Pub Date : 2019-06-27DOI: 10.1504/IJMSI.2019.10022238
Ashutosh Bijalwan, B. P. Patel
Volumetric locking is exhibited by nearly incompressible solids such as rubber, resulting in over-stiffening response of the finite element mesh. In this work, we developed the displacement-based computationally efficient volumetric locking-free 3D finite element using smoothening of determinant of deformation gradient (J-Bar method) within the framework of isotropic hyperelasticity. The developed methodology is employed to analyse a rubber block undergoing finite stretch and bending deformations. The convergence study for finite stretch and bending of rubber block is presented. Results of the analysis show that J-Bar method efficiently removes the volumetric locking.
{"title":"A new 3D finite element for the finite deformation of nearly incompressible hyperelastic solids","authors":"Ashutosh Bijalwan, B. P. Patel","doi":"10.1504/IJMSI.2019.10022238","DOIUrl":"https://doi.org/10.1504/IJMSI.2019.10022238","url":null,"abstract":"Volumetric locking is exhibited by nearly incompressible solids such as rubber, resulting in over-stiffening response of the finite element mesh. In this work, we developed the displacement-based computationally efficient volumetric locking-free 3D finite element using smoothening of determinant of deformation gradient (J-Bar method) within the framework of isotropic hyperelasticity. The developed methodology is employed to analyse a rubber block undergoing finite stretch and bending deformations. The convergence study for finite stretch and bending of rubber block is presented. Results of the analysis show that J-Bar method efficiently removes the volumetric locking.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"58 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41257612","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 : 2019-06-27DOI: 10.1504/IJMSI.2019.10022228
Khubilal Khatri, A. Lal
This manuscript presents the fracture behaviour of a slanted edge cracked plate with a circular hole subjected to various in-plane loadings, such as tensile, shear and combined (tensile and shear) loadings, through the mixed mode stress intensity factors (MMSIF). There is a lack of work in the direction of calculating the fracture behaviour of the slanted crack under the influence of a hole subjected to the various in-plane loadings. In this work, the crack is modelled using extended finite element method (XFEM) under plane strain condition using MATLAB. The MMSIFs are increased with the increment in the crack length but as the crack angle is increased the Mode-I SIFs are decreased whereas Mode-II SIFs are increased. The SIFs are critical for the plate with a hole as compared to the plate without a hole. The values of MMSIFs are the highest for the plate under combined loading and the least under tensile loading.
{"title":"Mixed mode stress intensity factors of slanted edge cracked plate with hole subjected to various in-plane loadings using XFEM","authors":"Khubilal Khatri, A. Lal","doi":"10.1504/IJMSI.2019.10022228","DOIUrl":"https://doi.org/10.1504/IJMSI.2019.10022228","url":null,"abstract":"This manuscript presents the fracture behaviour of a slanted edge cracked plate with a circular hole subjected to various in-plane loadings, such as tensile, shear and combined (tensile and shear) loadings, through the mixed mode stress intensity factors (MMSIF). There is a lack of work in the direction of calculating the fracture behaviour of the slanted crack under the influence of a hole subjected to the various in-plane loadings. In this work, the crack is modelled using extended finite element method (XFEM) under plane strain condition using MATLAB. The MMSIFs are increased with the increment in the crack length but as the crack angle is increased the Mode-I SIFs are decreased whereas Mode-II SIFs are increased. The SIFs are critical for the plate with a hole as compared to the plate without a hole. The values of MMSIFs are the highest for the plate under combined loading and the least under tensile loading.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44618660","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 : 2019-06-27DOI: 10.1504/IJMSI.2019.10022232
Vishal Agrawal, S. Gautam
It is known that during the simulation of the adhesive contact problems highly nonlinear responses of interaction forces occur within the very narrow adhesive zone. It leads to the loss of quadratic-rate of convergence during Newton-Raphson iterations and unstable computational behaviour. In case of standard finite element formulation, a very fine mesh resolution is needed for the stable computations, but a significant computational cost is associated. For minimising the cost without the loss of accuracy of the solution, contact surface enrichment approaches have been presented. These approaches utilise the higher-order Lagrangian polynomial functions for the enrichment of contact finite elements. In the present work, based on the incorporation of fifth- and seventh-order Hermite interpolation functions two new enriched contact finite elements are formulated. The performance of proposed enriched contact finite elements is demonstrated through the simulation of peeling of an initially flat deformable strip from a rigid substrate. A stable solution is obtained at a relatively coarser mesh than the fully Lagrangian discretised finite element mesh. It is shown that the proposed higher order Hermite enriched contact finite elements attain better performance when compared with earlier introduced enriched elements.
