The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite ...The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.展开更多
A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order...A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.展开更多
To investigate potential strengthening approaches,multi-layered zirconium–titanium(Zr-Ti)composites were fabricated by hot-rolling bonding and annealing.The microstructures of these composites were characterized usin...To investigate potential strengthening approaches,multi-layered zirconium–titanium(Zr-Ti)composites were fabricated by hot-rolling bonding and annealing.The microstructures of these composites were characterized using scanning electron microscopy with energy dispersive spectroscopy(SEM-EDS)and electron backscatter diffractometry(EBSD).Their mechanical properties were evaluated by uniaxial tension and compression measurements.It was found that the fabricated Zr–Ti composites are composed of alternating Zr/diffusion/Ti layers,and chemical compositions of Zr and Ti showed a gradient distribution in the diffusion layer.Compared with as-rolled samples,annealing can strengthen the layered gradient Zr–Ti composite,and this is mainly caused by solid-solution strengthening and microstructure refinement-induced strengthening.Compared with the raw materials,a synergistic improvement of strength and ductility is achieved in the Zr–Ti composite as a result of the layered gradient microstructure.Tension–compression asymmetry is observed in the Zr–Ti composites,which may be attributed to twinning and microvoids induced by unbalanced diffusion.展开更多
An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on e...An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on egg-shaped function and supplement its definition in the deviatoric section,and then a yield criterion suitable for 3D stress conditions is obtained;2)to elaborate its numerical implementation based on the drained triaxial tests.During the above discussion,a non-associated flow rule is proposed,in which the stress-dilatancy relationship in most classical theory is replaced by a linear dependence between the stress state parameterηand the rotation angleγof the plastic potential surface.Thereafter,isotropic and kinematic hardening behavior is considered by employing the hardening parameter H,which can be expressed as the function of plastic work Wp.Finally,comparisons between numerical results and test data on Taizhou soft clay are made to verify the effectiveness of the proposed model.展开更多
Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonli...Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonlinear yield criterion was proposed which gives a series of new failure criteria, establishes a relationship among various failure criteria, and encompasses previous yield criteria as special cases or approximations. The criterion is capable of being expressed in a simple mathematical expression and through a particular physical concept, it also agree with some experimental data. It may therefore serve as a possible admissible isotropic yield criterion.展开更多
The stability of long span steel arch structure of globe transportation center (GTC) in the Beijing Capital International Airport was studied. Different objective models such as single arch model, composite arch model...The stability of long span steel arch structure of globe transportation center (GTC) in the Beijing Capital International Airport was studied. Different objective models such as single arch model, composite arch model and global structural model were introduced to analyze the structural stability by means of the finite element technique. The eigen buckling factor of the steel arch structure was analyzed. The geometrical nonlinearity, elastic-plastic nonlinearity and initial imperfection were taken into account in the investigation of the structural buckling, and the nonlinearity reduction factors for the steel arch structure were discussed. The effects of geometrical nonlinearity and initial imperfection on the structural buckling are light while the effect of material nonlinearity is quite remarkable. For a single steel arch, the dominant buckling mode occurs in out-of-plane of arch structure. The out-of-plane buckling factor of the composite steel arch is greater than that of the single steel arch while the in-plane buckling factor of the former is somewhat less than that of the latter. Moreover, the webs near the steel arch feet have the lowest local buckling level and the local buckling is more serious than the global buckling for the global structure.展开更多
Nonlinear buckling behavior of stiffened composite B-Al plates was analyzed by means of finite element analysis(FEA) method. In the method, the composite material was taken as B matrix into which Al fibers were embedd...Nonlinear buckling behavior of stiffened composite B-Al plates was analyzed by means of finite element analysis(FEA) method. In the method, the composite material was taken as B matrix into which Al fibers were embedded in different configurations. The laminated B-Al material in the form of rectangular plates was subjected to lateral compressive loading. It is observed that stiffeners have significant effect on the buckling behavior of plates under compressive loading and for various geometrical configurations. The stiffeners used in the modeling are one-sided and have rectangular cross-sections. It is found that there are physically important loading intervals and the critical buckling modes make transitions back and forth between stable and unstable states. Bifurcation buckling regions resulting from various configurations of fiber orientations and different plate aspect ratios are determined. The whole analysis is performed by using ANSYS finite element computations. Only the buckling patterns of stiffened plate configurations under simply supported boundary conditions are studied. Distributions of compressive stresses(σx) vs in-plane contractions(u) and compressive stresses(σx) vs out-of plane deflections(δ) are obtained. Nonlinear analysis of the C2 fiber configuration yields the safest critical buckling stress amongst C1, C2, C3 and C4 configurations. It is concluded that FEA method for the nonlinear buckling analysis generates accurate results.展开更多
In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline's inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline a...In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline's inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline's nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simulations. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline's buckling deformation and contact between pipeline's inner walls, which forms the basis for further research on three-dimensional buckling propagation.展开更多
