A novel X-shaped variable stiffness vibration isolator(X-VSVI)is proposed.The Runge-Kutta method,harmonic balance method,and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under var...A novel X-shaped variable stiffness vibration isolator(X-VSVI)is proposed.The Runge-Kutta method,harmonic balance method,and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under various excitations.The layer number,the installation angle of the X-shaped structure,the stiffness,and the active control parameters are systematically analyzed.In addition,a prototype of the X-VSVI is manufactured,and vibration tests are carried out.The results show that the proposed X-VSVI has a superior adaptability to that of a traditional X-shaped mechanism,and shows excellent vibration isolation performance in response to different amplitudes and forms of excitations.Moreover,the vibration isolation efficiency of the device can be improved by appropriate adjustment of parameters.展开更多
Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid ...Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid element FEA models are built upon frame configuration details which are not feasible in the preliminary design stage, partially because of limited available design data of frames and heavy computation costs. This research develops 1D beam element FEA models for simulating frame structures. In this paper, the CAD model of a truck frame is first created. The solid element FEA analysis, which is adopted as the baseline in this study, is subsequently conducted for the stiffness of the frame, Next, beam element FEA analysis is performed for validating the feasibility of the beam element FEA model by comparing the results from the solid and beam element FEA models. It is found that the beam element FEA model can predict the frame stiffness with acceptable accuracy and reduce the computation cost significantly.展开更多
To improve the adaptability of TBMs in diverse geological environments,this paper proposes a reconfigurable Type-V thrust mechanism(V-TM)with rearrangeable working states,in which structural stiffness can be automatic...To improve the adaptability of TBMs in diverse geological environments,this paper proposes a reconfigurable Type-V thrust mechanism(V-TM)with rearrangeable working states,in which structural stiffness can be automatically altered during operation.Therefore,millions of configurations can be obtained,and thousands of instances of working status per configuration can be set respectively.Nonetheless,the complexity of configurations and diversity of working states contributes to further complications for the structural stiffness algorithm.This results in challenges such as difficulty calculating the payload compliance index and the environment adaptability index.To solve this problem,we use the configuration matrix to describe the relationship between propelling jacks under reconfiguration and adopt pattern vectors to describe the working state of each hydraulic cylinder.Then,both the dynamic compatible equation between propeller forces of the hydraulic cylinders and driving forces,and the kinematic harmonizing equation between the hydraulic cylinder displacements and their deformations are established.Next,we derive the stiffness analytical equation using Hooke’s law and the Jacobian Matrix.The proposed approach provides an effective algorithm to support structural rigidity analysis,and lays a solid theoretical foundation for calculating the performance indexes of the V-TM.We then analyze the rigidity characteristics of typical configurations under different working states,and obtain the main factors affecting structural stiffness of the V-TM.The results show the deviation degree of structural parameters in hydraulic cylinders within the same group,and the working status of propelling jacks.Finally,our constructive conclusions contribute valuable information for matching and optimization by drawing on the factors that affect the structural rigidity of the V-TM.展开更多
Stiffness is one of the basic performance parameters for railway track. The efficient and accurate stiffness measurement has been considered as the foundation for further development of railway engineering, and theref...Stiffness is one of the basic performance parameters for railway track. The efficient and accurate stiffness measurement has been considered as the foundation for further development of railway engineering, and therefore has great theoretical and practical significance. Based on a summary of the connotation and measurement of track stiffness, the state of the art of measurement methods for track stiffness was analyzed systematically. The standstill measurement of track stiffness can be performed with the traditional jack-loading method, impact hammer method, FWD (falling weight deflectometer) method, and track loading vehicle method. Although these methods can be adopted in stiffness measurement for a section of railway track, they are not desirable owning to small range and low efficiency. In the recent 20 years, researchers have proposed many methods like unbalancedloading laser displacement method, deflection basin deformation rate method, and eccentricity excitation method to continuously measure track stiffness; however, these methods have drawbacks like poor accuracy, low speed, and insufficient data analysis. In this work, the merits and demerits of these methods were summarized, and optimization suggestions were presented. Based on the wave transmission mechanism and principle of vibration energy harvesting, an overall conception on continuous measurement of stiffness and long-term stiffness monitoring for special sections was proposed.展开更多
