Post-buckling Analysis Research Articles

Nonlinear thermomechanical buckling and postbuckling analysis of sandwich FG-GPLRC complexly curved caps and circular plates with porous core

Nonlinear thermomechanical buckling and postbuckling analysis of sandwich FG-GPLRC complexly curved caps and circular plates with porous core

A simple but accurate FEM for lateral-torsional buckling loads of mono-symmetric thin-walled beams considering pre-buckling effects

This study intends to present a simple but accurate FE buckling analysis procedure in order to determine lateral-torsional buckling (LTB) loads of mono-symmetric steel beams considering pre-buckling effects. For this, a nonlinear co-rotational FEM for lateral-torsional post-buckling of a thin-walled beam system with non-symmetric cross sections is summarized in which all displacement parameters are defined at centroid. After that, an iterative LTB analysis method is newly proposed with consideration of in-plane deformations due to external loads. Through numerical examples, it is demonstrated that buckling solutions by this method are very well matched with those by lateral post-buckling analysis of the steel beam with lateral imperfections. Finally, numerical results on LTB of simple/cantilever beams under conservative moments, simple beams under gradient moments, simple beams under eccentric compression, a cantilever beam with an un-symmetric channel section, and a cantilever right-angle frame with I-section are presented using conventional LTB, iterative LTB, and post-buckling analysis methods.

Weak form quadrature shell elements based on absolute nodal coordinate formulation

Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Locking problems of shell analysis are discussed. Nonlinear analysis of various shell structures is conducted. The joint constraint equations for shells with discontinuous slopes are established. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.

Nonlinear deflection and thermal post-buckling analysis of sector annular poroelastic composite nanodisks using mathematical simulation and machine learning algorithm

Nonlinear deflection and thermal post-buckling analysis of sector annular poroelastic composite nanodisks using mathematical simulation and machine learning algorithm

Analysis and experimental evaluation framework for buckling and post-buckling of composite stiffened panels

The composite thin-walled stiffened panel exhibits considerable potential for post-buckling bearing capacity. However, due to the limitations in post-buckling analysis and experimental evaluation capabilities, local buckling under limited loads is not permissible for current aircraft composite panels, significantly diminishing the weight reduction effect of composite panels. In this paper, experimental research on composite fuselage curved panels under combined compression and shear loads was conducted with an experimental system. The buckling analysis and failure prediction of composite fuselage curved panels were performed by the finite element method, using the interlaminar failure criterion and an improved Tsai-Wu failure criterion. Meanwhile, interaction formulaes were utilized to predict buckling correlation curves and failure envelopes. The results show that the finite element model with improved criteria and the rapid analysis method based on interaction formulaes exhibit high accuracy, which are available for properties analysis of composite panels. The experimental techniques and analytical methods proposed in this paper can provide a way to evaluate the buckling and post-buckling performance of composite stiffened panels.

Thermal and thermo-mechanical post-buckling analysis of GNP-reinforced composite laminated plates

This research utilizes isogeometric analysis (IGA) method to analyze buckling and post-buckling responses of composite laminated plates embedded with graphene nanoplatelets (GNPs) subjected to three-dimensional (3D) conduction of heat or combined 3D heat conduction and mechanical edge compression. A formulation to determine temperature profile produced by 3D conduction of heat in the GNP-reinforced laminate is established, and a new function with smooth transition form of GNP volume fraction across the thickness is presented for dictating the volume fraction of layer. Shear deformable quasi-3D theory with the von Kármán type nonlinearity which takes initial geometric deformation and thermal effect into consideration is employed to construct the nonlinear equilibrium states. Four types of GNP arrangements encompassing uniform, O, X and V shapes are considered. The IGA approach presented, through the benchmark test, is evidenced to estimate the thermal buckling temperature accurately and to successfully trace the thermal post-buckling path. Additional parametric study is carried out to scrutinize the thermal and the thermo-mechanical post-buckling features of the GNP-reinforced composite laminated plates, and the new findings are sure to be served as the benchmark solutions.