In this study, a modelization of the viscoplastic behaviour of amorphous polymers is proposed, from an approach originally developed for metals behaviour at high temperature, in which state variable constitutive equat...In this study, a modelization of the viscoplastic behaviour of amorphous polymers is proposed, from an approach originally developed for metals behaviour at high temperature, in which state variable constitutive equations have been modified. The model includes the effect of strain rate sensitivity, strain softening and strain hardening. A procedure for the identification of model parameters is developed through the use of experimental data from uniaxial tests extracted from the literature, across a variety of strain rates and below the glass transition temperature ( Tg). The numerical algorithm shows that the predictions of this model well describe the intrinsic softening upon yield threshold and the subsequent progressive orientational hardening typical for amorphous glassy polymers.展开更多
In this paper, the strengthening of thin-walled metallic shells with the application of CFRP (carbon fibre reinforced polymer) has been investigated. To lower down the downside of the lower stiffness exhibited by CF...In this paper, the strengthening of thin-walled metallic shells with the application of CFRP (carbon fibre reinforced polymer) has been investigated. To lower down the downside of the lower stiffness exhibited by CFRP shells and to diminish the major problem associated with steel shells, a new composite sandwich structure has been introduced in this paper and effect of CFRP reinforcements under axial compression has been studied through three kinds of analytical procedures; the linear Eigen value problem, the modified RS (reduced stiffness) analysis and the fully nonlinear numerical experiment. With these multiple treatments it has been suggested that recently developed modified RS analysis which effectively compute the lower bounds provides the significant information to evaluate the buckling capacity of reinforced shells that display the unstable behaviour and imperfection-sensitivity than the general RS Analysis. This paper also illustrates the application of the methodology to cases of axial loaded shells with the varying thickness of veneers of CFRP.展开更多
A new double-yield-sarface (DYS) model was developed to characterize the strength and deformation behaviors of coarse granular materials (CGMs). Two kinds of deformation mechanisms, including the shear and compres...A new double-yield-sarface (DYS) model was developed to characterize the strength and deformation behaviors of coarse granular materials (CGMs). Two kinds of deformation mechanisms, including the shear and compressive plastic deformation, were taken into account in this model, These two deformation mechanisms were described by the shear and compressive yield functions, respectively. The Lode angle dependent formulations of proposed model were deduced by incorporating a 3D nonlinear unified failure criterion. Some comparisons were presented between the numerical predictions of proposed model and test data of true triaxial tests on the modeled rockfills. The model predictions are in good agreement with the test data and capture the strain hardening and plastic volumetric dilation of CGMs. These findings verify the reasonability of current DYS model, and indicate that this model is well suited to reproduce the stress-strain-volume change behavior of CGMs in general.展开更多
This paper studies the dynamic shell buckling behavior of multi-walled carbon nanotubes(MWNTs) embedded in an elastic medium under step axial load based on continuum mechanics model.It is shown that,for occurrence of ...This paper studies the dynamic shell buckling behavior of multi-walled carbon nanotubes(MWNTs) embedded in an elastic medium under step axial load based on continuum mechanics model.It is shown that,for occurrence of dynamic shell buckling of MWNTs or MWNTs embedded in an elastic medium,the buckling stress is higher than the critical buckling stress of the corresponding static shell buckling under otherwise identical conditions.Detailed results are demonstrated for dynamic shell buckling of individual double-walled carbon nanotubes(DWNTs) or DWNTs embedded in an elastic medium.A phenomenon is shown that DWNTs or embedded DWNTs in dynamic shell buckling are prone to axisymmetric buckling rather than non-axisymmetric buckling.Numerical results also indicate that the axial buckling form shifts from the lower buckling mode to the higher buckling mode with increasing buckling stress,but the buckling mode is invariable for a certain domain of buckling stress.Further,an approximate analytic formula is presented for the buckling stress and the associated buckling wavelength for dynamic axisymmetric buckling of embedded DWNTs.The effect of radii is also examined.展开更多
The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In th...The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy.However,this method only generates the first-order approximate solution for the nonlinear buckling.In the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain.The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.展开更多
文摘The equilibrium equations and the functional for tubing buckling in arbitrary straight wells are derived. The entire buckling process of tubing in deviated wells is analyzed for the first time by utilizing the finite element method. The effects of gravity and torques on the buckling are included in the analyses and the calculated results are well compared with existing solutions. It is shown that the buckling only occurs at the lower portion of the tubing where the axial load is the largest, and the contact force of the well, the bending moment of the tubing and the buckling displacement of this portion vary periodically. The buckling spreads upwards from the bit with the increase of axial load. There is no buckling at the upper portion of the tubing where the bending moment is zero. And the contact force of this section increases only slightly with the increase of the axial load. With the increase of the deviation angle, the length of buckling portion and buckling displacement amplitude decrease, the contact force increases with the increase of load at the upper portion and its amplitude decreases at the lower buckling section, the bending moment remains zero at the upper portion and its amplitude decreases at the lower buckling portion. The buckling displacement increases with the increase of the torque, but the increment is very small.
