Mechanical-guided assembly of three-dimensional(3D)mesostructures from pre-defined 2D precursors based on the deterministically controlled buckling has attracted increasing attention in both fundamental and applied re...Mechanical-guided assembly of three-dimensional(3D)mesostructures from pre-defined 2D precursors based on the deterministically controlled buckling has attracted increasing attention in both fundamental and applied research areas,owing to the compelling advantages in developing flexible electronic devices with complex 3D geometries and novel functions.Recently,a buckling-guided strategy was reported to enable assembly of complex 3D mesostructures and electronic devices on cylindrical and cylinder-like substrates,which can be integrated with vascular systems for monitoring of flow rate and other physical signals.A clear understanding of nonlinear buckling deformations of elastic beams assembled on cylindrical substrates is thereby essential for the relevant structural design.In this work,we present a systematic study on the nonlinear deformations of buckled ribbon-type structures on cylindrical substrates.Two representative classes of ribbon-type structures are considered,including arc structures and serpentine structures.Starting with the finite-deformation beam theory,a theoretical model is established to investigate deformed configurations resulted from the controlled buckling,including ribbons assembled on both outer and inner surfaces of the substrate.The structure-substrate contact and self-contact are taken into account in the analyses,which could lead to distinct deformed configurations.Both experimental studies and finite element analyses(FEA)were carried out to validate the developed theoretical model.A demonstrative device design based on the 3D ribbon network outside the cylindrical substrate suggests potential applications in energy harvesting across a broad range of frequency.The theoretical model presented herein could offer insights for the practical design of 3D electronic devices that can be conformally integrated with curvy biological surfaces.展开更多
A postbuckling analysis is presented for a stiffened cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulations are based on a boundary layer...A postbuckling analysis is presented for a stiffened cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stiffener' approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results are presented in dimensionless graphical form.展开更多
An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite ...An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von K′arm′an nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.展开更多
The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The m...The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected hy the variation of temperature and moisture, and are hosed on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular peturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.展开更多
In this paper, the problem of axisymmetric buckling and postbuckling of a circular thin-film delamination bridged by through-thickness fiber tows in 3D composites is presented. An iterative procedure based on Taylor&#...In this paper, the problem of axisymmetric buckling and postbuckling of a circular thin-film delamination bridged by through-thickness fiber tows in 3D composites is presented. An iterative procedure based on Taylor's series expansion is used to generate a family of nondimensionalized postbuckling solutions of the above problem by von Karman's nonlinear plate theory. Attention is focused, herein, on the effects of the bridge force of through-thickness fibers on the buckling and postbuckling behavior of the delamination. It is found that fiber bridge not only increases the ability of resisting delamination buckling and postbuckling, but also brings on the jump of the delamination deflection mode during the postbuckling phase. Consequently the behavior of the composite structure with delamination is greatly improved, such as increasing the residual strength and prolonging the service life.展开更多
This paper analyzes the nonlocal thermal buckling and postbuckling behaviors of a multi-layered graphene nanoplatelet(GPL)reinforced piezoelectric micro-plate.The GPLs are supposed to disperse as a gradient pattern in...This paper analyzes the nonlocal thermal buckling and postbuckling behaviors of a multi-layered graphene nanoplatelet(GPL)reinforced piezoelectric micro-plate.The GPLs are supposed to disperse as a gradient pattern in the composite micro-plate along its thickness.The effective material properties are calculated by the Halpin-Tsai parallel model and mixture rule for the functionally graded GPL reinforced piezoelectric(FG-GRP)micro-plate.Governing equations for the nonlocal thermal buckling and postbuckling behaviors of the FG-GRP micro-plate are obtained by the first-order shear deformation theory,the von Kármán nonlinear theory,and the minimum potential energy principle.The differential quadrature(DQ)method and iterative method are introduced to numerically analyze the effects of the external electric voltage,the distribution pattern and characteristic of GPLs,and the nonlocal parameter on the critical buckling behaviors and postbuckling equilibrium path of the FG-GRP micro-plate in thermal environment.展开更多
In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The propos...In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale parameters which describe the stiffness-softening and stiffness-hardening size effects of nanomaterials, respectively. By applying Hamilton's principle, the motion equation and the associated boundary condition are derived. A two-step perturbation method is introduced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically. Afterwards, the influence of geometrical, material, and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed. Numerical results show that the stability and precision of the perturbation solutions can be guaranteed, and the two types of size effects become increasingly important as the slenderness ratio increases. Moreover, the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.展开更多