{"title":"Higher order Hermite enriched contact finite elements for adhesive contact problems","authors":"Vishal Agrawal, S. Gautam","doi":"10.1504/IJMSI.2019.10022232","DOIUrl":"https://doi.org/10.1504/IJMSI.2019.10022232","url":null,"abstract":"It is known that during the simulation of the adhesive contact problems highly nonlinear responses of interaction forces occur within the very narrow adhesive zone. It leads to the loss of quadratic-rate of convergence during Newton-Raphson iterations and unstable computational behaviour. In case of standard finite element formulation, a very fine mesh resolution is needed for the stable computations, but a significant computational cost is associated. For minimising the cost without the loss of accuracy of the solution, contact surface enrichment approaches have been presented. These approaches utilise the higher-order Lagrangian polynomial functions for the enrichment of contact finite elements. In the present work, based on the incorporation of fifth- and seventh-order Hermite interpolation functions two new enriched contact finite elements are formulated. The performance of proposed enriched contact finite elements is demonstrated through the simulation of peeling of an initially flat deformable strip from a rigid substrate. A stable solution is obtained at a relatively coarser mesh than the fully Lagrangian discretised finite element mesh. It is shown that the proposed higher order Hermite enriched contact finite elements attain better performance when compared with earlier introduced enriched elements.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44982215","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 : 2019-06-27DOI: 10.1504/IJMSI.2019.10022236
P. Chakraborty, Wen Jiang
Nickel-based alloys are widely used in high temperature applications due to their favourable properties at extreme conditions. However, due to their high cost, efforts are being relentlessly made to extend the useful life of the components made from these alloys. Such life extension requires reliable constitutive models with detailed quantitative understanding of the factors contributing to property variations. Micromechanical analysis along with multi-scale methods can be a key enabler in developing the required high fidelity models. Particularly for properties such as creep that require long term prediction, accelerated tests with empirical models may prove insufficient. Thus, in the present work, a crystal plasticity-based creep model has been developed for solution strengthened nickel-based alloys. Through this model, the effect of microstructural variations in grain orientation, size, etc. on the secondary creep strain rate can be captured. The performance of the model is evaluated against creep data of alloy 617.
{"title":"Crystal plasticity-based creep model for solution-strengthened nickel-based alloys","authors":"P. Chakraborty, Wen Jiang","doi":"10.1504/IJMSI.2019.10022236","DOIUrl":"https://doi.org/10.1504/IJMSI.2019.10022236","url":null,"abstract":"Nickel-based alloys are widely used in high temperature applications due to their favourable properties at extreme conditions. However, due to their high cost, efforts are being relentlessly made to extend the useful life of the components made from these alloys. Such life extension requires reliable constitutive models with detailed quantitative understanding of the factors contributing to property variations. Micromechanical analysis along with multi-scale methods can be a key enabler in developing the required high fidelity models. Particularly for properties such as creep that require long term prediction, accelerated tests with empirical models may prove insufficient. Thus, in the present work, a crystal plasticity-based creep model has been developed for solution strengthened nickel-based alloys. Through this model, the effect of microstructural variations in grain orientation, size, etc. on the secondary creep strain rate can be captured. The performance of the model is evaluated against creep data of alloy 617.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48739552","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 : 2018-10-27DOI: 10.1504/IJMSI.2018.10017009
Swathika Meenraj, C. L. Rao, V. Balasubramanian
Shirodhara, an Ayurveda treatment, is idealised as an application of fluid impact on a piezoelectric plate completely bonded with another elastic plate. The human forehead is approximated as an isotropic homogeneous curved piezoelectric plate over another plate which is idealised as an elastic foundation. Displacement, stresses and voltages will be induced in the plate due to the impact of fluid. The fluids used for force analysis are Ksheerabala oil and Mahanarayana oil. A pure mechanical analysis was conducted to estimate displacements and stresses induced by fluid impact with different boundary conditions under static loading condition. Induced voltages due to fluid impact are estimated using appropriate piezoelectric constants. The implication of these generated voltages on the effectiveness of shirodhara treatment is discussed.
