Post-buckling Analysis Research Articles

Improved Finite Element Method for Inflated Beams with Local Wrinkles

An improved finite element method is proposed for inflatable beams with a global finite deformation and a local wrinkling behavior, based on the corotational approach and tension field theory. The finite deformation is decomposed into a rigid-body displacement in the global coordinate system and a small strain measured in the local coordinate system, by using the corotational approach. The tangent stiffness matrix of a three-node triangular membrane element is presented. With the modified bimodulus constitutive law, a wrinkling model is constructed for determination of the status of element (tension, wrinkled, or slack). To improve the rate of convergence, a consistent tangent material stiffness matrix is embedded into the local coordinate system. Numerical results are in good agreement with the existing experimental data. In some case, the proposed method can obtain more accurate deflection of inflatable beams than the postbuckling analysis of thin shells. A quadratic rate of convergence is observed for the proposed method, and thus the computational efficiency is improved greatly. The limitation of the method is also discussed.

Thermo-mechanical postbuckling analysis of sandwich cylindrical panels with functionally graded auxetic GRMMC core supported by elastic foundations

Modelling and analysis of compressive and thermal postbuckling of sandwich cylindrical panels supported by an elastic foundation are presented in this paper. The sandwich cylindrical panel is composed of auxetic graphene-reinforced metal matrix composite (GRMMC) core with negative Poisson's ratio (NPR) and two metal face sheets. Two cases of the compressive postbuckling of auxetic sandwich cylindrical panels under axial compression in thermal environments and the thermal postbuckling of auxetic sandwich cylindrical panels caused by uniform temperature rise are considered. In the GRMMC core, the volume fraction of graphene through the thickness domain is arranged as a piece-wise functionally graded (FG) pattern. The material properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The governing equations of the auxetic sandwich cylindrical panels are formulated based on the framework of the Reddy's third order shear deformation theory. The von Kármán-type kinematic nonlinearity, the thermal effect, the panel-foundation interaction and the initial geometric imperfection of the panel are also taken into account. The postbuckling solutions are obtained by employing a singular perturbation technique along with a two-step perturbation approach. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness on the postbuckling behavior of sandwich cylindrical panels with FG auxetic GRMMC core are studied in detail.

Simulation analysis method of expandable and flexible sensor networks based on the flexible printed circuit process

Aircraft structural health monitoring (SHM) technology is a revolutionary technology based on sensor networks, which has the advantages of ensuring flight safety, extending structural life, and reducing maintenance costs. Due to the large size of aircraft structures and large deformation of morphing wings, the sensor networks integrated into the aircraft structures should be large-area, expandable, and flexible. Island-interconnect structure design in flexible electronics is expected to realize such sensor networks, with the help of large-area and low-cost flexible printed circuit (FPC) process. Mechanical analysis can guide the design of island-interconnect sensor networks. However, few studies have been reported to analyze the mechanical properties of whole island-interconnect sensor networks. This paper proposes a simulation analysis method based on the finite element method for the mechanical analysis of expandable and flexible sensor networks. This method mainly includes two parts: extracting the buckling modes through linear buckling analysis and obtaining the deformation states and mechanical properties through postbuckling behavior analysis. It is applied on the mechanical analysis of island-interconnect sensor networks with different geometry designs, including serpentine, fractal, and irregular island-interconnect sensor networks. Tensile experiments of island-interconnect sensor networks manufactured by the FPC process show that the deformation of experimental results is basically consistent with that of simulation results. In conclusion, the proposed simulation analysis method is appliable for the mechanical analysis of serpentine, fractal, and irregular island-interconnect structure networks, guiding the structural design of expandable and flexible sensor networks for large-area SHM of aircraft.

An efficient method for postbuckling optimization of composite laminated plates with holes under compression and shear loading

Laminated composite plates with hole are commonly used in aeronautic and aerospace structure design, subjecting to the in-plane compression and shear loading. The existing of hole reduces both the in-plane and out-of-plane stiffness and influences the postbuckling behavior of the plate. The structural lightweight design can be further explored when the external load is allowed entering into the postbuckling regime. However, the lamination optimizations to maximize the postbuckling stiffness have high computational burden when the standard nonlinear finite element method is applied in each function call for postbuckling analysis. Thus, we propose a reduced-order modeling method based on the improved Koiter perturbation theory for buckling and postbuckling analysis. The low-scale reduced order model, instead of the full-scale FE model, is constructed and solved to obtain the initial postbuckling response. The postbuckling stiffness is defined to be the slope of the load-end shortening relation curve at the bifurcation point. A multi-start searching strategy based on the gradient-based algorithm is developed to maximize the postbuckling stiffness, efficiently and accurately. Laminated composite plates with different hole sizes, loading conditions and ply numbers, are considered to validate the excellent performance of proposed method.