To improve the vibration-isolation performance of cab seats,the optimization model of the seat suspension system of construction machinery cabs is proposed based on the negative stiffness structure.The negative stiffn...To improve the vibration-isolation performance of cab seats,the optimization model of the seat suspension system of construction machinery cabs is proposed based on the negative stiffness structure.The negative stiffness nonlinear kinetic equation is established by designing the seat negative stiffness suspension structure(NSS).Using MATLAB,the different parameters of the suspension system and their influences on the dynamic stiffness are analyzed.The ideal configuration parameter range of the suspension system is obtained.Meanwhile,the optimization model of NSS is proposed,and the vibration transmissibility characteristics are simulated and analyzed by different methods.The results show that the displacement and acceleration amplitudes of the optimized seat suspension system are evidently reduced,and the four-time power vibration dose value and root mean square calculation values in the vertical vibration direction of the seat decrease by 86%and 87%,respectively.Seat effective amplitude transmissibility(SEAT)and the vibration transmissibility ratio values also decrease.Moreover,the peak frequencies of the vibration transmitted to the driver deviate from the key frequency values,which easily cause human discomfort.Thus,the design of the seat suspension system has no effect on the health condition of the driver after being vibrated.The findings also illustrate that the NSS suspension system has good vibration-isolation performance,and the driver's ride comfort is improved.展开更多
In slab column-shear wall structures,both the whole structure′s seismic behavior and failure mode are greatly influenced by the distribution of horizontal seismic forces between slab-column and shear wall.In this pap...In slab column-shear wall structures,both the whole structure′s seismic behavior and failure mode are greatly influenced by the distribution of horizontal seismic forces between slab-column and shear wall.In this paper,a pushover analysis of topical slab column-shear wall structure was carried out,the seismic shear force that the slab-column and shear wall should undertake was worked out,the influences of plastic internal force redistribution and structure stiffness characteristic value on horizontal seismic distribution were studied and the calculation formula was given.The analysis results showed that with the yield of the shear walls,the story shear force was undertaken by slab-columns correspondingly increased while with the decrease of characteristic value of stiffness of a structure,and the horizontal seismic force was undertaken by slab-columns correspondingly decreased.According to the code,the design of horizontal force distribution may be cause insecurity problems,so it is necessary to give the distribution law of horizontal seismic forces in slab-column shear wall structures as the supplement to the corresponding regulation of the Code.展开更多
Robots are playing an increasingly important role in engineering applications.Soft robots have promising applications in several fields due to their inherent advantages of compliance,low density,and soft interactions....Robots are playing an increasingly important role in engineering applications.Soft robots have promising applications in several fields due to their inherent advantages of compliance,low density,and soft interactions.A soft gripper based on bio-inspiration is proposed in this study.We analyze the cushioning and energy absorption mechanism of human fingertips in detail and provide insights for designing a soft gripper with a variable stiffness structure.We investigate the grasping modes through a large deformation modeling approach,which is verified through experiments.The characteristics of the three grasping modes are quantified through testing and can provide guidance for robotics manipulation.First,the adaptability of the soft gripper is verified by grasping multi-scale and extremely soft objects.Second,a cushioning model of the soft gripper is proposed,and the effectiveness of cushioning is verified by grasping extremely sharp objects and living organisms.Notably,we validate the advantages of the variable stiffness of the soft gripper,and the results show that the soft robot can robustly complete assemblies with a gap of only 0.1 mm.Owing to the unstructured nature of the engineering environment,the soft gripper can be applied in complex environments based on the abovementioned experimental analysis.Finally,we design the soft robotics system with feedback capture based on the inspiration of human catching behavior.The feasibility of engineering applications is initially verified through fast capture experiments on moving objects.The design concept of this robot can provide new insights for bionic machinery.展开更多