{"title":"Characterisation of electromechanical response of forehead tissues due to fluid impact during shirodhara treatment","authors":"Swathika Meenraj, C. L. Rao, V. Balasubramanian","doi":"10.1504/IJMSI.2018.10017009","DOIUrl":"https://doi.org/10.1504/IJMSI.2018.10017009","url":null,"abstract":"Shirodhara, an Ayurveda treatment, is idealised as an application of fluid impact on a piezoelectric plate completely bonded with another elastic plate. The human forehead is approximated as an isotropic homogeneous curved piezoelectric plate over another plate which is idealised as an elastic foundation. Displacement, stresses and voltages will be induced in the plate due to the impact of fluid. The fluids used for force analysis are Ksheerabala oil and Mahanarayana oil. A pure mechanical analysis was conducted to estimate displacements and stresses induced by fluid impact with different boundary conditions under static loading condition. Induced voltages due to fluid impact are estimated using appropriate piezoelectric constants. The implication of these generated voltages on the effectiveness of shirodhara treatment is discussed.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"12 1","pages":"353"},"PeriodicalIF":0.0,"publicationDate":"2018-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49145993","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 : 2018-10-27DOI: 10.1504/IJMSI.2018.10017012
A. Naidu, Vinay Pittala
The electromechanical impedance (EMI) technique for structural health monitoring (SHM) relies on the analysis of the electrical admittance response, known as the admittance signature, of a piezoelectric ceramic (PZT) chip bonded on or embedded within a structure. Damage in the structure alters its mechanical impedance. Owing to the dynamic coupling that exists between the mechanical impedances of the structure and the PZT chip, this is in turn reflected in the changed admittance signature. The changes in the admittance signature due to deterioration of the PZT characteristics need to be distinguished from those due to structural damage for effective SHM. This paper presents the results of a numerical study carried out to understand the influence of PZT material parameters and geometric characteristics on the admittance signature, which may be useful for effective analysis of diagnostic signals for SHM purposes.
{"title":"Influence of piezoelectric parameters on admittance diagnostic signals for structural health monitoring: a numerical study","authors":"A. Naidu, Vinay Pittala","doi":"10.1504/IJMSI.2018.10017012","DOIUrl":"https://doi.org/10.1504/IJMSI.2018.10017012","url":null,"abstract":"The electromechanical impedance (EMI) technique for structural health monitoring (SHM) relies on the analysis of the electrical admittance response, known as the admittance signature, of a piezoelectric ceramic (PZT) chip bonded on or embedded within a structure. Damage in the structure alters its mechanical impedance. Owing to the dynamic coupling that exists between the mechanical impedances of the structure and the PZT chip, this is in turn reflected in the changed admittance signature. The changes in the admittance signature due to deterioration of the PZT characteristics need to be distinguished from those due to structural damage for effective SHM. This paper presents the results of a numerical study carried out to understand the influence of PZT material parameters and geometric characteristics on the admittance signature, which may be useful for effective analysis of diagnostic signals for SHM purposes.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"12 1","pages":"316"},"PeriodicalIF":0.0,"publicationDate":"2018-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48146079","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 : 2018-10-27DOI: 10.1504/IJMSI.2018.10017008
V. Murugesan, P. Sreejith, S. B. Tiwari, K. Kumar
One of the single point failure modes identified for the electro hydraulic control actuators of launch vehicles, is the fatigue failure of the hydraulic plumbing and its joints due to severe vibration environments. This paper presents a case study of the fatigue analysis on the hydraulic plumbing with flared coupling joint, subjected to high vibration levels. An evaluation of the vibration response of the system is made through analysis and experimentation. A finite element model of the plumbing is made to capture the dynamic behaviour of the system. The alternating stresses are assessed by dynamic stress analysis using the validated model. Fatigue life cycle estimation and reliability of the joint are determined pragmatically through stress life methods, based on the local peak stress, the corresponding local strength, and their statistical distribution. Based on the study, a simple design solution is suggested to improve the robustness of the critical control actuator of the launch vehicle.