Semi-analytical and numerical post-buckling analysis of nanobeam using two-phase nonlocal integral models

Semi-analytical and numerical post-buckling analysis of nanobeam using two-phase nonlocal integral models

The reformulated Koiter–Newton method for thermal–mechanical buckling and postbuckling analysis of thin‐walled structures

AbstractThe reduced‐order modeling method, termed as the Koiter–Newton method, is reformulated to be applicable for geometrically nonlinear thermal–mechanical analysis of thin‐walled structures. The thermal load is treated as the independently unchanged load corresponding to the initial temperature field. The internal force space is expanded using the mechanical load, the thermal load, and the predefined perturbation loads. The thermal–mechanical reduced‐order model is constructed using the first to fourth‐order derivatives of strain energy with thermal effects in terms of the degrees of freedom (DOFs). An additional DOF related to the thermal load appears in the construction of reduced‐order model based on the novel Koiter theory. The path‐following scheme is proposed to make the method able to trace the entire geometrically nonlinear thermoelastic response. A much larger step size can be achieved benefiting from the favorable prediction of the reduced‐order model, compared to the classical Newton‐like methods. Both the temperature‐independent and temperature‐dependent material properties are considered. The thermal–mechanical buckling and postbuckling behaviors obtained by the proposed method are validated and discussed using various numerical examples.

Postbuckling Analysis of Ultra-Low Rigidity Serpentine Structures

Abstract Serpentine structures are of growing interest due to its unique mechanical and physical properties for applications in stretchable electronics, mechanical sensing, and biomedical devices. Mechanics-guided, deterministic three-dimensional (3D) assembly provides routes to form remarkable 3D structures, which in turn significantly improve its potential for applications. Therefore, an accurate postbuckling analysis is essential to the complex 3D serpentine structures with arbitrary geometry/material parameters. Here, simple, analytical expressions are obtained for the displacement and effective rigidity of serpentine structures during postbuckling. By tuning geometry parameters, the amplitude of assembled 3D serpentine structures can span a very broad range from zero to that of a straight ribbon. The analytical model can be used in design, fabrication, and application of versatile 3D serpentine structures to ensure their compatibility with the ultra-low rigidity biological tissues. A hierarchical 3D serpentine structure with ultra-low rigidity is presented to demonstrate the application of the analytical model.

Nonlinear static simulation for thermal post-buckling analysis of composite annular system coupled with shape memory alloy fibers

The provided research deals with a mathematical formulation to achieve nonlinear statics for the sandwich annular structure’s thermal post-buckling behavior. The structure’s core is filled by graphene nanoplatelets (GPLs), while its face sheets have been made of SMA/graphite/epoxy. The first-order shear deformation (FOSD) model has been employed for modeling face sheets, and quasi-3D hybrid and quadratic kind of higher-order shear deformation (Q-3D-HSD) model is supposed for core’s in-plane transverse and displacements, respectively. The boundary conditions (BCs) and nonlinear governing equations have been modeled by employing the Hamiltonian, and they have been solved applying the generalized differential quadrature (GDQ) approach. The direct-iterative method has been provided for solving the set of equations, including highly nonlinear factors. Ultimately, the outcomes reveal that the radius ratio of outer to the inner, SMA fiber, GPLs’ configurational factors, and large amplitude would play a vital role in the annular sandwich structure’s thermal post-buckling response. Moreover, the system with GPL-O distribution pattern has maximum thermal post-buckling load while GPL-X type of distribution would result in the minimum thermal post-buckling to thermal buckling ratio for the annular structure.