This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The non-linear govern...This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The non-linear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge-Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance （10^-5）. The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.展开更多
Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbu...Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbuckling and nonlinear panel flutter motions of VSCLs,a full-order numerical model is developed based on the linear quadratic regulator(LQR)algorithm in control theory,the classical laminate plate theory(CLPT)considering von Kármán geometrical nonlinearity,and the first-order Piston theory.The critical buckling temperature and the critical aerodynamic pressure of VSCLs are parametrically investigated.The location and shape of piezoelectric actuators for optimal control of the dynamic responses of VSCLs are determined through comparing the norms of feedback control gain(NFCG).Numerical simulations show that the temperature field has a great effect on aeroelastic tailoring of VSCLs;the curvilinear fiber path of VSCLs can significantly affect the optimal location and shape of piezoelectric actuator for flutter suppression;the unstable panel flutter and the thermal postbuckling deflection can be suppressed effectively through optimal design of piezoelectric patches.展开更多
The elasto-plastic buckling and postbuckling of fiber metal laminates （FML） are studied in this research. Considering the geometric nonlinearity of the structure and the elasto- plastic deformation of the metal laye...The elasto-plastic buckling and postbuckling of fiber metal laminates （FML） are studied in this research. Considering the geometric nonlinearity of the structure and the elasto- plastic deformation of the metal layers, the incremental Von Karman geometric relation of the FML with initial deflection is established. Moreover, an incremental elasto-plastic constitutive relation adopting the mixed hardening rule is introduced to depict the stress-strain relationship of the metal layers. Subsequently, the incremental nonlinear governing equations of the FML subjected to in-plane compressive loads are derived, and the whole problem is solved by the iterative method according to the finite difference method. In numerical examples, the effects of the initial deflection, the loading state, and the geometric parameters on the elasto-plastic buckling and postbuckling of FML are investigated, respectively.展开更多
The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effect...The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.展开更多
This work explores the postbuckling behavior of a marine stifened composite plate in the presence of initial imperfections.The imperfection shapes are derived from buckling mode shapes and their combinations.Thereafte...This work explores the postbuckling behavior of a marine stifened composite plate in the presence of initial imperfections.The imperfection shapes are derived from buckling mode shapes and their combinations.Thereafter,these imperfection shapes are applied to the model,and nonlinear large defection fnite element and progressive failure analyses are performed in ANSYS 18.2 software.The Hashin failure criterion is employed to model the progressive failure in the stifened composite plate.The efect of the initial geometric imperfection on the stifened composite plate is investigated by considering various imperfection patterns and magnitudes.Results show that when the magnitude of the imperfection is 20 mm,the ultimate strength of the stifened composite plate decreases by 31%.Moreover,global imperfection shapes are found to be fundamental in determining the ultimate strength of stifened composite plates and their postbuckling.展开更多
Large deflection postbuckling responses of metamaterial cylindrical shells perforated by arrayed circular holes are investigated through a newly proposed theoretical model incorporating with finite element method and ...Large deflection postbuckling responses of metamaterial cylindrical shells perforated by arrayed circular holes are investigated through a newly proposed theoretical model incorporating with finite element method and experiment.The triggering of an unusual pattern transformation under compressive load(that shows special hyperelastic metamaterial characteristics)contributes to the particularity of the postbucklingmodes,in which the axisymmetric waisted and non-axisymmetric postbuckling configurations of perforated cylindrical shells are identified.The transformations of postbucking modes are mainly affected by global outline sizes of the shell and local geometrical parameters of holes.The structural load-carrying capacity for the waisted postbuckling response suffers a sudden drop and recovers when the holes collapse.Comparatively,the shell would undergo a sustained fall off under non-axisymmetric postbuckling states.The negative Poisson’s ratio induced by pattern transformation plays a key role and a critical effective threshold value exists,inducing the waisted postbuckling mode.The revealed principles would be of benefit for achieving a controllable structural stability that is usually difficult to implement on those conventional structures.展开更多
This paper deals with the problem of the postbuckling response of a thin cantilever beam ofnon-linear material, subjected to subtangential follower forces. Based on the well-knownBernoulli-Euler bending moment-curvatu...This paper deals with the problem of the postbuckling response of a thin cantilever beam ofnon-linear material, subjected to subtangential follower forces. Based on the well-knownBernoulli-Euler bending moment-curvature relation, the proposed problem is reduced to a specialeigenvalue problem of non-linear differential equation. An approximate solution is achieved byusing a simple and very effective technique, which leads to reliable results even in the case of verylarge deflections. The initial postbuckling path depending on the subtangential follower forces inequilibrium is then obtained. Moreover, the individual and coupling effect of the subtangential fol-lower force, the material non-linearity and the beam slenderness ratio on the initial postbucklingpath are also discussed in detail.展开更多
