Pub Date : 2024-12-01DOI: 10.1007/s00419-024-02710-6
Masoud Ajri
This research analyzes the buckling and post-buckling behavior of composite cylindrical shells with a polymer core and carbon nanotube-reinforced inner and outer copper layers with functional distribution under axial compressive loading. For this purpose, the differential equations governing the nonlinear buckling behavior of these shells were extracted while considering large deformations. Employing the Ritz energy method and considering the Airy function, analytical relations for the buckling load and the critical stress of the structure are extracted. In the following, considering different distributions, the equivalent mechanical properties of the composite structure have been calculated using the law of mixtures. Finally, the effect of different parameters, such as distribution types and volume fraction of nanotubes, on nonlinear buckling loads and post-buckling behavior of these materials is investigated. Results show that increasing the volume fraction of carbon nanotubes reduces the change in the critical length of the cylindrical shell, which happens as a result of increasing Young's modulus and the equivalent stiffness of the shell.
{"title":"The nonlinear post-buckling behavior of FG cylindrical copper shell reinforced with carbon nanotubes with a polymer core","authors":"Masoud Ajri","doi":"10.1007/s00419-024-02710-6","DOIUrl":"10.1007/s00419-024-02710-6","url":null,"abstract":"<div><p>This research analyzes the buckling and post-buckling behavior of composite cylindrical shells with a polymer core and carbon nanotube-reinforced inner and outer copper layers with functional distribution under axial compressive loading. For this purpose, the differential equations governing the nonlinear buckling behavior of these shells were extracted while considering large deformations. Employing the Ritz energy method and considering the Airy function, analytical relations for the buckling load and the critical stress of the structure are extracted. In the following, considering different distributions, the equivalent mechanical properties of the composite structure have been calculated using the law of mixtures. Finally, the effect of different parameters, such as distribution types and volume fraction of nanotubes, on nonlinear buckling loads and post-buckling behavior of these materials is investigated. Results show that increasing the volume fraction of carbon nanotubes reduces the change in the critical length of the cylindrical shell, which happens as a result of increasing Young's modulus and the equivalent stiffness of the shell.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142757917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Crack shape evolution of single edge through cracked specimens under mode-I loading is studied by means of theoretical analysis, numerical simulation and experimental investigation. Firstly, based on the Paris formula and taking into account the effective stress intensity factor range ratio (U), which characterizes the degree of crack closure, a modified crack growth rate equation is derived. Then, taking the 10 mm thick Al 6061-T6 alloy plate as an example, numerical simulation analysis is conducted. The shape change of crack front during crack propagation is characterized by tunnel depth and surface angle. Finally, fatigue crack growth test is conducted adopting the crack front marking technique to validate the simulation results. The results indicate that the crack growth rate is mainly controlled by the maximum stress intensity factor (Kmax) and the U under a certain stress ratio (R). The crack propagation mainly includes two stages, the initial crack propagation stage and the stable crack propagation stage. During the initial crack propagation stage, the crack growth rate in the central layer is greater than that in the surface layer. After approximately 4 mm of crack growth in the central layer, the crack propagation enters the stable stage. In the stable crack propagation stage, the growth rate of the entire crack front is similar, and the shape of the crack front remains almost unchanged.