Post-buckling analysis of GPLs reinforced porous cylindrical shells under axial compression and hydrostatic pressure

Research works on post-buckling of cylindrical shells under combined loads are usually presented with insufficient accuracy. It is mainly related to the inherent complexity compared to the case subjected to a single load, particularly when the problem is investigated based on the moderately thick shell theory. In the present study, post-buckling analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) porous cylindrical shells under the action of axial compression and hydrostatic pressure is performed. The main aim is to obtain reasonably accurate post-buckling characteristic quantities of the problem at hand for a wide range of thicknesses. For this purpose, elaborately constructed boundary conditions, complete post-buckling deformation modes, and a unified shell theory, which is efficient and suitable for extremely thin and moderately thick structures, are carefully taken into account. The solutions based on the symmetric and asymmetric post-buckling modes are established by combining an analytical procedure and the Galerkin’s method. The obtained results from the present solutions agree well with those of existing theoretical and experimentally observed data. The effects of the geometry and the material properties on the post-buckling behavior and knockdown factor (KDF) of the FG-GPLRC porous cylindrical shell are explored. The discrepancies between the results of the classical thin-walled shell theory and those of the moderately thick shell theory are then explained and discussed in detail.

Thermo-mechanical postbuckling analysis of sandwich cylindrical shells with functionally graded auxetic GRMMC core surrounded by an elastic medium

In this paper, modeling and analysis of postbuckling of sandwich cylindrical shells surrounded by an elastic medium are presented. The sandwich cylindrical shells consist of two metal face sheets and auxetic graphene-reinforced metal matrix composite (GRMMC) core with in-plane negative Poisson’s ratio (NPR). Two cases of the compressive postbuckling of sandwich cylindrical shells under axial compression in thermal environments and the thermal postbuckling of sandwich cylindrical shells caused by a uniform temperature rise are considered. Each ply of auxetic GRMMC core possesses in-plane NPR and can have different graphene volume fraction to achieve a piece-wise functionally graded (FG) distribution through the thickness domain of the core. The thermo-mechanical properties of both metal face sheets and the GRMMC core are temperature dependent. The governing equations are formulated based on the Reddy’s third order shear deformation shell theory coupled with von Kármán kinematic nonlinearity. The shell-foundation interaction and the thermal effects are considered in the modeling. Applying a singular perturbation technique in conjunction with a two-step perturbation approach, we obtain the postbuckling solutions for perfect and imperfect sandwich cylindrical shells. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and the foundation stiffness on the postbuckling behaviors of sandwich cylindrical shells with auxetic GRMMC core are studied in detail.

Transversally loaded stainless steel beams under fire: Local/global behaviour, strength and design

This paper presents and discusses the results of a numerical investigation concerning the post-buckling behaviour, strength and design of stainless steel I-section beams prone to local or global (lateral-torsional) buckling under elevated temperatures. Non-linear shell finite element models are employed to assess the structural response and failure loads of I-beams (i) subjected to distinct loading conditions, namely uniform bending, uniform transverse loading, 3 and 4-point bending (the transverse loadings are applied along either the shear centre, top flange-web or bottom flange-web longitudinal axes), (ii) made from three common stainless steel grades (ferritic 1.4003, austenitic 1.4301 and duplex 1.4462), (iii) subjected to eight temperatures (θ = 100 to 800 °C), and (iv) covering wide local and global slenderness ranges. Special attention is paid to the influence of the transverse loading location (load height effect), a topic lacking research in the context of local buckling, by means of (i) Generalised Beam Theory (GBT) buckling and (ii) ABAQUS shell finite element post-buckling analyses. The last part of the paper is devoted to design considerations, based on the numerical failure loads obtained and involving the assessment of the current Eurocode 3 design rules for stainless steel beams failing in local and global modes.

Post-buckling analysis of two-layer contact concentric tubular strings in pipe

Buckling of concentric tubular strings in pipe is an essential problem in the fields of medical, biological, and nanomaterials, especially in petroleum engineering. Completely different from the buckling of the classic Euler compression columns, the buckling of concentric tubular strings involves geometric nonlinearity and contact nonlinearity, and has more complicated geometric deformations and buckling configurations. In this paper, a finite element method combining the spatial beam element and the two-layer contact gap element is proposed, and a virtual transient dynamic method is introduced to solve the static buckling of concentric tubular strings. The internal concentric tubular strings are discretized into spatial beam elements, and the contact relationships between tubular strings are described by two-layer contact gap element. Meanwhile, the larger damping is used to attenuate the dynamic response of the system, so as to find the static part of the transient dynamic solution. Appropriate damping and element length are determined by numerical simulation. The structural characteristics and contact states of eight post-buckling configurations are studied. The helix pitch values of specific configurations are in good agreement with the theoretical solutions. In addition, the distribution of bending moment, shear force and contact force in various post-buckling configurations is studied. For the full helical buckling, it is found that there is only one non-contact section in the transition section of inner tube and two non-contact sections in the transition section of middle tube. The research results of this paper provide a theoretical basis and reference for further study on the buckling of multi-layer concentric tubular strings.

