Pub Date : 2024-09-03DOI: 10.1016/j.euromechsol.2024.105433
Honeycomb crash absorbers are known as mechanical energy-absorbing systems in both automotive and aerospace industries. However, the gap of knowledge in the transverse impacts of multi-foam-filled or stiffener-reinforced honeycombs is still unfilled. This paper investigates the energy absorption process in large crash boxes applied onto a road maintenance vehicle, exploring four aluminium honeycomb absorbers with design factors like added aluminium foam, corrugated sheet thicknesses, and stiffener reinforcements. The optimised foam-filled honeycomb structures are analysed for four crash scenarios in two different directions; frontal impact (T-direction) and lateral impact (L-direction) subjected to 50 km/h crash speed. The objective of this research is to identify the most efficient design that achieves a maximum acceleration of up to 20g while absorbing a specific energy of 145 kJ. The FE models were developed in ABAQUS to explore various scenarios related to damage zones, impact energy capabilities, and multi-foam-filled crash boxes. Finally, the lightest design of honeycomb absorbers which can maximise energy absorption while maintaining acceleration below the specified threshold of 20g will be recommended.
{"title":"Development of multi aluminium foam-filled crash box systems to improve crashworthiness performance of road Service vehicle","authors":"","doi":"10.1016/j.euromechsol.2024.105433","DOIUrl":"10.1016/j.euromechsol.2024.105433","url":null,"abstract":"<div><p>Honeycomb crash absorbers are known as mechanical energy-absorbing systems in both automotive and aerospace industries. However, the gap of knowledge in the transverse impacts of multi-foam-filled or stiffener-reinforced honeycombs is still unfilled. This paper investigates the energy absorption process in large crash boxes applied onto a road maintenance vehicle, exploring four aluminium honeycomb absorbers with design factors like added aluminium foam, corrugated sheet thicknesses, and stiffener reinforcements. The optimised foam-filled honeycomb structures are analysed for four crash scenarios in two different directions; frontal impact (T-direction) and lateral impact (L-direction) subjected to 50 km/h crash speed. The objective of this research is to identify the most efficient design that achieves a maximum acceleration of up to 20g while absorbing a specific energy of 145 kJ. The FE models were developed in ABAQUS to explore various scenarios related to damage zones, impact energy capabilities, and multi-foam-filled crash boxes. Finally, the lightest design of honeycomb absorbers which can maximise energy absorption while maintaining acceleration below the specified threshold of 20g will be recommended.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0997753824002134/pdfft?md5=2b9040cfcfb3c23806848d95cd7cadfb&pid=1-s2.0-S0997753824002134-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142149792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-09-03DOI: 10.1016/j.euromechsol.2024.105428
Non-pneumatic tires (NPTs) fundamentally avoid the risk of tire blowout of traditional pneumatic tires, but the overall and key component performance inevitably degrades due to factors such as high temperature, variable load, variable working conditions and impact in its service process. Once this leads to failure, it will significantly impact on vehicle safety. To this end, this paper studied the influence of local structural damage on the dynamic response of NPTs, which lays the foundation for realizing health monitoring of intelligent non-pneumatic tires (INPTs). Firstly, a three-dimensional nonlinear finite element model of NPTs was established, and the failure locations of NPTs were determined by fracture mechanics and maximum strain energy density; Secondly, the influence of structural damage on the static and dynamic performance of NPTs was analyzed; Finally, the sensitivity of the acceleration signal and sensor position of the tire inner liner to the local structural damage was studied. The research results show that structural damage will cause the stress of the spokes and shear layer to increase, and as the number of broken spokes increases, the shear layer will bear a larger load. Compared with the circumferential and lateral acceleration, the radial acceleration has the highest sensitivity to the damage of NPTs. The sensor closest to the damage location is the most sensitive to the damage. The research results provide a reference for the structural optimization design and health monitoring of INPTs.