通过理论分析、数值模拟和实验研究,研究了单边贯通裂纹试样在模态 I 加载下的裂纹形状演变。首先,以巴黎公式为基础,考虑到表征裂纹闭合程度的有效应力强度因子范围比(U),推导出修正的裂纹增长率方程。然后,以 10 毫米厚的 Al 6061-T6 合金板为例,进行了数值模拟分析。裂纹扩展过程中裂纹前沿的形状变化由隧道深度和表面角度表征。最后,采用裂纹前沿标记技术进行了疲劳裂纹生长试验,以验证模拟结果。结果表明,裂纹增长速度主要受最大应力强度因子(Kmax)和一定应力比(R)下的 U 控制。裂纹扩展主要包括两个阶段,即初始裂纹扩展阶段和稳定裂纹扩展阶段。在初始裂纹扩展阶段,中心层的裂纹增长速度大于表层。在中心层裂纹增长约 4 毫米后,裂纹扩展进入稳定阶段。在稳定的裂纹扩展阶段,整个裂纹前沿的增长速度相似,裂纹前沿的形状几乎保持不变。
{"title":"Crack shape evolution of single edge through cracked specimens under mode-I loading","authors":"Yongfang Li, Mingming Ren, Hao Chen, Yali Yang, Sha Xu, Ruoping Zhang","doi":"10.1007/s00419-024-02705-3","DOIUrl":"10.1007/s00419-024-02705-3","url":null,"abstract":"<div><p>Crack shape evolution of single edge through cracked specimens under mode-I loading is studied by means of theoretical analysis, numerical simulation and experimental investigation. Firstly, based on the Paris formula and taking into account the effective stress intensity factor range ratio (<i>U</i>), which characterizes the degree of crack closure, a modified crack growth rate equation is derived. Then, taking the 10 mm thick Al 6061-T6 alloy plate as an example, numerical simulation analysis is conducted. The shape change of crack front during crack propagation is characterized by tunnel depth and surface angle. Finally, fatigue crack growth test is conducted adopting the crack front marking technique to validate the simulation results. The results indicate that the crack growth rate is mainly controlled by the maximum stress intensity factor (<i>K</i><sub>max</sub>) and the <i>U</i> under a certain stress ratio (<i>R</i>). The crack propagation mainly includes two stages, the initial crack propagation stage and the stable crack propagation stage. During the initial crack propagation stage, the crack growth rate in the central layer is greater than that in the surface layer. After approximately 4 mm of crack growth in the central layer, the crack propagation enters the stable stage. In the stable crack propagation stage, the growth rate of the entire crack front is similar, and the shape of the crack front remains almost unchanged.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-29DOI: 10.1007/s00419-024-02715-1
X. Fagan, J. -J. Sinou, S. Besset, L. Jézéquel, A. Hamdi
Friction-induced vibration emanating from aircraft braking system is a key issue in the design phase, due to the significant damage it can cause to the brake structure. Although the problem of unstable vibrations in aircraft braking systems has been studied by a number of researchers, the suitability of the mechanical modeling strategy for predicting instabilities remains an open problem. The need for relevant numerical models is therefore essential in order to be as predictive as possible during the design phase. Preliminary studies must therefore be carried out to validate or invalidate the modeling hypotheses traditionally used. Indeed the stability analysis of an aircraft braking system is performed in order to study a low-frequency instability. An industrial model is used, hence reducing the number of degrees of freedom (DoF) is of utmost importance in order to have reasonable computation times. When studying low-frequency phenomena, this can be achieved by neglecting the deformations of the disks. However, no current study has shown that this hypothesis is realistic. So the aim of this paper is to assess the effect of the rigidity hypothesis on the results predicted by the stability analysis. In order to do so, the stability analysis results of a model with rigid disks and one with non-rigid disks are compared, with a particular attention on the main instability phenomenon. It is found that considering rigid disks has a very limited influence on the frequency of the low-frequency eigenmodes, but it over-predicts the real part of the unstable eigenmode. Besides, a component mode synthesis (CMS) technique is shown to reduce significantly the size of the non-rigid disks model while ensuring a satisfying precision regarding eigenmodes prediction.