In this paper, Dynamic Relaxation Method is applied to study the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading. The phenomenon that loading paths do not...In this paper, Dynamic Relaxation Method is applied to study the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading. The phenomenon that loading paths do not coincide with unloading paths has been found. Numerical results are given for cylindrically curved cross-ply panels subjected to uniform uniaxial compression under two types of boundary conditions. The influence of the number of layers, the panels curvature and the initial imperfection on the postbuckling paths is discussed.展开更多
It is proved that the ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression is far higher than their buckling stress through the tests of 283 rectangular composite ...It is proved that the ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression is far higher than their buckling stress through the tests of 283 rectangular composite thin laminates in this paper. The ultimate strength of the composite thin plates is studied using large-deflection theory and small-deflection theory of thin plates. According to the failure criterion of the composites ultimate strength is found finally. It is in accordance with the experimental values for the plates having 45 degrees off-axial, and for longitudinal and latitudinal plates, when beta < 0.11, the theoretical values are higher. The coefficient C given in this paper may be referred to in product designing.展开更多
Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionles...Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.展开更多
Buckling and postbuckling behaviors of perfect and imperfect, stringer and ortho/ropically stiffened cylindrical shells have been studied under axial compression. Based on the boundary la ver theory for the buckling o...Buckling and postbuckling behaviors of perfect and imperfect, stringer and ortho/ropically stiffened cylindrical shells have been studied under axial compression. Based on the boundary la ver theory for the buckling oj thin elastic shells suggested in ref. [1], a theoretical analysis is presented. The effects of material properties of stiffenefs and skin, which are made of different materials, on the huckling load and postbuckling behavior of stiffened cylindrical shells have also been discussed.展开更多
The buckling and postbuckling behaviors of perfect and imperfect antisymmetrically angle-ply laminated composite plates under uniaxial compression have been studied by perturbation technique which takes deflection as ...The buckling and postbuckling behaviors of perfect and imperfect antisymmetrically angle-ply laminated composite plates under uniaxial compression have been studied by perturbation technique which takes deflection as its perturbation parameter.In this paper, the effects of in-plane boundary conditions, angles, total number of layers and initial geometric imperfection on the postbuckling behavior of laminated plates have been discussed.展开更多
Full-range analysis for the buckling and post buck ling at rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as its perturbation parameter.In this paper the e...Full-range analysis for the buckling and post buck ling at rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as its perturbation parameter.In this paper the effects of initial geometric imperfection on the postbuc kling behavior of plates have been discussed. It is seen that the effect of initial imperfection on the inelastic postbuckling oj plates is sensitive. By comparison, it is found that the theoretical results of this paper are in good agreement with experiments.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12225206 and 11921002)the Tsinghua National Laboratory for Information Science and Technology,and a grant from the Institute for Guo Qiang,Tsinghua University(Grant No.2021GQG1009).
文摘Mechanical-guided assembly of three-dimensional(3D)mesostructures from pre-defined 2D precursors based on the deterministically controlled buckling has attracted increasing attention in both fundamental and applied research areas,owing to the compelling advantages in developing flexible electronic devices with complex 3D geometries and novel functions.Recently,a buckling-guided strategy was reported to enable assembly of complex 3D mesostructures and electronic devices on cylindrical and cylinder-like substrates,which can be integrated with vascular systems for monitoring of flow rate and other physical signals.A clear understanding of nonlinear buckling deformations of elastic beams assembled on cylindrical substrates is thereby essential for the relevant structural design.In this work,we present a systematic study on the nonlinear deformations of buckled ribbon-type structures on cylindrical substrates.Two representative classes of ribbon-type structures are considered,including arc structures and serpentine structures.Starting with the finite-deformation beam theory,a theoretical model is established to investigate deformed configurations resulted from the controlled buckling,including ribbons assembled on both outer and inner surfaces of the substrate.The structure-substrate contact and self-contact are taken into account in the analyses,which could lead to distinct deformed configurations.Both experimental studies and finite element analyses(FEA)were carried out to validate the developed theoretical model.A demonstrative device design based on the 3D ribbon network outside the cylindrical substrate suggests potential applications in energy harvesting across a broad range of frequency.The theoretical model presented herein could offer insights for the practical design of 3D electronic devices that can be conformally integrated with curvy biological surfaces.
文摘A postbuckling analysis is presented for a stiffened cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stiffener' approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results are presented in dimensionless graphical form.
文摘An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von K′arm′an nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.