{"title":"Fatigue life cycle estimation and reliability analysis of hydraulic plumbing of a launch vehicle control actuator","authors":"V. Murugesan, P. Sreejith, S. B. Tiwari, K. Kumar","doi":"10.1504/IJMSI.2018.10017008","DOIUrl":"https://doi.org/10.1504/IJMSI.2018.10017008","url":null,"abstract":"One of the single point failure modes identified for the electro hydraulic control actuators of launch vehicles, is the fatigue failure of the hydraulic plumbing and its joints due to severe vibration environments. This paper presents a case study of the fatigue analysis on the hydraulic plumbing with flared coupling joint, subjected to high vibration levels. An evaluation of the vibration response of the system is made through analysis and experimentation. A finite element model of the plumbing is made to capture the dynamic behaviour of the system. The alternating stresses are assessed by dynamic stress analysis using the validated model. Fatigue life cycle estimation and reliability of the joint are determined pragmatically through stress life methods, based on the local peak stress, the corresponding local strength, and their statistical distribution. Based on the study, a simple design solution is suggested to improve the robustness of the critical control actuator of the launch vehicle.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"12 1","pages":"277"},"PeriodicalIF":0.0,"publicationDate":"2018-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42509099","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 : 2018-10-27DOI: 10.1504/IJMSI.2018.10017010
A. Upadhyay, C. Ramdas, K. Simha
Cylindrical tubes made of special alloy steels such as HNS, Maraging steel and EN19 for defence applications are often subjected to blast loads. However, there is very limited information available in the literature for the design of such tubes in case of blast loading due to explosion. In this paper, a mild steel tube is subjected to blast loading using TNT explosive, where the detonation was carried out at a distance of 0.3 m from the outer surface of the tube. The cylindrical charge is kept on mild steel plate for explosion. Experimentally, strains have been recorded at different positions across the circumference and along the length of the tube and acceleration of the tube is recorded at multiple locations. Numerical analysis is carried out using Abacus and CONWEPR code for comparison and for developing engineering concepts. Average pressure is also estimated near to the charge using brute force technique.