A couple-stress-based moving Kriging meshfree shell model for axial postbuckling analysis of random checkerboard composite cylindrical microshells

The current investigation intends to devise a couple stress continuum-based moving Kriging meshfree shell model for axial nonlinear buckling and postbuckling responses of random checkerboard composite cylindrical microshells. Accordingly, the graphene nanoplatelet reinforcements are supposed to be randomly dispersed based upon a checkerboard scheme within the resin matrix, the effective material properties of which are estimated based upon a probabilistic method. The modified couple stress continuum elasticity is implemented into the higher-order shear deformation shell theory incorporating geometrical nonlinearity. The established microstructural-dependent shell model is then numerically analyzed via the moving Kriging meshfree technique with the ability to take the essential boundary conditions into account accurately by employing proper moving Kriging shape function. By tracing the postbuckling paths, the snap-through phenomenon is observed. It is found that for a higher graphene nanoplatelet volume fraction, the significance of the stiffening character associated with the rotation gradient tensor increases. Furthermore, for a specific value of graphene nanoplatelet volume fraction, by reducing the length to width aspect ratio of graphene nanoplatelet reinforcements, the role of couple stress size dependency in the critical buckling load and critical shortening of an axially compressed cylindrical microshell becomes more important.

Buckling Knockdown Factors of Composite Cylinders under Both Compression and Internal Pressure

The internal pressure of a thin-walled cylindrical structure under axial compression may improve the buckling stability by relieving loads and reducing initial imperfections. In this study, the effect of internal pressure on the buckling knockdown factor is investigated for axially compressed thin-walled composite cylinders with different shell thickness ratios and slenderness ratios. Various shell thickness ratios and slenderness ratios are considered when the buckling knockdown factor is derived for the thin-walled composite cylinders under both axial compression and internal pressure. Nonlinear post-buckling analyses are conducted using the nonlinear finite element analysis program, ABAQUS. The single perturbation load approach is used to represent the geometric initial imperfection of thin-walled composite cylinders. For cases with the axial compressive force only, the buckling knockdown factor decreases as the shell thickness ratio increases or as the slenderness ratio increases. When the internal pressure is considered simultaneously with the axial compressive force, the buckling knockdown factor decreases as the slenderness ratio increases but increases as the shell thickness ratio increases. The buckling knockdown factors considering the internal pressure and axial compressions are higher by 2.67% to 38.98% compared with the knockdown factors considering the axial compressive force only. The results show the significant effect of the internal pressure, particularly for thinner composite cylinders, and that the buckling knockdown factors may be enhanced for all the shell thickness ratios and slenderness ratios considered in this study when the internal pressure is applied to the cylinder.

Thermal post-buckling analyses of magneto-electro-elastic laminated beams via generalized differential quadrature method

The present paper is concerned with the thermal post-buckling behaviors of magneto-electro-elastic laminated beams. Timoshenko beam theory accompanying the von Kármán geometric nonlinearity is considered to model the beams. Temperature and magneto-electric fields are obtained based on satisfying the interfacial continuity conditions and corresponding boundary conditions, and then introduced into the stress-strain constitutive relationships. Afterwards, three governing equations of motion are established with respect to the generalized kinematical variables according to Hamilton's principle, and solved by the generalized differential quadrature method and pseudo-arc length continuation technique. The numerical results aim at the studies on thermal post-buckling paths, post-buckling vibration characteristics and magneto-electric potential responses, the effects on which the lay-up modes, thermal load types and magneto-electric fields exert are discussed.