{"title":"The influence of disks deformation on the stability analysis of an aircraft braking system","authors":"X. Fagan, J. -J. Sinou, S. Besset, L. Jézéquel, A. Hamdi","doi":"10.1007/s00419-024-02715-1","DOIUrl":"10.1007/s00419-024-02715-1","url":null,"abstract":"<div><p>Friction-induced vibration emanating from aircraft braking system is a key issue in the design phase, due to the significant damage it can cause to the brake structure. Although the problem of unstable vibrations in aircraft braking systems has been studied by a number of researchers, the suitability of the mechanical modeling strategy for predicting instabilities remains an open problem. The need for relevant numerical models is therefore essential in order to be as predictive as possible during the design phase. Preliminary studies must therefore be carried out to validate or invalidate the modeling hypotheses traditionally used. Indeed the stability analysis of an aircraft braking system is performed in order to study a low-frequency instability. An industrial model is used, hence reducing the number of degrees of freedom (DoF) is of utmost importance in order to have reasonable computation times. When studying low-frequency phenomena, this can be achieved by neglecting the deformations of the disks. However, no current study has shown that this hypothesis is realistic. So the aim of this paper is to assess the effect of the rigidity hypothesis on the results predicted by the stability analysis. In order to do so, the stability analysis results of a model with rigid disks and one with non-rigid disks are compared, with a particular attention on the main instability phenomenon. It is found that considering rigid disks has a very limited influence on the frequency of the low-frequency eigenmodes, but it over-predicts the real part of the unstable eigenmode. Besides, a component mode synthesis (CMS) technique is shown to reduce significantly the size of the non-rigid disks model while ensuring a satisfying precision regarding eigenmodes prediction.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-024-02715-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Intelligent magneto-responsive structures are widely used due to their fast response speed and noncontact control. In this study, the peeling behavior of a slender magneto-responsive sheet under the magnetic field's action is investigated experimentally and theoretically. Firstly, two identical magneto-responsive sheets, with the liquid film adhesion and the absence of the liquid film respectively, are analyzed under the control of a cylindrical magnet. In addition, the peeling process is abstracted via the classical elastica model, and the expression of the potential energy functional is established. The approximate solutions of the deflection and the adhesion length of the magneto-responsive sheets during the peeling process are obtained based on the Rayleigh–Ritz method. The effects of the magnetic field generated by cylindrical magnets and the work of adhesion on the maximum deflection and adhesion length of magneto-responsive sheets are further predicted. The theoretically approximate solution agrees very well with the experimental data. These findings can provide new implications in a wide range of industrial areas, such as medical microsensors and intelligent structures for drug delivery.
{"title":"Peeling and large deformation of the magneto-responsive slender sheet adhered by a liquid film","authors":"Yizhe Zhu, Gongqi Cao, Xiaoxuan Ding, Shiyang Liu, Yuchen Jin, Jianlin Liu","doi":"10.1007/s00419-024-02726-y","DOIUrl":"10.1007/s00419-024-02726-y","url":null,"abstract":"<div><p>Intelligent magneto-responsive structures are widely used due to their fast response speed and noncontact control. In this study, the peeling behavior of a slender magneto-responsive sheet under the magnetic field's action is investigated experimentally and theoretically. Firstly, two identical magneto-responsive sheets, with the liquid film adhesion and the absence of the liquid film respectively, are analyzed under the control of a cylindrical magnet. In addition, the peeling process is abstracted via the classical elastica model, and the expression of the potential energy functional is established. The approximate solutions of the deflection and the adhesion length of the magneto-responsive sheets during the peeling process are obtained based on the Rayleigh–Ritz method. The effects of the magnetic field generated by cylindrical magnets and the work of adhesion on the maximum deflection and adhesion length of magneto-responsive sheets are further predicted. The theoretically approximate solution agrees very well with the experimental data. These findings can provide new implications in a wide range of industrial areas, such as medical microsensors and intelligent structures for drug delivery.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The use of a simplified physical model of the tire of road vehicles is an efficient and simultaneous method to study the specifications of the entire chassis, including the tire specifications. Therefore, it is important to develop a simplified physical model that can be used in the early design phase when detailed computer-aided design data are not available. In this study, a vibration analysis of tires in road contact is described using frequency-based substructuring in a three-dimensional elastic ring model of a tire that includes a brush model simulating the tread rubber. By modeling the brush as a contact spring between the tire and the road surface, the natural frequencies and mode shapes of the tire under load conditions can be calculated using point-coupled three-way contact spring constraints. The experimental results show that the natural frequency changes significantly with road contact and does not depend on the vertical load. The theoretical analysis also showed that the natural frequency does not change when the stiffness of the contact spring is large enough to limit the displacement of the road contact, which is consistent with the experimental results. Unlike previous studies, this method calculates the mode shape with road contact based on the mode shape without road contact; therefore, the required model parameters can be determined based on the experimental modal analysis for the free-free condition.