文摘A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.
基金financially supported by the National Natural Science Foundation of China(No.51971041)the Natural Science Foundation of Chongqing,China(No.cstc2019jcyj-msxm X0234)。
文摘To investigate potential strengthening approaches,multi-layered zirconium–titanium(Zr-Ti)composites were fabricated by hot-rolling bonding and annealing.The microstructures of these composites were characterized using scanning electron microscopy with energy dispersive spectroscopy(SEM-EDS)and electron backscatter diffractometry(EBSD).Their mechanical properties were evaluated by uniaxial tension and compression measurements.It was found that the fabricated Zr–Ti composites are composed of alternating Zr/diffusion/Ti layers,and chemical compositions of Zr and Ti showed a gradient distribution in the diffusion layer.Compared with as-rolled samples,annealing can strengthen the layered gradient Zr–Ti composite,and this is mainly caused by solid-solution strengthening and microstructure refinement-induced strengthening.Compared with the raw materials,a synergistic improvement of strength and ductility is achieved in the Zr–Ti composite as a result of the layered gradient microstructure.Tension–compression asymmetry is observed in the Zr–Ti composites,which may be attributed to twinning and microvoids induced by unbalanced diffusion.
基金Project(41672264)supported by the National Natural Science Foundation of ChinaProject(2019C03103)supported by the Key Research and Development Program of Zhejiang Province,China。
文摘An exploratory discussion is presented on the application of egg-shaped function in elasto-plastic constitutive analysis for soft clay.Two main tasks of the paper are:1)to propose a complete yield criterion based on egg-shaped function and supplement its definition in the deviatoric section,and then a yield criterion suitable for 3D stress conditions is obtained;2)to elaborate its numerical implementation based on the drained triaxial tests.During the above discussion,a non-associated flow rule is proposed,in which the stress-dilatancy relationship in most classical theory is replaced by a linear dependence between the stress state parameterηand the rotation angleγof the plastic potential surface.Thereafter,isotropic and kinematic hardening behavior is considered by employing the hardening parameter H,which can be expressed as the function of plastic work Wp.Finally,comparisons between numerical results and test data on Taizhou soft clay are made to verify the effectiveness of the proposed model.
文摘Many experimental results show that a wide class of ductile materials obey often nonlinear behavior, thus it is important to propose a nonlinear criterion describing nonlinear behavior of ductile material. A new nonlinear yield criterion was proposed which gives a series of new failure criteria, establishes a relationship among various failure criteria, and encompasses previous yield criteria as special cases or approximations. The criterion is capable of being expressed in a simple mathematical expression and through a particular physical concept, it also agree with some experimental data. It may therefore serve as a possible admissible isotropic yield criterion.
基金Key Project of Chinese Ministry of Educa-tion (No. 104079)National Natural Sci-ence Foundation of China (No. 10572091)
文摘The stability of long span steel arch structure of globe transportation center (GTC) in the Beijing Capital International Airport was studied. Different objective models such as single arch model, composite arch model and global structural model were introduced to analyze the structural stability by means of the finite element technique. The eigen buckling factor of the steel arch structure was analyzed. The geometrical nonlinearity, elastic-plastic nonlinearity and initial imperfection were taken into account in the investigation of the structural buckling, and the nonlinearity reduction factors for the steel arch structure were discussed. The effects of geometrical nonlinearity and initial imperfection on the structural buckling are light while the effect of material nonlinearity is quite remarkable. For a single steel arch, the dominant buckling mode occurs in out-of-plane of arch structure. The out-of-plane buckling factor of the composite steel arch is greater than that of the single steel arch while the in-plane buckling factor of the former is somewhat less than that of the latter. Moreover, the webs near the steel arch feet have the lowest local buckling level and the local buckling is more serious than the global buckling for the global structure.