Linear and Post-Buckling Analysis of Biocompatible Polymer Microneedle for Transdermal Drug Delivery

To facilitate the delivery of drugs into the skin structure, microneedles play a pivotal role. Unlike conventional hypodermic syringes, microneedles penetrate only the dermis layer, avoiding nerve receptors and resulting in a painless injection. However, when a drug is administered into the skin, microneedles may undergo bending and buckling, leading to structural failure. Such failure can cause the drug to remain beneath the skin, potentially creating complications. Preventing the catastrophe of microneedle failure necessitates a close examination of parameters involved in the bending and buckling process. In this paper, we focus on buckling analysis, as the majority of microneedle failures are attributed to the buckling effect. We perform buckling analysis through finite element analysis to predict the critical buckling load (Pcr). This analysis helps determine the maximum load that a microneedle can withstand. We conduct this analysis using two modes: linear and non-linear (post-buckling analysis). By varying the tip diameter of the microneedle (20µm, 40µm, 60µm, 80µm, 100µm), we can identify the safe insertion load.

Nonlinear dynamic analyses of sandwich porous FG cylindrical shells with dual-layered FG porous cores

This research examines the nonlinear vibrations and dynamic postbuckling (DPB) analyses of sandwich porous functionally graded (SPFG) cylindrical shells with dual-layered FG porous (FGP) cores exposed to external excitation, using a semi-analytical method. The study investigates two types of FG layers: one with evenly distributed porosities (FG-EPD) and another with unevenly distributed porosities (FG-UEPD). It also studies the FGP cores in four configurations: one featuring symmetric porosity distribution with stiffening in the surface areas (SPD-Stiff), another with softening in the surface areas (SPD-Soft), a third with nonsymmetric porosity distribution (NSPD), and a fourth with uniform porosity distribution (UPD). Therefore, the SPFG cylindrical shells with dual-layered FGP cores with eight different configurations are investigated. Utilizing the classical shell theory (CST) alongside the geometrical nonlinearity in von Kármán–Donnell framework, and Galerkin’s method, this study addresses the nonlinear dynamic problem. An approximate solution for the deflection shape using three terms is selected, and the relationship between frequency and amplitude in nonlinear vibration is clearly defined. The nonlinear dynamic behaviors including vibration and DPB responses are examined using the P-T method, which is named for its use of the piecewise constant argument in conjunction with the Taylor series expansion. The critical dynamic buckling load of SPFG cylindrical shells with dual-layered FGP cores is investigated via the Budiansky–Roth criterion.

A novel approach for the optimum cross-section design of thin-walled box section beams subject to oblique bending based on both adequate-strength and local stability conditions

This study presents a new analytical procedure developed for the optimum cross-section design of the thin-walled box sections subject to oblique bending. The box sections designed in this study have been assumed to be achieved by hollowing out the rectangular solid sections at different subtraction ratios including arbitrary, optimum, and maximum. The optimum subtraction ratio has been determined based on the adequate-strength condition while the maximum subtraction ratio has been determined taking into account both adequate-strength and local buckling conditions. The optimal design of the box sections for the arbitrary subtraction ratio has been attained by minimizing the maximum normal stress, taking into account the adequate-strength condition. Conversely, the cross-sections of the box profiles for the optimum and maximum subtraction ratios have been optimized by minimizing their cross-section area, accounting for the defined combined strength condition involving adequate- strength and local stability requirements. An equivalent box section design model that allows checking the local stability of the box sections possessing dissimilar wall segment thicknesses has been developed to perform the local buckling control on the designed optimum box sections with unequal wall thicknesses. The new local stability conditions have been defined relying on this developed equivalent box section design model. The analytical results, validated through numerical predictions obtained from linear elastic local buckling and post-buckling analyses performed using Abaqus software, have shown that the optimally designed box section achieves substantial material savings per unit length compared to its corresponding equivalent box section.

Three-dimensional elastoplastic post-buckling analysis of functionally graded plates using a novel meshfree Tchebychev-radial point interpolation approach

This paper presents a three-dimensional (3D) analysis of the post-buckling behavior of functionally graded (FG) plates for the first time using an elastoplasticity-based meshfree formulation. A novel 3D Tchebychev-radial point interpolation approach, which combines radial basis functions with Tchebychev polynomials, is developed to solve the nonlinear post-buckling problem. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The governing equations are derived using the principle of virtual work by considering the 3D full Green–Lagrange strain components. The Newton–Raphson technique along with the arc-length method is used to determine post-buckling equilibrium paths of FG plates. The effective elastoplastic properties of the functionally graded material are assessed by exploiting the homogenization method, named Tamura–Tomota–Ozawa (TTO) model. It has been demonstrated that the accuracy of the solution is improved by incorporating Tchebychev polynomials into the radial point interpolation method (RPIM) shape function, and the stability and robustness of the results are independent of variations in the shape parameter. Furthermore, it is confirmed that TRPIM, with a slightly higher CPU time compared to RPIM, exhibits a higher convergence rate. The excellent agreement of the results with those existing in the literature shows that the proposed meshfree method can be used as a robust and accurate numerical tool to predict the elastoplastic post-buckling behavior of FG plates. Further numerical assessments indicate that post-buckling paths are significantly affected by factors such as geometric parameters, material gradient, loading ratio, and boundary conditions (BCs).