{"title":"Tire vibration analysis of three-dimensional flexible ring with brush model under static contact conditions by using frequency-based substructuring","authors":"Masami Matsubara, Akira Saito, Chang Po-Siang, Shozo Kawamura","doi":"10.1007/s00419-024-02725-z","DOIUrl":"10.1007/s00419-024-02725-z","url":null,"abstract":"<div><p>The use of a simplified physical model of the tire of road vehicles is an efficient and simultaneous method to study the specifications of the entire chassis, including the tire specifications. Therefore, it is important to develop a simplified physical model that can be used in the early design phase when detailed computer-aided design data are not available. In this study, a vibration analysis of tires in road contact is described using frequency-based substructuring in a three-dimensional elastic ring model of a tire that includes a brush model simulating the tread rubber. By modeling the brush as a contact spring between the tire and the road surface, the natural frequencies and mode shapes of the tire under load conditions can be calculated using point-coupled three-way contact spring constraints. The experimental results show that the natural frequency changes significantly with road contact and does not depend on the vertical load. The theoretical analysis also showed that the natural frequency does not change when the stiffness of the contact spring is large enough to limit the displacement of the road contact, which is consistent with the experimental results. Unlike previous studies, this method calculates the mode shape with road contact based on the mode shape without road contact; therefore, the required model parameters can be determined based on the experimental modal analysis for the free-free condition.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-024-02725-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-29DOI: 10.1007/s00419-024-02712-4
Thanh Q. Nguyen, Tu B. Vu, Niusha Shafiabady, Thuy T. Nguyen, Phuoc T. Nguyen
This study presents a novel approach to real-time structural health monitoring employing convolutional neural networks (CNN) to calculate a loss factor that measures energy dissipation in structures. As mechanical properties degrade over time due to service loads, timely detection of defects is crucial for ensuring safety. The loss factor, derived from the vibration energy spectrum, is used to identify structural changes, distinguishing between normal operation, the presence of defects, and noise interference. Using large data from real-time vibration signals, this method enables continuous and accurate monitoring of structural integrity. The proposed CNN model outperforms traditional models such as multilayer perceptron and long short-term memory, demonstrating superior accuracy in detecting early-stage defects and predicting structural changes. Applied to the Saigon Bridge, the method offers valuable insight into long-term structural behavior and provides a reliable tool for proactive maintenance and safety management. This research contributes to a machine learning-based solution for improving structural health monitoring systems in critical infrastructure.