文摘Nonlinear buckling behavior of stiffened composite B-Al plates was analyzed by means of finite element analysis(FEA) method. In the method, the composite material was taken as B matrix into which Al fibers were embedded in different configurations. The laminated B-Al material in the form of rectangular plates was subjected to lateral compressive loading. It is observed that stiffeners have significant effect on the buckling behavior of plates under compressive loading and for various geometrical configurations. The stiffeners used in the modeling are one-sided and have rectangular cross-sections. It is found that there are physically important loading intervals and the critical buckling modes make transitions back and forth between stable and unstable states. Bifurcation buckling regions resulting from various configurations of fiber orientations and different plate aspect ratios are determined. The whole analysis is performed by using ANSYS finite element computations. Only the buckling patterns of stiffened plate configurations under simply supported boundary conditions are studied. Distributions of compressive stresses(σx) vs in-plane contractions(u) and compressive stresses(σx) vs out-of plane deflections(δ) are obtained. Nonlinear analysis of the C2 fiber configuration yields the safest critical buckling stress amongst C1, C2, C3 and C4 configurations. It is concluded that FEA method for the nonlinear buckling analysis generates accurate results.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51239008 and 51179126)the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2011ZX05026-005)
文摘In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline's inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline's nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simulations. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline's buckling deformation and contact between pipeline's inner walls, which forms the basis for further research on three-dimensional buckling propagation.
文摘In this study, a modelization of the viscoplastic behaviour of amorphous polymers is proposed, from an approach originally developed for metals behaviour at high temperature, in which state variable constitutive equations have been modified. The model includes the effect of strain rate sensitivity, strain softening and strain hardening. A procedure for the identification of model parameters is developed through the use of experimental data from uniaxial tests extracted from the literature, across a variety of strain rates and below the glass transition temperature ( Tg). The numerical algorithm shows that the predictions of this model well describe the intrinsic softening upon yield threshold and the subsequent progressive orientational hardening typical for amorphous glassy polymers.
文摘In this paper, the strengthening of thin-walled metallic shells with the application of CFRP (carbon fibre reinforced polymer) has been investigated. To lower down the downside of the lower stiffness exhibited by CFRP shells and to diminish the major problem associated with steel shells, a new composite sandwich structure has been introduced in this paper and effect of CFRP reinforcements under axial compression has been studied through three kinds of analytical procedures; the linear Eigen value problem, the modified RS (reduced stiffness) analysis and the fully nonlinear numerical experiment. With these multiple treatments it has been suggested that recently developed modified RS analysis which effectively compute the lower bounds provides the significant information to evaluate the buckling capacity of reinforced shells that display the unstable behaviour and imperfection-sensitivity than the general RS Analysis. This paper also illustrates the application of the methodology to cases of axial loaded shells with the varying thickness of veneers of CFRP.
基金Project(50825901)supported by the National Natural Science Foundation for Distinguished Young Scholar of ChinaProject(2009492011)supported by State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Nanjing Hydraulic Research Institute,China+1 种基金Project(GH200903)supported by Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering(Hohai University),ChinaProject(Y1090151)supported by Natural Science Foundation of Zhejiang Province,China
文摘A new double-yield-sarface (DYS) model was developed to characterize the strength and deformation behaviors of coarse granular materials (CGMs). Two kinds of deformation mechanisms, including the shear and compressive plastic deformation, were taken into account in this model, These two deformation mechanisms were described by the shear and compressive yield functions, respectively. The Lode angle dependent formulations of proposed model were deduced by incorporating a 3D nonlinear unified failure criterion. Some comparisons were presented between the numerical predictions of proposed model and test data of true triaxial tests on the modeled rockfills. The model predictions are in good agreement with the test data and capture the strain hardening and plastic volumetric dilation of CGMs. These findings verify the reasonability of current DYS model, and indicate that this model is well suited to reproduce the stress-strain-volume change behavior of CGMs in general.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11172304,11202210,11021262 and 10972010)the National Basic Research Program of China (Grant No. 2012CB937500)
文摘This paper studies the dynamic shell buckling behavior of multi-walled carbon nanotubes(MWNTs) embedded in an elastic medium under step axial load based on continuum mechanics model.It is shown that,for occurrence of dynamic shell buckling of MWNTs or MWNTs embedded in an elastic medium,the buckling stress is higher than the critical buckling stress of the corresponding static shell buckling under otherwise identical conditions.Detailed results are demonstrated for dynamic shell buckling of individual double-walled carbon nanotubes(DWNTs) or DWNTs embedded in an elastic medium.A phenomenon is shown that DWNTs or embedded DWNTs in dynamic shell buckling are prone to axisymmetric buckling rather than non-axisymmetric buckling.Numerical results also indicate that the axial buckling form shifts from the lower buckling mode to the higher buckling mode with increasing buckling stress,but the buckling mode is invariable for a certain domain of buckling stress.Further,an approximate analytic formula is presented for the buckling stress and the associated buckling wavelength for dynamic axisymmetric buckling of embedded DWNTs.The effect of radii is also examined.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002077 and 11072215)
文摘The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy.However,this method only generates the first-order approximate solution for the nonlinear buckling.In the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain.The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.