{"title":"Numerical study of steady-state dynamic characteristic of non-pneumatic tire with local structural damage","authors":"","doi":"10.1016/j.euromechsol.2024.105428","DOIUrl":"10.1016/j.euromechsol.2024.105428","url":null,"abstract":"<div><p>Non-pneumatic tires (NPTs) fundamentally avoid the risk of tire blowout of traditional pneumatic tires, but the overall and key component performance inevitably degrades due to factors such as high temperature, variable load, variable working conditions and impact in its service process. Once this leads to failure, it will significantly impact on vehicle safety. To this end, this paper studied the influence of local structural damage on the dynamic response of NPTs, which lays the foundation for realizing health monitoring of intelligent non-pneumatic tires (INPTs). Firstly, a three-dimensional nonlinear finite element model of NPTs was established, and the failure locations of NPTs were determined by fracture mechanics and maximum strain energy density; Secondly, the influence of structural damage on the static and dynamic performance of NPTs was analyzed; Finally, the sensitivity of the acceleration signal and sensor position of the tire inner liner to the local structural damage was studied. The research results show that structural damage will cause the stress of the spokes and shear layer to increase, and as the number of broken spokes increases, the shear layer will bear a larger load. Compared with the circumferential and lateral acceleration, the radial acceleration has the highest sensitivity to the damage of NPTs. The sensor closest to the damage location is the most sensitive to the damage. The research results provide a reference for the structural optimization design and health monitoring of INPTs.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-30DOI: 10.1016/j.euromechsol.2024.105429
The linear forced vibration characteristics of viscoelastic variable stiffness laminated composite plates (VVSLC) are studied using a generalized Maxwell model and finite element method. The integral form of the viscoelastic constitutive relation is converted to the incremental form for finite element formulation based on the Reissner–Mindlin plate theory. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response directly in the time domain is obtained using shooting technique coupled with Newmark’s time integration method. The implementation of shooting technique for Boltzmann integral-based viscoelasticity for curvilinear fibre composite plates is done for the first time in this study. For the comparison purpose, the response/resonance frequency/modal loss factor is also obtained using equivalent complex modulus based viscoelastic correspondence principle. It is observed that the variation in fibre orientation and boundary conditions leads to significant variations in response, stress/moment resultant amplitude and the damping factor of the VVSLC plates. Further, the present time domain based approach is capable of predicting damping factor at all forcing frequencies whereas complex eigenvalue analysis can predict damping factor only at discrete resonance frequency. Based on the detailed studies, it is found that the curvilinear fibre composite plates depict a significant reduction in response/moment resultants compared to straight fibre composite plates.
{"title":"Forced vibration characteristics of viscoelastic variable stiffness laminated composite plates using time and frequency domain approaches","authors":"","doi":"10.1016/j.euromechsol.2024.105429","DOIUrl":"10.1016/j.euromechsol.2024.105429","url":null,"abstract":"<div><p>The linear forced vibration characteristics of viscoelastic variable stiffness laminated composite plates (VVSLC) are studied using a generalized Maxwell model and finite element method. The integral form of the viscoelastic constitutive relation is converted to the incremental form for finite element formulation based on the Reissner–Mindlin plate theory. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response directly in the time domain is obtained using shooting technique coupled with Newmark’s time integration method. The implementation of shooting technique for Boltzmann integral-based viscoelasticity for curvilinear fibre composite plates is done for the first time in this study. For the comparison purpose, the response/resonance frequency/modal loss factor is also obtained using equivalent complex modulus based viscoelastic correspondence principle. It is observed that the variation in fibre orientation and boundary conditions leads to significant variations in response, stress/moment resultant amplitude and the damping factor of the VVSLC plates. Further, the present time domain based approach is capable of predicting damping factor at all forcing frequencies whereas complex eigenvalue analysis can predict damping factor only at discrete resonance frequency. Based on the detailed studies, it is found that the curvilinear fibre composite plates depict a significant reduction in response/moment resultants compared to straight fibre composite plates.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142129012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-30DOI: 10.1016/j.euromechsol.2024.105427
The work presented here proposes a contribution on the analysis of brake squeal phenomenon using a transient coupled finite element-discrete element method (FEM-DEM) simulation with pad surface topography evolution. To build the coupled FEM-DEM model, a non-overlapping strong coupling is first employed between the FEM and DEM subdomains. Second, a new calibration methodology of the DEM microscopic properties is proposed based on the eigenvalue analysis of the full model. The results of the coupled FEM-DEM model show a good agreement in terms of unstable frequencies and the evolution of the pad contact state history when compared to full FEM models, both for new and worn pad topographies. The evolution of the pad surface topography during the transient analysis results in a complex frequency behaviour, with abrupt shifts of instabilities and new operating deflection shapes, in agreement with reported experimental results. The proposed coupled FEM-DEM model thus seems to be a valuable tool for a better understanding of the squeal triggering due to the evolution of the pad surface topography. This contribution paves the way to advanced numerical analyses of brake squeal phenomenon, which triggering conditions are still under investigation.