{"title":"Loss factor analysis in real-time structural health monitoring using a convolutional neural network","authors":"Thanh Q. Nguyen, Tu B. Vu, Niusha Shafiabady, Thuy T. Nguyen, Phuoc T. Nguyen","doi":"10.1007/s00419-024-02712-4","DOIUrl":"10.1007/s00419-024-02712-4","url":null,"abstract":"<div><p>This study presents a novel approach to real-time structural health monitoring employing convolutional neural networks (CNN) to calculate a loss factor that measures energy dissipation in structures. As mechanical properties degrade over time due to service loads, timely detection of defects is crucial for ensuring safety. The loss factor, derived from the vibration energy spectrum, is used to identify structural changes, distinguishing between normal operation, the presence of defects, and noise interference. Using large data from real-time vibration signals, this method enables continuous and accurate monitoring of structural integrity. The proposed CNN model outperforms traditional models such as multilayer perceptron and long short-term memory, demonstrating superior accuracy in detecting early-stage defects and predicting structural changes. Applied to the Saigon Bridge, the method offers valuable insight into long-term structural behavior and provides a reliable tool for proactive maintenance and safety management. This research contributes to a machine learning-based solution for improving structural health monitoring systems in critical infrastructure.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 numerically investigates the thermal behavior in a cylindrical tissue under non-Fourier boundary condition with dual-phase-lag bioheat transfer problem during thermal ablation. A hybrid method based on Legendre wavelets and finite difference approach are applied to determine an approximate analytic solution of the current problem. The correctness and feasibility of the present numerical scheme has been shown by comparing with exact solution under particular case. It has been observed that lower blood temperature gives rise to lower tissue temperature at the thermal ablation position. So, in order to get precise thermal data for treatment, blood temperature of particular patient must be taken into consideration for patient specific treatment. One of the main objective of this article is to minimize thermal damage outside the thermal ablation position. Our study demonstrates that outside the tumor position, normothermia condition exists, throughout the treatment time that reduces the risk of infection, minimizes thermal damages and ensure that patient feel comfortably well during the period. The specific heating plays a key role in the success of thermal ablation treatment and selection of Gaussian distribution source term helps to achieve the purpose. The radius of heat source, effective radius of heat flux and maximum heat flux generated are the important parameters of Gaussian heat source and computed thermal data strongly depends on them. The variation in the values of radius of heat source allows us specific heating(heating at a particular position) in the thermal ablation process so that the specific tumor can be treated. Both effective radius of heat flux and maximum heat flux applied gives the control of temperature at the thermal ablation position. Moreover, temperature rise at the tumor location is uniform in case of maximum heat flux applied. The present analysis will be helpful for medical community for better use of thermal data during thermal ablation.
{"title":"Wavelet analysis of DPL bioheat transfer model for cylindrical tissues during thermal ablation","authors":"Pappu Kumar, Dinesh Kumar, Arvind Kumar Yadav, Rakhi Tiwari","doi":"10.1007/s00419-024-02707-1","DOIUrl":"10.1007/s00419-024-02707-1","url":null,"abstract":"<div><p>This paper numerically investigates the thermal behavior in a cylindrical tissue under non-Fourier boundary condition with dual-phase-lag bioheat transfer problem during thermal ablation. A hybrid method based on Legendre wavelets and finite difference approach are applied to determine an approximate analytic solution of the current problem. The correctness and feasibility of the present numerical scheme has been shown by comparing with exact solution under particular case. It has been observed that lower blood temperature gives rise to lower tissue temperature at the thermal ablation position. So, in order to get precise thermal data for treatment, blood temperature of particular patient must be taken into consideration for patient specific treatment. One of the main objective of this article is to minimize thermal damage outside the thermal ablation position. Our study demonstrates that outside the tumor position, normothermia condition exists, throughout the treatment time that reduces the risk of infection, minimizes thermal damages and ensure that patient feel comfortably well during the period. The specific heating plays a key role in the success of thermal ablation treatment and selection of Gaussian distribution source term helps to achieve the purpose. The radius of heat source, effective radius of heat flux and maximum heat flux generated are the important parameters of Gaussian heat source and computed thermal data strongly depends on them. The variation in the values of radius of heat source allows us specific heating(heating at a particular position) in the thermal ablation process so that the specific tumor can be treated. Both effective radius of heat flux and maximum heat flux applied gives the control of temperature at the thermal ablation position. Moreover, temperature rise at the tumor location is uniform in case of maximum heat flux applied. The present analysis will be helpful for medical community for better use of thermal data during thermal ablation.\u0000</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-29DOI: 10.1007/s00419-024-02720-4
Jakob C. Schilling, Christian Mittelstedt
This paper introduces a closed-form analytical approach to the postbuckling analysis of simply supported shear-deformable composite laminated plates under uniaxial compression. The analysis is based on three different laminate theories in order to explicitly account for transverse shear deformations and uses a geometrically nonlinear formulation in conjunction with the Ritz method in order to enable closed-form analytical expressions for the state variables of buckled composite plates. Results are presented for several different plate configurations, and a comparison is performed with literature results as well as comparative finite element computations which leads to a very satisfying results accuracy. The presented analysis method delivers results without any significant numerical effort and is thus especially suited for practical applications where such postbuckling analyses are performed many times.