Gas foil bearing faces severe and complex thermal-fluid–solid coupling issues when in ultra-high speed and miniaturized impeller machineries.In this study,a Thermo-Elasto-Hydrodynamic(TEHD)analysis of a specific mult...Gas foil bearing faces severe and complex thermal-fluid–solid coupling issues when in ultra-high speed and miniaturized impeller machineries.In this study,a Thermo-Elasto-Hydrodynamic(TEHD)analysis of a specific multi-layer gas foil thrust bearing on the continuous loading process within a steady rotational speed is numerically investigated by a three-dimensional thermal-fluid–solid coupling method.Results indicate that the multi-layer foil exhibits nonlinear overall stiffness,with the thrust bottom foil serving as the primary elastic deformation structure,while the thrust top foil maintains a well-defined aerodynamic shape during a loading process,which helps reduce frictional damage and achieve an adequate loading capacity.For low loads,the fluctuation of the gas film is extremely sensitive,and it weakens dramatically as the load increases.The viscous heating and friction torque exhibit a linear relationship with an increasing bearing load after a rapid growth.Depending on the exact stacking sequence and contact position of the multi-layer gas foil,the overlapping configuration allows for efficient transfer of viscous-shearing heat accumulated at the smallest air film through thermal conduction while providing elastic support.Due to the strong inhomogeneity of the viscous heat under varying loads,the temperature distribution on the top foil surface shows pronounced variations,while the difference between the peak and average temperatures of the thrust plate and top foil surfaces widens substantially with an increasing load.展开更多
A novel re-entrant triangles-filled tube(RTT)is proposed through decoupling structural stiffness and energy absorption.Inner re-entrant triangles are employed to satisfy energy absorption,and outer thin wall is used t...A novel re-entrant triangles-filled tube(RTT)is proposed through decoupling structural stiffness and energy absorption.Inner re-entrant triangles are employed to satisfy energy absorption,and outer thin wall is used to acquire high stiffness.This paper starts from establishment of theoretical models between geometric parameters of re-entrant triangles and relative density,equivalent elastic modulus and energy absorption characteristics,which are validated by experiments.On this basis,the optimal geometric parameters of unit cell are sought to maximize unit volume energy absorption and minimize relative density by adopting NSGA-II method.Subsequently,the cross-section of tube with optimal stiffness is obtained with targets for maximizing axial stiffness and lateral stiffness by employing static topology optimization method.To verify the proposed optimization method,RTT is analyzed and compared with positive Poisson’s ratio foam-filled tube(PFT),non-filled traditionally optimized tube(NTT)and pre-optimized square tube(PST).The results show that the novel RTT can improve stiffness and energy absorption performance simultaneously.Compared with the positive Poisson’s ratio material,re-entrant triangles honeycomb shows superior advantages in energy absorption.In comparison with the PFT,energy absorption of the RTT increases by 17.23%,and the peak crush force reduces by 5.04%.Therefore,the proposed decoupling design method demonstrates superiority in satisfying various performance requirements simultaneously.展开更多
The self-assembly of surface-order structures based on the surface wrinkling of stiff film-compliant substrate structures(SFCS)is potentially useful in the fabrication of functional devices,the manufacture of superhyd...The self-assembly of surface-order structures based on the surface wrinkling of stiff film-compliant substrate structures(SFCS)is potentially useful in the fabrication of functional devices,the manufacture of superhydrophobic or self-cleaning surfaces,and so on.Due to the influence of the intrinsic characteristic length(g),the surface wrinkling behavior of SFCS at the micro scale is different from that at the macro scale.In this work,based on the strain gradient theory,a trans-scale surface wrinkling model for SFCS is established.First,the effectiveness of this model is verified by previous experiments.Then,based on the model and dimensional analysis,the effect of g on the surface wrinkling behavior is investigated,and the scaling relationship of surface wrinkling of SFCS at different scales is analyzed.The results show that the influence of g cannot be neglected when the film thickness decreases to the one comparable to g.At the micro scale,g will lead to the increase of the critical wrinkling wavelength and load.In addition,the scaling relationship of surface wrinkling at the micro scale will not follow the traditional one.Our study explains the underlying mechanism of the dissimilarity of surface wrinkling behaviors of SFCS at different scales and lays a theoretical foundation for the precise control of surface-order structures.展开更多
A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic...A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic(MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12022213,12002329,U23A2066,12272240,and 12002217)。
文摘A novel X-shaped variable stiffness vibration isolator(X-VSVI)is proposed.The Runge-Kutta method,harmonic balance method,and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under various excitations.The layer number,the installation angle of the X-shaped structure,the stiffness,and the active control parameters are systematically analyzed.In addition,a prototype of the X-VSVI is manufactured,and vibration tests are carried out.The results show that the proposed X-VSVI has a superior adaptability to that of a traditional X-shaped mechanism,and shows excellent vibration isolation performance in response to different amplitudes and forms of excitations.Moreover,the vibration isolation efficiency of the device can be improved by appropriate adjustment of parameters.
