera, B. Wu","doi":"10.15625/0866-7136/15042","DOIUrl":"https://doi.org/10.15625/0866-7136/15042","url":null,"abstract":"The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second PiolaKirchhoff (PK2) stress distributions are evaluated, and lowerto higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125018650","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}
Pub Date : 2020-09-27DOI: 10.15625/0866-7136/15372
Chien H. Thai, H. Nguyen-Xuan
In this study, a simple size-dependent isogeometric approach for bending analysis of functionally graded (FG) microplates using the modified strain gradient theory (MSGT), simple first-order shear deformation theory (sFSDT) and isogeometric analysis is presented for the first time. The present approach reduces one variable when comparing with the original first-order shear deformation theory (FSDT) within five variables and only considers three material length scale parameters (MLSPs) to capture size effects. Effective material properties as Young’s modulus, Poisson’s ratio and density mass are computed by a rule of mixture. Thanks to the principle of virtual work, the essential equations which are solved by the isogeometric analysis method, are derived. Rectangular and circular FG microplates with different boundary conditions, volume fraction and material length scale parameter are exampled to evaluate the deflections of FG microplates.
{"title":"A simple size-dependent isogeometric approach for bending analysis of functionally graded microplates using the modified strain gradient elasticity theory","authors":"Chien H. Thai, H. Nguyen-Xuan","doi":"10.15625/0866-7136/15372","DOIUrl":"https://doi.org/10.15625/0866-7136/15372","url":null,"abstract":"In this study, a simple size-dependent isogeometric approach for bending analysis of functionally graded (FG) microplates using the modified strain gradient theory (MSGT), simple first-order shear deformation theory (sFSDT) and isogeometric analysis is presented for the first time. The present approach reduces one variable when comparing with the original first-order shear deformation theory (FSDT) within five variables and only considers three material length scale parameters (MLSPs) to capture size effects. Effective material properties as Young’s modulus, Poisson’s ratio and density mass are computed by a rule of mixture. Thanks to the principle of virtual work, the essential equations which are solved by the isogeometric analysis method, are derived. Rectangular and circular FG microplates with different boundary conditions, volume fraction and material length scale parameter are exampled to evaluate the deflections of FG microplates.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131043015","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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