文摘The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected hy the variation of temperature and moisture, and are hosed on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular peturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.
基金The project supported by post doctoral science foundation of China
文摘In this paper, the problem of axisymmetric buckling and postbuckling of a circular thin-film delamination bridged by through-thickness fiber tows in 3D composites is presented. An iterative procedure based on Taylor's series expansion is used to generate a family of nondimensionalized postbuckling solutions of the above problem by von Karman's nonlinear plate theory. Attention is focused, herein, on the effects of the bridge force of through-thickness fibers on the buckling and postbuckling behavior of the delamination. It is found that fiber bridge not only increases the ability of resisting delamination buckling and postbuckling, but also brings on the jump of the delamination deflection mode during the postbuckling phase. Consequently the behavior of the composite structure with delamination is greatly improved, such as increasing the residual strength and prolonging the service life.
基金Project supported by the National Natural Science Foundation of China(Nos.11802005,12172012,11832002,and 11427801)the General Program of Science and Technology Development Project of Beijing Municipal Education Commission of China(No.KM201910005035)
文摘This paper analyzes the nonlocal thermal buckling and postbuckling behaviors of a multi-layered graphene nanoplatelet(GPL)reinforced piezoelectric micro-plate.The GPLs are supposed to disperse as a gradient pattern in the composite micro-plate along its thickness.The effective material properties are calculated by the Halpin-Tsai parallel model and mixture rule for the functionally graded GPL reinforced piezoelectric(FG-GRP)micro-plate.Governing equations for the nonlocal thermal buckling and postbuckling behaviors of the FG-GRP micro-plate are obtained by the first-order shear deformation theory,the von Kármán nonlinear theory,and the minimum potential energy principle.The differential quadrature(DQ)method and iterative method are introduced to numerically analyze the effects of the external electric voltage,the distribution pattern and characteristic of GPLs,and the nonlocal parameter on the critical buckling behaviors and postbuckling equilibrium path of the FG-GRP micro-plate in thermal environment.
基金supported by the National Natural Science Foundation of China(Nos.11672252 and11602204)the Fundamental Research Funds for the Central Universities,Southwest Jiaotong University(No.2682016CX096)
文摘In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale parameters which describe the stiffness-softening and stiffness-hardening size effects of nanomaterials, respectively. By applying Hamilton's principle, the motion equation and the associated boundary condition are derived. A two-step perturbation method is introduced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically. Afterwards, the influence of geometrical, material, and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed. Numerical results show that the stability and precision of the perturbation solutions can be guaranteed, and the two types of size effects become increasingly important as the slenderness ratio increases. Moreover, the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.
文摘This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The non-linear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge-Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance （10^-5）. The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.
基金Project(JCYJ20190808175801656)supported by the Science and Technology Innovation Commission of Shenzhen,ChinaProject(2021M691427)supported by Postdoctoral Science Foundation of ChinaProject(9680086)supported by the City University of Hong Kong,China。
文摘Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbuckling and nonlinear panel flutter motions of VSCLs,a full-order numerical model is developed based on the linear quadratic regulator(LQR)algorithm in control theory,the classical laminate plate theory(CLPT)considering von Kármán geometrical nonlinearity,and the first-order Piston theory.The critical buckling temperature and the critical aerodynamic pressure of VSCLs are parametrically investigated.The location and shape of piezoelectric actuators for optimal control of the dynamic responses of VSCLs are determined through comparing the norms of feedback control gain(NFCG).Numerical simulations show that the temperature field has a great effect on aeroelastic tailoring of VSCLs;the curvilinear fiber path of VSCLs can significantly affect the optimal location and shape of piezoelectric actuator for flutter suppression;the unstable panel flutter and the thermal postbuckling deflection can be suppressed effectively through optimal design of piezoelectric patches.
基金supported by the National Natural Science Foundation of China(No.11272117)
文摘The elasto-plastic buckling and postbuckling of fiber metal laminates （FML） are studied in this research. Considering the geometric nonlinearity of the structure and the elasto- plastic deformation of the metal layers, the incremental Von Karman geometric relation of the FML with initial deflection is established. Moreover, an incremental elasto-plastic constitutive relation adopting the mixed hardening rule is introduced to depict the stress-strain relationship of the metal layers. Subsequently, the incremental nonlinear governing equations of the FML subjected to in-plane compressive loads are derived, and the whole problem is solved by the iterative method according to the finite difference method. In numerical examples, the effects of the initial deflection, the loading state, and the geometric parameters on the elasto-plastic buckling and postbuckling of FML are investigated, respectively.
文摘The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.