{"title":"Closed-form postbuckling analysis of shear-deformable composite laminated panels","authors":"Jakob C. Schilling, Christian Mittelstedt","doi":"10.1007/s00419-024-02720-4","DOIUrl":"10.1007/s00419-024-02720-4","url":null,"abstract":"<div><p>This paper introduces a closed-form analytical approach to the postbuckling analysis of simply supported shear-deformable composite laminated plates under uniaxial compression. The analysis is based on three different laminate theories in order to explicitly account for transverse shear deformations and uses a geometrically nonlinear formulation in conjunction with the Ritz method in order to enable closed-form analytical expressions for the state variables of buckled composite plates. Results are presented for several different plate configurations, and a comparison is performed with literature results as well as comparative finite element computations which leads to a very satisfying results accuracy. The presented analysis method delivers results without any significant numerical effort and is thus especially suited for practical applications where such postbuckling analyses are performed many times.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-024-02720-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-29DOI: 10.1007/s00419-024-02729-9
Mohammad Mahdi Nazari, Abbas Rahi, Roohollah Sarfaraz Khabbaz
Rotor stability analysis is essential to ensure rotating composite structures' safe and efficient operation. In this paper, the stability analysis of a hybrid composite shaft with two disks placed on elastic supports is investigated by the three-node finite element method. The strain potential energy of the hybrid composite shaft is calculated by considering the Timoshenko beam theory and using shape functions and the ABD matrix's effective components. The governing equations of the composite rotor are derived by replacing the kinetic energy of the shaft and disks, the strain potential energy, and the force of the bearings in the Lagrange equation. The equations of motion obtained from the finite element method are coded in the state space using MATLAB script. Their eigenvalues are calculated as a function of the rotor rotation speed, and the instability threshold of the composite rotor is evaluated. To validate the simulation results of the composite shaft in the free–free state in the ANSYS software, a hybrid composite shaft is made using the filament winding method, and its natural frequencies are extracted by performing the experimental modal analysis test. The instability threshold of the non-hybrid composite rotor of the presented model in different stacking sequences is compared with the results of the previous studies, and the validity of the three-node finite element method is confirmed. Finally, the effect of the fiber angle and the arrangement of the layers in the usage of carbon/epoxy and glass/epoxy in a specific stacking sequence on the stability of the hybrid composite rotor is studied.