Thermal postbuckling analysis of sandwich beams with functionally graded auxetic GRMMC core on elastic foundations

This article deals with thermal postbuckling of sandwich beams caused by uniform temperature rise and resting on elastic foundations. The sandwich beam is composed of auxetic graphene-reinforced metal matrix composite (GRMMC) core with negative Poisson's ratio (NPR) and two metal face sheets. The volume fraction of graphene through the thickness domain of the GRMMC core is arranged as a functionally graded (FG) pattern. The thermo-mechanical properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The governing equations of the auxetic sandwich beam are formulated based on the higher order shear deformation beam theory coupled with von Kármán-type kinematic nonlinearity. The thermal effects and the beam-foundation interaction are also taken into account in the modeling. Thermal postbuckling solutions are obtained by employing a two-step perturbation approach. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness on thermal postbuckling behavior of sandwich beams with FG auxetic GRMMC core are studied in detail.

Study on the Effect of Geometrical Parameters of a Hexagonal Trigger on Energy Absorber Performance Using ANN.

Thin-walled structures are commonly used as energy absorbers in motor vehicles. Their function is to protect the structural components of vehicles and to absorb energy completely during collisions up to 20 km/h. This paper focuses on maintaining crush axiality during research. To verify the numerical analyses, physical specimens were made and then subjected to dynamic crushing. Force and shortening values as well as high-speed camera images were used for data analysis. Through time-lapse shots, plastic deformation within the crush initiator was observed. Such detailed analysis allowed the determination of the influence of hexagonal triggers in the form of notches on the post-buckling progressive analysis. In this paper, neural networks were used to examine the importance of each variable. Data from numerical analyses were used for this purpose. Based on the analyses performed, the effects of both the width and height of the triggers on the crush load efficiency (CLE) and total efficiency (TE) ratios can be seen. The width of the crush initiator has the greatest influence on Crash-box performance. Nevertheless, increasing both the height and the width of the initiator can result in crush non-axiality and underperformance of the energy absorber.

Thermo-mechanical postbuckling analysis of sandwich plates with functionally graded auxetic GRMMC core on elastic foundations

This paper investigates the thermo-mechanical postbuckling behaviors of sandwich plates with auxetic graphene-reinforced metal matrix composite (GRMMC) core resting on elastic foundations. Two cases of the compressive postbuckling of sandwich plates subjected to uni-axial compression in thermal environments and the thermal postbuckling of sandwich plates subjected to a uniform temperature rise are considered. The auxetic GRMMC core having negative Poisson's ratio (NPR) is assumed to be piece-wise functionally graded (FG) by changing the volume fraction of graphene through the thickness domain of the core. The material properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The Reddy’s third order shear deformation plate theory and the von Kármán-type kinematic nonlinearity are used to formulated the governing equations of the sandwich plate which account for the plate-foundation interaction and the thermal effects. The postbuckling solutions are obtained by employing a two-step perturbation approach. The results reveal that the compressive postbuckling and thermal postbuckling behaviors of sandwich plates with auxetic GRMMC core are significantly influenced by the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness.

Thermal post-buckling analysis of graded sandwich curved structures under variable thermal loadings

Thermal post-buckling analysis of graded sandwich curved structures under variable thermal loadings

An analogy between analytical, approximate and numerical methods in nonlinear buckling of functionally graded columns

Purpose The purpose of this study is to investigate the post-buckling analysis of functionally graded columns by using three analytical, approximate and numerical methods. A pre-defined function as an initial assumption for the post-buckling path is introduced to solve the differential equation. The finite difference method is used to approximate the lateral deflection of the column based on the differential equation. Moreover, the finite element method is used to derive the tangent stiffness matrix of the column. Design/methodology/approach The non-linear buckling analysis of functionally graded materials is carried out by using three analytical, finite difference and finite element methods. The elastic deformation and Euler-Bernoulli beam theory are considered to establish the constitutive and kinematics relations, respectively. The governing differential equation of the post-buckling problem is derived through the energy method and the calculus variation. Findings An incremental iterative solution and the perturbation of the displacement vector at the critical buckling point are performed to determine the post-buckling path. The convergence of the finite element results and the effects of geometric and material characteristics on the post-buckling path are investigated. Originality/value The key point of the research is to compare three methods and to detect error sources by considering the derivation process of relations. This comparison shows that a non-incremental solution in the analytical and finite difference methods and an initial assumption in the analytical method lead to an error in results. However, the post-buckling path in the finite element method is traced by the updated tangent stiffness matrix in each load step without any initial limitation.