文摘This work explores the postbuckling behavior of a marine stifened composite plate in the presence of initial imperfections.The imperfection shapes are derived from buckling mode shapes and their combinations.Thereafter,these imperfection shapes are applied to the model,and nonlinear large defection fnite element and progressive failure analyses are performed in ANSYS 18.2 software.The Hashin failure criterion is employed to model the progressive failure in the stifened composite plate.The efect of the initial geometric imperfection on the stifened composite plate is investigated by considering various imperfection patterns and magnitudes.Results show that when the magnitude of the imperfection is 20 mm,the ultimate strength of the stifened composite plate decreases by 31%.Moreover,global imperfection shapes are found to be fundamental in determining the ultimate strength of stifened composite plates and their postbuckling.
基金State Key Laboratory of Structural Analysis for Industrial Equipment(S22303)Fundamental Research Funds for the CentralUniversities(DUT22LK16,DUT21LK35)National Natural Science Foundation of China(12002071).
文摘Large deflection postbuckling responses of metamaterial cylindrical shells perforated by arrayed circular holes are investigated through a newly proposed theoretical model incorporating with finite element method and experiment.The triggering of an unusual pattern transformation under compressive load(that shows special hyperelastic metamaterial characteristics)contributes to the particularity of the postbucklingmodes,in which the axisymmetric waisted and non-axisymmetric postbuckling configurations of perforated cylindrical shells are identified.The transformations of postbucking modes are mainly affected by global outline sizes of the shell and local geometrical parameters of holes.The structural load-carrying capacity for the waisted postbuckling response suffers a sudden drop and recovers when the holes collapse.Comparatively,the shell would undergo a sustained fall off under non-axisymmetric postbuckling states.The negative Poisson’s ratio induced by pattern transformation plays a key role and a critical effective threshold value exists,inducing the waisted postbuckling mode.The revealed principles would be of benefit for achieving a controllable structural stability that is usually difficult to implement on those conventional structures.
文摘This paper deals with the problem of the postbuckling response of a thin cantilever beam ofnon-linear material, subjected to subtangential follower forces. Based on the well-knownBernoulli-Euler bending moment-curvature relation, the proposed problem is reduced to a specialeigenvalue problem of non-linear differential equation. An approximate solution is achieved byusing a simple and very effective technique, which leads to reliable results even in the case of verylarge deflections. The initial postbuckling path depending on the subtangential follower forces inequilibrium is then obtained. Moreover, the individual and coupling effect of the subtangential fol-lower force, the material non-linearity and the beam slenderness ratio on the initial postbucklingpath are also discussed in detail.
文摘In this paper, Dynamic Relaxation Method is applied to study the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading. The phenomenon that loading paths do not coincide with unloading paths has been found. Numerical results are given for cylindrically curved cross-ply panels subjected to uniform uniaxial compression under two types of boundary conditions. The influence of the number of layers, the panels curvature and the initial imperfection on the postbuckling paths is discussed.
文摘It is proved that the ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression is far higher than their buckling stress through the tests of 283 rectangular composite thin laminates in this paper. The ultimate strength of the composite thin plates is studied using large-deflection theory and small-deflection theory of thin plates. According to the failure criterion of the composites ultimate strength is found finally. It is in accordance with the experimental values for the plates having 45 degrees off-axial, and for longitudinal and latitudinal plates, when beta < 0.11, the theoretical values are higher. The coefficient C given in this paper may be referred to in product designing.
基金Project supported by the National Natural Science Foundation of China (No.10572049)
文摘Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.
文摘Buckling and postbuckling behaviors of perfect and imperfect, stringer and ortho/ropically stiffened cylindrical shells have been studied under axial compression. Based on the boundary la ver theory for the buckling oj thin elastic shells suggested in ref. [1], a theoretical analysis is presented. The effects of material properties of stiffenefs and skin, which are made of different materials, on the huckling load and postbuckling behavior of stiffened cylindrical shells have also been discussed.
文摘The buckling and postbuckling behaviors of perfect and imperfect antisymmetrically angle-ply laminated composite plates under uniaxial compression have been studied by perturbation technique which takes deflection as its perturbation parameter.In this paper, the effects of in-plane boundary conditions, angles, total number of layers and initial geometric imperfection on the postbuckling behavior of laminated plates have been discussed.
文摘Full-range analysis for the buckling and post buck ling at rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as its perturbation parameter.In this paper the effects of initial geometric imperfection on the postbuc kling behavior of plates have been discussed. It is seen that the effect of initial imperfection on the inelastic postbuckling oj plates is sensitive. By comparison, it is found that the theoretical results of this paper are in good agreement with experiments.