Fast analysis approach for instability problems of thin shells utilizing ANNs and a Bayesian regularization back-propagation algorithm

Abstract This research develops a data-driven methodology for structural instability problems with highly nonlinear, difficult, noisy, and small data. A fast analysis and prediction (FAP) approach for instability problems of thin shells is first proposed. This approach contains two phases: the fast numerical analysis and the pure prediction utilizing artificial neural networks (ANNs) incorporated with the Bayesian regularization (B-R) algorithm as follows: (1) in Phase 1 (the fast numerical analysis), post-buckling analysis is conducted utilizing a minor amount of load steps. The load–displacement relation achieved from Phase 1 is not exact because of the small number of load steps utilized; (2) in Phase 2 (the prediction), the loads and deflections achieved from Phase 1 were employed as the data for training ANNs. The trained networks, including the load and displacement networks, were employed to fast predict loads and deflections at any step of the post-buckling analysis. After utilizing Phase 2, a smooth, complete and exact load–displacement curve was achieved. In Phase 1, the available formulation for post-buckling analysis of thin shells in the literature was utilized. Five popular types of instabilities chosen to confirm the effectiveness and exactness of the FAP were snap-through, snap-back, softening–hardening, kink instabilities, and delamination buckling and post-buckling of composites. The high exactness and effectiveness of the FAP were confirmed in the numerical verification section. The present approach saves a huge computation compared to the other ones. It was found that ANNs incorporated with the B-R algorithm have notable advantages compared to numerous neural networks. The proposed approach is applicable to simulations or experiments where data are “expensive”, highly nonlinear, difficult, and limited. Utilizing the proposed approach for these fields can dramatically save time and money.

Wrinkle-free membranes through spatioselective exposure

The extreme flexibility-induced wrinkling significantly hampers the promising engineering applications of membranes, while the existing wrinkling-suppression approaches have challenges for area loss, weight increase and interfacial delamination. Here we propose a facile wrinkle-free technique that enables stiffness modulation through spatioselective ultraviolet (UV) exposure, regulates stress distribution to eliminate compressive stresses and achieves robust wrinkle-free membranes. A small-deformation theoretical model with the Marguerre function is implemented to evaluate the wrinkling capability of a stiffness-modulated membrane, the non-gradient particle swarm optimization (PSO) algorithm is performed to obtain the optimal material distribution, and the related robust wrinkle-free performance is verified through both finite-deformation post-buckling analyses and physical experiments. In addition, an empirical wrinkle-free solution is also given without the requirement of excessive optimization. This wrinkle-free approach, with neither area loss, weight increase nor interfacial delamination, provides useful guidance for the research on wrinkle-free membranes.

Post-buckling behaviour of corrugated-edge shells: Numerical insights

We provided the detailed buckling and post-buckling analysis of corrugated shallow spherical shells. Such shells are extensively used in civil and mechanical engineering. Here the main attention is paid to a corrugation as a key parameter affecting the instability. Three types of corrugation are introduced and discussed. The latter includes the following types: edge corrugated, half corrugated, and fully corrugated shells. Since the effect on instability is highly affected by the imperfections, a customised set of defects is proposed compared to a perfect structure. Several boundary conditions and load cases are analysed. An increase in the load multiplication factors highlights the effects of corrugation in shallow shells mechanics. Being inspired by the fascinating Nervi’s Flaminio dome in Rome, we introduce a novel way to improve the shells design against the instability effects.