转子稳定性分析对于确保旋转复合材料结构的安全高效运行至关重要。本文采用三节点有限元法研究了置于弹性支撑上的双盘混合复合材料轴的稳定性分析。考虑到季莫申科梁理论,并利用形状函数和 ABD 矩阵的有效分量计算了混合复合材料轴的应变势能。通过将轴和盘的动能、应变势能以及轴承的力代入拉格朗日方程,得出了复合转子的控制方程。使用 MATLAB 脚本在状态空间中对有限元法得到的运动方程进行编码。计算其特征值与转子转速的函数关系,并评估复合转子的失稳阈值。为了验证 ANSYS 软件中复合材料转轴自由状态下的仿真结果,使用丝状缠绕法制作了混合复合材料转轴,并通过实验模态分析测试提取了其固有频率。将所提出模型的非混合复合材料转子在不同堆叠顺序下的失稳阈值与之前的研究结果进行了比较,并证实了三节点有限元法的有效性。最后,研究了在特定堆叠顺序中使用碳/环氧树脂和玻璃/环氧树脂时纤维角度和层的排列对混合复合材料转子稳定性的影响。
{"title":"Stability analysis of a hybrid composite rotor with the three-node finite element method","authors":"Mohammad Mahdi Nazari, Abbas Rahi, Roohollah Sarfaraz Khabbaz","doi":"10.1007/s00419-024-02729-9","DOIUrl":"10.1007/s00419-024-02729-9","url":null,"abstract":"<div><p>Rotor stability analysis is essential to ensure rotating composite structures' safe and efficient operation. In this paper, the stability analysis of a hybrid composite shaft with two disks placed on elastic supports is investigated by the three-node finite element method. The strain potential energy of the hybrid composite shaft is calculated by considering the Timoshenko beam theory and using shape functions and the ABD matrix's effective components. The governing equations of the composite rotor are derived by replacing the kinetic energy of the shaft and disks, the strain potential energy, and the force of the bearings in the Lagrange equation. The equations of motion obtained from the finite element method are coded in the state space using MATLAB script. Their eigenvalues are calculated as a function of the rotor rotation speed, and the instability threshold of the composite rotor is evaluated. To validate the simulation results of the composite shaft in the free–free state in the ANSYS software, a hybrid composite shaft is made using the filament winding method, and its natural frequencies are extracted by performing the experimental modal analysis test. The instability threshold of the non-hybrid composite rotor of the presented model in different stacking sequences is compared with the results of the previous studies, and the validity of the three-node finite element method is confirmed. Finally, the effect of the fiber angle and the arrangement of the layers in the usage of carbon/epoxy and glass/epoxy in a specific stacking sequence on the stability of the hybrid composite rotor is studied.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-29DOI: 10.1007/s00419-024-02706-2
Yong-Kang Jiang, Yan Shang
In this work, a novel quadrilateral four-node element capable of simulating the axisymmetric-torsion deformation of small-scale solids of revolution is developed based on the consistent couple stress theory (CCST). To establish the element formulation, the C1 requirement for displacement in the CCST is enforced in weak sense by using the penalty function method and the independent nodal rotation degrees of freedom are introduced into element construction to approximate the mechanical rotation fields. Besides, the stress functions that can satisfy the relevant equilibrium equation of the axisymmetric-torsion deformation are adopted as the basic functions for designing the element’s stress trial function. Several numerical tests are carried out and the results are compared to the solutions obtained using the analytical method or hexahedral solid element from the literature. It is shown that the new element exhibits good accuracy and captures the size dependences efficiently in prediction of the axisymmetric-torsion behavior of small-scale solids.
{"title":"Penalty 4-node quadrilateral element formulation for axisymmetric-torsion problems within consistent couple stress theory","authors":"Yong-Kang Jiang, Yan Shang","doi":"10.1007/s00419-024-02706-2","DOIUrl":"10.1007/s00419-024-02706-2","url":null,"abstract":"<div><p>In this work, a novel quadrilateral four-node element capable of simulating the axisymmetric-torsion deformation of small-scale solids of revolution is developed based on the consistent couple stress theory (CCST). To establish the element formulation, the <i>C</i><sup>1</sup> requirement for displacement in the CCST is enforced in weak sense by using the penalty function method and the independent nodal rotation degrees of freedom are introduced into element construction to approximate the mechanical rotation fields. Besides, the stress functions that can satisfy the relevant equilibrium equation of the axisymmetric-torsion deformation are adopted as the basic functions for designing the element’s stress trial function. Several numerical tests are carried out and the results are compared to the solutions obtained using the analytical method or hexahedral solid element from the literature. It is shown that the new element exhibits good accuracy and captures the size dependences efficiently in prediction of the axisymmetric-torsion behavior of small-scale solids.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}