本文所介绍的工作是利用瞬态耦合有限元-离散元方法(FEM-DEM)模拟刹车片表面形貌演变,对刹车异响现象进行分析。为了建立 FEM-DEM 耦合模型,首先在 FEM 和 DEM 子域之间采用了非重叠强耦合。其次,基于完整模型的特征值分析,提出了一种新的 DEM 微观属性校准方法。FEM-DEM 耦合模型的结果表明,与完整的 FEM 模型相比,无论是新的还是磨损的衬垫形貌,在不稳定频率和衬垫接触状态历史演变方面都有很好的一致性。在瞬态分析过程中,衬垫表面形貌的演变导致了复杂的频率行为,不稳定性和新的工作挠度形状发生了突变,这与报告的实验结果一致。因此,所提出的 FEM-DEM 耦合模型似乎是一种有价值的工具,可用于更好地理解因衬垫表面形貌演变而引发的尖叫声。这一贡献为制动尖叫现象的高级数值分析铺平了道路,而制动尖叫的触发条件仍在研究之中。
{"title":"A coupled finite element-discrete element method for the modelling of brake squeal instabilities","authors":"","doi":"10.1016/j.euromechsol.2024.105427","DOIUrl":"10.1016/j.euromechsol.2024.105427","url":null,"abstract":"<div><p>The work presented here proposes a contribution on the analysis of brake squeal phenomenon using a transient coupled finite element-discrete element method (FEM-DEM) simulation with pad surface topography evolution. To build the coupled FEM-DEM model, a non-overlapping strong coupling is first employed between the FEM and DEM subdomains. Second, a new calibration methodology of the DEM microscopic properties is proposed based on the eigenvalue analysis of the full model. The results of the coupled FEM-DEM model show a good agreement in terms of unstable frequencies and the evolution of the pad contact state history when compared to full FEM models, both for new and worn pad topographies. The evolution of the pad surface topography during the transient analysis results in a complex frequency behaviour, with abrupt shifts of instabilities and new operating deflection shapes, in agreement with reported experimental results. The proposed coupled FEM-DEM model thus seems to be a valuable tool for a better understanding of the squeal triggering due to the evolution of the pad surface topography. This contribution paves the way to advanced numerical analyses of brake squeal phenomenon, which triggering conditions are still under investigation.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142117764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-28DOI: 10.1016/j.euromechsol.2024.105424
The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when expressed in the same configuration, enabling the definition of a unified general model. The ability of this general model to reproduce the main features of the behavior of rubbers is then explored. First, its responses are compared to those of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, a comparison is made between a classic generalized Maxwell rheological scheme and a Zener one with a non-constant viscosity, exploring the relevance of both options within the general model’s constitutive equations.