{"title":"Response of cylindrical tube under blast: experiment and numerical simulation","authors":"A. Upadhyay, C. Ramdas, K. Simha","doi":"10.1504/IJMSI.2018.10017010","DOIUrl":"https://doi.org/10.1504/IJMSI.2018.10017010","url":null,"abstract":"Cylindrical tubes made of special alloy steels such as HNS, Maraging steel and EN19 for defence applications are often subjected to blast loads. However, there is very limited information available in the literature for the design of such tubes in case of blast loading due to explosion. In this paper, a mild steel tube is subjected to blast loading using TNT explosive, where the detonation was carried out at a distance of 0.3 m from the outer surface of the tube. The cylindrical charge is kept on mild steel plate for explosion. Experimentally, strains have been recorded at different positions across the circumference and along the length of the tube and acceleration of the tube is recorded at multiple locations. Numerical analysis is carried out using Abacus and CONWEPR code for comparison and for developing engineering concepts. Average pressure is also estimated near to the charge using brute force technique.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"12 1","pages":"339"},"PeriodicalIF":0.0,"publicationDate":"2018-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45330770","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 : 2018-10-27DOI: 10.1504/ijmsi.2018.10017011
Daolian Wang, C. Liao, Wenqian Li, Hao Lu
The composite overwrapped pressure vessel (COPV) is sensitive to impact, and even small impact damage may cause serious consequences. In order to investigate the impact damage to the COPV, both the finite element (FE) method and the experimental method are employed. Based on the ANSYS software, the FE model is developed, and the drop test module provided by ANSYS/LS-DYNA is used to analyse the impact of the COPV. In order to carry out experimental studies, there are three positions that are selected as the impact positions on the cylindrical section of the COPV. In every impact position, there are five impact spots, and the impact energies are 10J, 15J, 20J, 25J, and 30J, separately. Four experiments were successively carried out, including the impact test, the ultrasonic detection of impact damage, the depth detection of impact pit, and the experiment of thermal deply. The calculated results from the proposed FE model were compared with the corresponding test results. The relations of impact damage to both impact energy and impact position were revealed, and some characteristics and laws of the impact damage were illuminated.
{"title":"Analyses and experimental study about impact damage of COPV","authors":"Daolian Wang, C. Liao, Wenqian Li, Hao Lu","doi":"10.1504/ijmsi.2018.10017011","DOIUrl":"https://doi.org/10.1504/ijmsi.2018.10017011","url":null,"abstract":"The composite overwrapped pressure vessel (COPV) is sensitive to impact, and even small impact damage may cause serious consequences. In order to investigate the impact damage to the COPV, both the finite element (FE) method and the experimental method are employed. Based on the ANSYS software, the FE model is developed, and the drop test module provided by ANSYS/LS-DYNA is used to analyse the impact of the COPV. In order to carry out experimental studies, there are three positions that are selected as the impact positions on the cylindrical section of the COPV. In every impact position, there are five impact spots, and the impact energies are 10J, 15J, 20J, 25J, and 30J, separately. Four experiments were successively carried out, including the impact test, the ultrasonic detection of impact damage, the depth detection of impact pit, and the experiment of thermal deply. The calculated results from the proposed FE model were compared with the corresponding test results. The relations of impact damage to both impact energy and impact position were revealed, and some characteristics and laws of the impact damage were illuminated.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"12 1","pages":"302"},"PeriodicalIF":0.0,"publicationDate":"2018-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45316966","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 : 2018-08-09DOI: 10.1504/IJMSI.2018.10014946
Y. Chen, Yingwei Song, Jianxun Yang, Teng Teng
In this paper, the control equation is first set up by using the reciprocal theory method when considering the section rotation of deep beam, shear deformation of adjacent cross section and the transverse stress. Then the control equation of deep beams under three kinds of boundary conditions is established. According to the comparison between the numerical value and finite element simulation value, we can know that the control equation and the deflection equation of the forced vibration of deep beams are correct. This is a new computing method of the forced vibration problem of deep beams under distributed harmonic load.
{"title":"A new method of forced vibration problem of deep beams under distributed harmonic load","authors":"Y. Chen, Yingwei Song, Jianxun Yang, Teng Teng","doi":"10.1504/IJMSI.2018.10014946","DOIUrl":"https://doi.org/10.1504/IJMSI.2018.10014946","url":null,"abstract":"In this paper, the control equation is first set up by using the reciprocal theory method when considering the section rotation of deep beam, shear deformation of adjacent cross section and the transverse stress. Then the control equation of deep beams under three kinds of boundary conditions is established. According to the comparison between the numerical value and finite element simulation value, we can know that the control equation and the deflection equation of the forced vibration of deep beams are correct. This is a new computing method of the forced vibration problem of deep beams under distributed harmonic load.","PeriodicalId":39035,"journal":{"name":"International Journal of Materials and Structural Integrity","volume":"12 1","pages":"179"},"PeriodicalIF":0.0,"publicationDate":"2018-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42857169","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：