文摘Truck frames should be designed and fabricated with enough rigidity to avoid excessive deflections. Finite element analysis (FEA) plays an important role in all stages of frame designs. While being accurate, 3D solid element FEA models are built upon frame configuration details which are not feasible in the preliminary design stage, partially because of limited available design data of frames and heavy computation costs. This research develops 1D beam element FEA models for simulating frame structures. In this paper, the CAD model of a truck frame is first created. The solid element FEA analysis, which is adopted as the baseline in this study, is subsequently conducted for the stiffness of the frame, Next, beam element FEA analysis is performed for validating the feasibility of the beam element FEA model by comparing the results from the solid and beam element FEA models. It is found that the beam element FEA model can predict the frame stiffness with acceptable accuracy and reduce the computation cost significantly.
基金Supported by National Natural Science Foundation of China(Grant No.51675180)National Key Basic Research Program of China(973 Program,Grant No.2013CB037503)
文摘To improve the adaptability of TBMs in diverse geological environments,this paper proposes a reconfigurable Type-V thrust mechanism(V-TM)with rearrangeable working states,in which structural stiffness can be automatically altered during operation.Therefore,millions of configurations can be obtained,and thousands of instances of working status per configuration can be set respectively.Nonetheless,the complexity of configurations and diversity of working states contributes to further complications for the structural stiffness algorithm.This results in challenges such as difficulty calculating the payload compliance index and the environment adaptability index.To solve this problem,we use the configuration matrix to describe the relationship between propelling jacks under reconfiguration and adopt pattern vectors to describe the working state of each hydraulic cylinder.Then,both the dynamic compatible equation between propeller forces of the hydraulic cylinders and driving forces,and the kinematic harmonizing equation between the hydraulic cylinder displacements and their deformations are established.Next,we derive the stiffness analytical equation using Hooke’s law and the Jacobian Matrix.The proposed approach provides an effective algorithm to support structural rigidity analysis,and lays a solid theoretical foundation for calculating the performance indexes of the V-TM.We then analyze the rigidity characteristics of typical configurations under different working states,and obtain the main factors affecting structural stiffness of the V-TM.The results show the deviation degree of structural parameters in hydraulic cylinders within the same group,and the working status of propelling jacks.Finally,our constructive conclusions contribute valuable information for matching and optimization by drawing on the factors that affect the structural rigidity of the V-TM.
基金supported by the project (51425804) of the National Science Fund for Distinguished Young Scholars of Chinathe National Natural Science Foundation of China (NSFC) under grants U1234201, U1334203, and 51378439
文摘Stiffness is one of the basic performance parameters for railway track. The efficient and accurate stiffness measurement has been considered as the foundation for further development of railway engineering, and therefore has great theoretical and practical significance. Based on a summary of the connotation and measurement of track stiffness, the state of the art of measurement methods for track stiffness was analyzed systematically. The standstill measurement of track stiffness can be performed with the traditional jack-loading method, impact hammer method, FWD (falling weight deflectometer) method, and track loading vehicle method. Although these methods can be adopted in stiffness measurement for a section of railway track, they are not desirable owning to small range and low efficiency. In the recent 20 years, researchers have proposed many methods like unbalancedloading laser displacement method, deflection basin deformation rate method, and eccentricity excitation method to continuously measure track stiffness; however, these methods have drawbacks like poor accuracy, low speed, and insufficient data analysis. In this work, the merits and demerits of these methods were summarized, and optimization suggestions were presented. Based on the wave transmission mechanism and principle of vibration energy harvesting, an overall conception on continuous measurement of stiffness and long-term stiffness monitoring for special sections was proposed.