{"title":"A comparison of finite strain viscoelastic models based on the multiplicative decomposition","authors":"","doi":"10.1016/j.euromechsol.2024.105424","DOIUrl":"10.1016/j.euromechsol.2024.105424","url":null,"abstract":"<div><p>The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when expressed in the same configuration, enabling the definition of a unified <em>general model</em>. The ability of this <em>general model</em> to reproduce the main features of the behavior of rubbers is then explored. First, its responses are compared to those of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, a comparison is made between a classic generalized Maxwell rheological scheme and a Zener one with a non-constant viscosity, exploring the relevance of both options within the <em>general model</em>’s constitutive equations.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-28DOI: 10.1016/j.euromechsol.2024.105425
The paper studies a penny-shaped crack in an infinite three-dimensional body of two-dimensional hexagonal quasicrystal media with piezoelectric effect. The crack surfaces are applied combined electric and normal phonon loadings. Such a Model I crack problem is transformed into a mixed boundary value problem in the upper half-space, which is analytically solved using Fabrikant's potential theory method. The boundary integral-differential equations governing Model I crack problems are presented for two-dimensional hexagonal piezoelectric quasicrystals. The normal phonon displacement discontinuity and electric potential discontinuity across crack surfaces are taken as the unknown variables of boundary governing equations. Analytical solutions of all field variables are derived not only for the crack plane but also for the full space. Solutions in integral form are provided for the penny-shaped crack under arbitrarily distributed electric and normal phonon loadings. Closed-form solutions in terms of elementary functions are given for concentrated point loadings and uniformly distributed loadings, respectively. Key fracture mechanics parameters, such as crack surface extended displacements (i.e., normal phonon displacement, electric potential), crack tip extended stresses (i.e., normal phonon stress, electric displacement) distribution, and corresponding extended stress intensity factors, are clearly derived. Numerical results are utilized to verify the present analytical solutions and graphically illustrate the distribution of phonon-phason-electric coupling fields around the crack. The present solution can serve as a benchmark for both experimental and numerical investigations.
本文研究了具有压电效应的二维六方准晶介质无限三维体中的一分钱形裂缝。裂缝表面施加了电和法向声子组合载荷。这种 I 型裂缝问题被转化为上半空间的混合边界值问题,并使用 Fabrikant 势理论方法进行分析求解。针对二维六方压电准晶体,提出了支配模型 I 裂纹问题的边界积分微分方程。裂缝表面的法向声子位移不连续和电势不连续被作为边界控制方程的未知变量。不仅对裂缝平面,而且对整个空间都得出了所有场变量的解析解。在任意分布的电荷和法向声子荷载作用下,以积分形式给出了一分钱形裂缝的解。对于集中点载荷和均匀分布载荷,分别给出了基本函数的闭式解。明确推导出了关键的断裂力学参数,如裂纹表面扩展位移(即法向声子位移、电势)、裂纹顶端扩展应力(即法向声子应力、电位移)分布以及相应的扩展应力强度因子。利用数值结果验证了本分析解,并以图形说明了裂纹周围声子-声子-电耦合场的分布。本解决方案可作为实验和数值研究的基准。
{"title":"Analytical solutions to Mode I penny-shaped crack problems in two-dimensional hexagonal quasicrystals with piezoelectric effect","authors":"","doi":"10.1016/j.euromechsol.2024.105425","DOIUrl":"10.1016/j.euromechsol.2024.105425","url":null,"abstract":"<div><p>The paper studies a penny-shaped crack in an infinite three-dimensional body of two-dimensional hexagonal quasicrystal media with piezoelectric effect. The crack surfaces are applied combined electric and normal phonon loadings. Such a Model I crack problem is transformed into a mixed boundary value problem in the upper half-space, which is analytically solved using Fabrikant's potential theory method. The boundary integral-differential equations governing Model I crack problems are presented for two-dimensional hexagonal piezoelectric quasicrystals. The normal phonon displacement discontinuity and electric potential discontinuity across crack surfaces are taken as the unknown variables of boundary governing equations. Analytical solutions of all field variables are derived not only for the crack plane but also for the full space. Solutions in integral form are provided for the penny-shaped crack under arbitrarily distributed electric and normal phonon loadings. Closed-form solutions in terms of elementary functions are given for concentrated point loadings and uniformly distributed loadings, respectively. Key fracture mechanics parameters, such as crack surface extended displacements (i.e., normal phonon displacement, electric potential), crack tip extended stresses (i.e., normal phonon stress, electric displacement) distribution, and corresponding extended stress intensity factors, are clearly derived. Numerical results are utilized to verify the present analytical solutions and graphically illustrate the distribution of phonon-phason-electric coupling fields around the crack. The present solution can serve as a benchmark for both experimental and numerical investigations.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-28DOI: 10.1016/j.euromechsol.2024.105423
The current investigation explores the behavior of pre-stressed viscoelastic Timoshenko nanobeams under the influence of surface effects and a longitudinal magnetic field. Utilizing a modified version of non-local strain gradient theory through the Kelvin–Voigt viscoelastic model, a closed-form dispersion relation using a suitable analytical approach has been derived. To account for surface stresses, Gurtin–Murdouch surface elasticity theory has been employed. Additionally, the study delves into the impact of a longitudinal magnetic field on a single-walled carbon nanotube, considering Lorentz magnetic forces. The validity of the findings is established by deriving results in the absence of surface effects and magnetic fields, aligning well with existing literature. The investigation indicates that pre-stress has marginal effects on flexural and shear waves, while surface effects, magnetic fields, non-locality, characteristic length, and nanotube diameter significantly influence the phase velocity. Additionally, the threshold velocity and blocking diameter are discussed for the model.
{"title":"Characteristics of wave propagation in pre-stressed viscoelastic Timoshenko nanobeams with surface stress and magnetic field influences","authors":"","doi":"10.1016/j.euromechsol.2024.105423","DOIUrl":"10.1016/j.euromechsol.2024.105423","url":null,"abstract":"<div><p>The current investigation explores the behavior of pre-stressed viscoelastic Timoshenko nanobeams under the influence of surface effects and a longitudinal magnetic field. Utilizing a modified version of non-local strain gradient theory through the Kelvin–Voigt viscoelastic model, a closed-form dispersion relation using a suitable analytical approach has been derived. To account for surface stresses, Gurtin–Murdouch surface elasticity theory has been employed. Additionally, the study delves into the impact of a longitudinal magnetic field on a single-walled carbon nanotube, considering Lorentz magnetic forces. The validity of the findings is established by deriving results in the absence of surface effects and magnetic fields, aligning well with existing literature. The investigation indicates that pre-stress has marginal effects on flexural and shear waves, while surface effects, magnetic fields, non-locality, characteristic length, and nanotube diameter significantly influence the phase velocity. Additionally, the threshold velocity and blocking diameter are discussed for the model.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142122762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-28DOI: 10.1016/j.euromechsol.2024.105421
The current article appraises the vibration and stability of tri-directional functionally graded porous microscale beams with rectangular cross-sections integrated with piezoelectric layers under spinning and axial movements in complex environments. The microbeam is surrounded by a three-parameter Winkler-Pasternak-Hetenyi medium, and its material characteristics are graded in thickness, width, and longitudinal spatial directions by considering non-uniform and uniform porosity models. Dynamic equations, vibration frequencies, and stability criteria of the system are determined with the aid of the Galerkin approach and Laplace transform. The Campbell diagram and stability maps are drawn. Frequency and stability analyses, as well as comparison and parametric analyses, are conducted. The impacts of piezoelectric voltage, magneto-hygro-thermal fields, axial and tangential distributed follower forces, substrate characteristics, scale parameter, aspect ratio, porosity factor, and material gradation on flutter and divergence instability boundaries are assessed in detail. It is deduced that instability regions are condensed, and the instability threshold is enhanced by fine-adjusting the porosity and material gradient. It is discovered that destructive environmental effects can be alleviated by regulating the piezoelectric voltage. In addition, compared with the case of a square cross-section, the divergence/flutter instability region of the microbeam with a rectangular cross-section is smaller/larger. The outcomes of the present research can be helpful in the design of next-generation bi-gyroscopic systems.