基金The National Natural Science Foundation of China(No.11902207,No.52072072)the Natural Science Foundation of Hebei Province(A2020210018)Higher Education Teaching Research Project(No.Y2020-15).
文摘To improve the vibration-isolation performance of cab seats,the optimization model of the seat suspension system of construction machinery cabs is proposed based on the negative stiffness structure.The negative stiffness nonlinear kinetic equation is established by designing the seat negative stiffness suspension structure(NSS).Using MATLAB,the different parameters of the suspension system and their influences on the dynamic stiffness are analyzed.The ideal configuration parameter range of the suspension system is obtained.Meanwhile,the optimization model of NSS is proposed,and the vibration transmissibility characteristics are simulated and analyzed by different methods.The results show that the displacement and acceleration amplitudes of the optimized seat suspension system are evidently reduced,and the four-time power vibration dose value and root mean square calculation values in the vertical vibration direction of the seat decrease by 86%and 87%,respectively.Seat effective amplitude transmissibility(SEAT)and the vibration transmissibility ratio values also decrease.Moreover,the peak frequencies of the vibration transmitted to the driver deviate from the key frequency values,which easily cause human discomfort.Thus,the design of the seat suspension system has no effect on the health condition of the driver after being vibrated.The findings also illustrate that the NSS suspension system has good vibration-isolation performance,and the driver's ride comfort is improved.
文摘In slab column-shear wall structures,both the whole structure′s seismic behavior and failure mode are greatly influenced by the distribution of horizontal seismic forces between slab-column and shear wall.In this paper,a pushover analysis of topical slab column-shear wall structure was carried out,the seismic shear force that the slab-column and shear wall should undertake was worked out,the influences of plastic internal force redistribution and structure stiffness characteristic value on horizontal seismic distribution were studied and the calculation formula was given.The analysis results showed that with the yield of the shear walls,the story shear force was undertaken by slab-columns correspondingly increased while with the decrease of characteristic value of stiffness of a structure,and the horizontal seismic force was undertaken by slab-columns correspondingly decreased.According to the code,the design of horizontal force distribution may be cause insecurity problems,so it is necessary to give the distribution law of horizontal seismic forces in slab-column shear wall structures as the supplement to the corresponding regulation of the Code.
基金financially supported by the Fundamental Research Funds for the Central UniversitiesHeilongjiang Provincial Natural Science Foundation of China (YQ2020E009)。
基金supported by the General Program(Grant No.12272222)Key Program(Grant No.11932001)of the National Natural Science Foundation of China,for which the authors are grateful.
文摘Robots are playing an increasingly important role in engineering applications.Soft robots have promising applications in several fields due to their inherent advantages of compliance,low density,and soft interactions.A soft gripper based on bio-inspiration is proposed in this study.We analyze the cushioning and energy absorption mechanism of human fingertips in detail and provide insights for designing a soft gripper with a variable stiffness structure.We investigate the grasping modes through a large deformation modeling approach,which is verified through experiments.The characteristics of the three grasping modes are quantified through testing and can provide guidance for robotics manipulation.First,the adaptability of the soft gripper is verified by grasping multi-scale and extremely soft objects.Second,a cushioning model of the soft gripper is proposed,and the effectiveness of cushioning is verified by grasping extremely sharp objects and living organisms.Notably,we validate the advantages of the variable stiffness of the soft gripper,and the results show that the soft robot can robustly complete assemblies with a gap of only 0.1 mm.Owing to the unstructured nature of the engineering environment,the soft gripper can be applied in complex environments based on the abovementioned experimental analysis.Finally,we design the soft robotics system with feedback capture based on the inspiration of human catching behavior.The feasibility of engineering applications is initially verified through fast capture experiments on moving objects.The design concept of this robot can provide new insights for bionic machinery.