{"title":"Dynamics of axially moving spinning microbeams composed of tri-directional graded porous materials with axisymmetric cross-sections and piezoelectric layers in complex fields","authors":"","doi":"10.1016/j.euromechsol.2024.105421","DOIUrl":"10.1016/j.euromechsol.2024.105421","url":null,"abstract":"<div><p>The current article appraises the vibration and stability of tri-directional functionally graded porous microscale beams with rectangular cross-sections integrated with piezoelectric layers under spinning and axial movements in complex environments. The microbeam is surrounded by a three-parameter Winkler-Pasternak-Hetenyi medium, and its material characteristics are graded in thickness, width, and longitudinal spatial directions by considering non-uniform and uniform porosity models. Dynamic equations, vibration frequencies, and stability criteria of the system are determined with the aid of the Galerkin approach and Laplace transform. The Campbell diagram and stability maps are drawn. Frequency and stability analyses, as well as comparison and parametric analyses, are conducted. The impacts of piezoelectric voltage, magneto-hygro-thermal fields, axial and tangential distributed follower forces, substrate characteristics, scale parameter, aspect ratio, porosity factor, and material gradation on flutter and divergence instability boundaries are assessed in detail. It is deduced that instability regions are condensed, and the instability threshold is enhanced by fine-adjusting the porosity and material gradient. It is discovered that destructive environmental effects can be alleviated by regulating the piezoelectric voltage. In addition, compared with the case of a square cross-section, the divergence/flutter instability region of the microbeam with a rectangular cross-section is smaller/larger. The outcomes of the present research can be helpful in the design of next-generation bi-gyroscopic systems.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142135816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-26DOI: 10.1016/j.euromechsol.2024.105426
The static and dynamic stabilities of modified gradient elastic Kirchhoff–Love plates (MGEKLPs), which incorporate two length-scale parameters related to strain gradient and rotation gradient effects, are comprehensively analyzed under various load forms and boundary conditions (BCs). The study of static stability employs static balance method and an improved energy method by introducing higher-order deformation gradients and corresponding energy terms. Utilizing the variational method, a sixth-order fundamental buckling differential equation for MGEKLPs under both transverse and in-plane loads is derived, serving as the foundation for the static balance method. The static stability analysis of MGEKLPs examines the combined effects of strain and rotation gradients on size-dependent critical buckling loads. Building on generalized strain energy with higher-order deformation energy, the energy method of classical elastic thin plate model is enhanced and applied to the static stability analysis of MGEKLPs. This approach enables the investigation of static stability without being constrained by the need to solve complex differential equations, making it applicable to various BCs and load scenarios. While static stability provides a description of stable state of an elastic system, dynamic stability offers a more scientific and rigorous analysis. The dynamic stability of simplified gradient elastic Kirchhoff–Love plates (SGEKLPs) with curved edges and different BCs is further investigated by combining the generalized strain energy with Lyapunov’s second stability method, presenting the dynamic stability criterion in the form of norms. A strict description of the dynamic stability of a SGEKLP over the entire time domain is provided for different supporting conditions, including case where all edges are supported and case with free edges. The analysis of size-dependent static and dynamic stabilities offers theoretical guidance for designing elastic thin plates with microstructures.
本文综合分析了改良梯度弹性基尔霍夫-洛夫板(MGEKLPs)在各种载荷形式和边界条件(BCs)下的静态和动态稳定性,MGEKLPs 包含与应变梯度和旋转梯度效应相关的两个长度尺度参数。静态稳定性研究采用了静态平衡法和改进的能量法,引入了高阶变形梯度和相应的能量项。利用变分法,推导出了横向和平面载荷作用下 MGEKLP 的六阶基本屈曲微分方程,为静力平衡法奠定了基础。MGEKLP 的静态稳定性分析研究了应变梯度和旋转梯度对与尺寸有关的临界屈曲载荷的综合影响。在广义应变能与高阶变形能的基础上,增强了经典弹性薄板模型的能量方法,并将其应用于 MGEKLP 的静态稳定性分析。这种方法无需求解复杂的微分方程就能研究静态稳定性,因此适用于各种 BC 和负载情况。静态稳定性提供了对弹性系统稳定状态的描述,而动态稳定性则提供了更加科学和严谨的分析。通过将广义应变能与 Lyapunov 第二稳定性方法相结合,进一步研究了具有弯曲边缘和不同 BC 的简化梯度弹性基尔霍夫-洛夫板(SGEKLP)的动态稳定性,并以规范的形式提出了动态稳定性准则。针对不同的支撑条件,包括所有边缘都有支撑和边缘自由的情况,对 SGEKLP 在整个时域的动态稳定性进行了严格描述。与尺寸相关的静态和动态稳定性分析为设计具有微结构的弹性薄板提供了理论指导。