基金the financial supports provided by the Natural Science Fund of Jiangsu Province,China(No.BK20200448)the Postdoctoral Science Foundation of China(No.2020TQ0143)。
文摘Gas foil bearing faces severe and complex thermal-fluid–solid coupling issues when in ultra-high speed and miniaturized impeller machineries.In this study,a Thermo-Elasto-Hydrodynamic(TEHD)analysis of a specific multi-layer gas foil thrust bearing on the continuous loading process within a steady rotational speed is numerically investigated by a three-dimensional thermal-fluid–solid coupling method.Results indicate that the multi-layer foil exhibits nonlinear overall stiffness,with the thrust bottom foil serving as the primary elastic deformation structure,while the thrust top foil maintains a well-defined aerodynamic shape during a loading process,which helps reduce frictional damage and achieve an adequate loading capacity.For low loads,the fluctuation of the gas film is extremely sensitive,and it weakens dramatically as the load increases.The viscous heating and friction torque exhibit a linear relationship with an increasing bearing load after a rapid growth.Depending on the exact stacking sequence and contact position of the multi-layer gas foil,the overlapping configuration allows for efficient transfer of viscous-shearing heat accumulated at the smallest air film through thermal conduction while providing elastic support.Due to the strong inhomogeneity of the viscous heat under varying loads,the temperature distribution on the top foil surface shows pronounced variations,while the difference between the peak and average temperatures of the thrust plate and top foil surfaces widens substantially with an increasing load.
基金National Nature Science Foundation of China(No.2016YFB0101601)Jilin Province Scientific Research Program(No.SXGJQY2017-7)。
文摘A novel re-entrant triangles-filled tube(RTT)is proposed through decoupling structural stiffness and energy absorption.Inner re-entrant triangles are employed to satisfy energy absorption,and outer thin wall is used to acquire high stiffness.This paper starts from establishment of theoretical models between geometric parameters of re-entrant triangles and relative density,equivalent elastic modulus and energy absorption characteristics,which are validated by experiments.On this basis,the optimal geometric parameters of unit cell are sought to maximize unit volume energy absorption and minimize relative density by adopting NSGA-II method.Subsequently,the cross-section of tube with optimal stiffness is obtained with targets for maximizing axial stiffness and lateral stiffness by employing static topology optimization method.To verify the proposed optimization method,RTT is analyzed and compared with positive Poisson’s ratio foam-filled tube(PFT),non-filled traditionally optimized tube(NTT)and pre-optimized square tube(PST).The results show that the novel RTT can improve stiffness and energy absorption performance simultaneously.Compared with the positive Poisson’s ratio material,re-entrant triangles honeycomb shows superior advantages in energy absorption.In comparison with the PFT,energy absorption of the RTT increases by 17.23%,and the peak crush force reduces by 5.04%.Therefore,the proposed decoupling design method demonstrates superiority in satisfying various performance requirements simultaneously.
基金supported by the Postdoctoral Science Foundation of China for Innovative Talents(Grant No.BX2022008)the National Natural Science Foundation of China(Grant Nos.12202007,11890681,12032001 and 11521202)。
文摘The self-assembly of surface-order structures based on the surface wrinkling of stiff film-compliant substrate structures(SFCS)is potentially useful in the fabrication of functional devices,the manufacture of superhydrophobic or self-cleaning surfaces,and so on.Due to the influence of the intrinsic characteristic length(g),the surface wrinkling behavior of SFCS at the micro scale is different from that at the macro scale.In this work,based on the strain gradient theory,a trans-scale surface wrinkling model for SFCS is established.First,the effectiveness of this model is verified by previous experiments.Then,based on the model and dimensional analysis,the effect of g on the surface wrinkling behavior is investigated,and the scaling relationship of surface wrinkling of SFCS at different scales is analyzed.The results show that the influence of g cannot be neglected when the film thickness decreases to the one comparable to g.At the micro scale,g will lead to the increase of the critical wrinkling wavelength and load.In addition,the scaling relationship of surface wrinkling at the micro scale will not follow the traditional one.Our study explains the underlying mechanism of the dissimilarity of surface wrinkling behaviors of SFCS at different scales and lays a theoretical foundation for the precise control of surface-order structures.
基金supported by National Natural Science Foundation of China (Nos. U1333201, 11502123 and 11262012 )
文摘A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic(MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.