{"title":"Static and dynamic stabilities of modified gradient elastic Kirchhoff–Love plates","authors":"","doi":"10.1016/j.euromechsol.2024.105426","DOIUrl":"10.1016/j.euromechsol.2024.105426","url":null,"abstract":"<div><p>The static and dynamic stabilities of modified gradient elastic Kirchhoff–Love plates (MGEKLPs), which incorporate two length-scale parameters related to strain gradient and rotation gradient effects, are comprehensively analyzed under various load forms and boundary conditions (BCs). The study of static stability employs static balance method and an improved energy method by introducing higher-order deformation gradients and corresponding energy terms. Utilizing the variational method, a sixth-order fundamental buckling differential equation for MGEKLPs under both transverse and in-plane loads is derived, serving as the foundation for the static balance method. The static stability analysis of MGEKLPs examines the combined effects of strain and rotation gradients on size-dependent critical buckling loads. Building on generalized strain energy with higher-order deformation energy, the energy method of classical elastic thin plate model is enhanced and applied to the static stability analysis of MGEKLPs. This approach enables the investigation of static stability without being constrained by the need to solve complex differential equations, making it applicable to various BCs and load scenarios. While static stability provides a description of stable state of an elastic system, dynamic stability offers a more scientific and rigorous analysis. The dynamic stability of simplified gradient elastic Kirchhoff–Love plates (SGEKLPs) with curved edges and different BCs is further investigated by combining the generalized strain energy with Lyapunov’s second stability method, presenting the dynamic stability criterion in the form of norms. A strict description of the dynamic stability of a SGEKLP over the entire time domain is provided for different supporting conditions, including case where all edges are supported and case with free edges. The analysis of size-dependent static and dynamic stabilities offers theoretical guidance for designing elastic thin plates with microstructures.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2024-08-23DOI: 10.1016/j.euromechsol.2024.105422
Unshearable and inextensible planar beams, in a static regime of finite displacements, are studied in this paper. A nonlinear mixed model is derived via a direct approach, in which displacements and reactive internal forces are taken as unknowns. The elasto-static problem is then addressed, and the role of the boundary conditions is systematically discussed. The relevant solutions for selected classes of problems are pursued via a perturbation method. It is shown that each considered class calls for a specific algorithm, accounting for a proper scaling and expansion of the variables. Finally, the asymptotic solutions are compared with benchmark numerical computations, grounded on finite-element analyses. The paper is focused on the case of longitudinal force significantly smaller than the buckling load, leaving the case of large force to future developments, where a different perturbation scheme is required.
{"title":"Revisiting the nonlinear elastic problem of internally constrained beams in a perturbation perspective","authors":"","doi":"10.1016/j.euromechsol.2024.105422","DOIUrl":"10.1016/j.euromechsol.2024.105422","url":null,"abstract":"<div><p>Unshearable and inextensible planar beams, in a static regime of finite displacements, are studied in this paper. A nonlinear mixed model is derived via a direct approach, in which displacements and reactive internal forces are taken as unknowns. The elasto-static problem is then addressed, and the role of the boundary conditions is systematically discussed. The relevant solutions for selected classes of problems are pursued via a perturbation method. It is shown that each considered class calls for a specific algorithm, accounting for a proper scaling and expansion of the variables. Finally, the asymptotic solutions are compared with benchmark numerical computations, grounded on finite-element analyses. The paper is focused on the case of longitudinal force significantly smaller than the buckling load, leaving the case of large force to future developments, where a different perturbation scheme is required.</p></div>","PeriodicalId":50483,"journal":{"name":"European Journal of Mechanics A-Solids","volume":null,"pages":null},"PeriodicalIF":4.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S099775382400202X/pdfft?md5=ed98320556714dfd7ec0ed409783d3cc&pid=1-s2.0-S099775382400202X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}