A geometrically nonlinear Hellinger–Reissner shell element for the postbuckling analysis of variable stiffness composite laminate structures

Variable stiffness (VS) composite laminates provide larger freedom to design thin-walled structures than constant stiffness (CS) composite laminates. They showed to allow the redistributing of stresses, improving buckling and post-buckling performance and, therefore, reducing material weight and costs. This work extends a recently developed mixed shell element, MISS-4C, to the postbuckling analysis of VS composite laminate structures. MISS-4C has a linear elastic closed-form solution for the stress interpolation of symmetric composite materials. Its stress field interpolation is obtained by the minimum number of parameters, making it an isostatic element. Moreover, its kinematic is only assumed along its contour, leading to an efficient evaluation of all operators obtained through analytical integration along the element contour. MISS-4C uses a corotational approach within a fast multi-modal Koiter algorithm to efficiently obtain the initial post-buckling response of VS composite laminate structures.First, the element performance is investigated by analysing a carbon fibre VS composite laminate plate subjected to compressive stresses. Numerical results obtained with MISS-4C are compared with those obtained with the MISS-4 element, showing good accuracy and a high convergence rate. Subsequently, the structural response of a glass fibre VS composite laminate girder of a short-length bridge is optimised through a multi-objective optimisation that exploits the robustness of the MISS-4C element and the efficiency of the multi-modal Koiter algorithm.

Numerical and Experimental Analysis of Buckling and Post-Buckling Behaviour of TWCFS Lipped Channel Section Members Subjected to Eccentric Compression.

The paper presents a static analysis of the buckling and post-buckling state of thin-walled cold-formed steel (TWCFS) lipped channel section beam-columns subjected to eccentric compression. Eccentricity is taken into consideration relative to both major and minor principal axes. An analytical-numerical solution to the buckling and post-buckling problems is described. The solution is based on the theory of thin plates. Equations of equilibrium of section walls are derived from the principle of stationary energy. Then, to solve the problem, the finite difference (FDM) and Newton-Raphson methods are applied. Linear (buckling) and nonlinear (post-buckling) analyses are performed. As a result, pre- and post-buckling equilibrium paths are determined. Comparisons of the obtained numerical results, FE simulation results, and experimental test results are carried out and presented in comparative load-shortening diagrams. Additionally, a comparison of the buckling forces and buckling modes obtained from theoretical analysis and experiments is presented.

Isogeometric method for buckling prediction and post-buckling analysis of variable stiffness composite underwater pressure shell

Composite cylindrical pressure hulls are thin-walled structures widely used for autonomous underwater vehicles. Buckling failure is one of the most important failure modes for these shells under external pressure. In existing buckling studies of cylindrical pressure hulls, FEM is the most popular analysis method but not efficient enough when dealing with structures with complex material distributions such as the variable stiffness composite shells. Motivated by this, an isogeometric method for buckling prediction and post-buckling analysis of variable stiffness composite underwater pressure shell is proposed in this article. In this method, based on Reissner–Mindlin shell formulas undergoing large deformation, a buckling analysis framework in IGA forms is established. Then a modified arc-length method is proposed based on kinematics used in the shell formulas, and is used to overcome the inaccuracy caused by the 2 degrees of freedom node rotation in the prediction step of arc-length method. In addition, the influence of bifurcation is considered, which may seriously affect the precision of buckling behavior simulation when the limit point is close to a bifurcation point. The computational accuracy of this framework has been validated in a series of constant stiffness composite shell cases involving buckling load prediction and post-buckling behavior simulation. For variable stiffness composite hull cases, this framework achieves the same precision as FEM with fewer elements. Therefore, the proposed framework provides an efficient way for the buckling design of underwater variable stiffness composite pressure hulls.

Elastic Post-Buckling Analysis of Single-Layer Domes with Circular Plated Connections

Elastic Post-Buckling Analysis of Single-Layer Domes with Circular Plated Connections

Three-dimensional elastoplastic post-buckling analysis of porous FG plates resting on Winkler/Pasternak foundation using meshless RRKPM

This paper presents a three-dimensional (3D) analysis of the elastoplastic post-buckling behavior of porous functionally graded (FG) plates resting on Winkler/Pasternak foundations under uniaxial and biaxial in-plane loadings using an enhanced meshless approach. The principle of virtual work is used to derive the governing equations, and 3D nonlinear Green–Lagrange strains are considered. Plastic deformation is modeled employing the Prandtl–Reuss flow law and the isotropic hardening von Mises criterion. A novel meshless radial basis reproducing kernel particle approach is used to obtain the discretized system of equations. The Newton–Raphson method, coupled with the arc-length technique, is used to compute post-buckling paths of porous FG plates. Numerical assessments show that post-buckling paths are significantly influenced by porosity parameter, porosity distribution, foundation parameters, material gradient, plate thickness, loading ratio, and boundary conditions (BCs).

Virtual Full Scale Static Test of a Civil Tilt Rotor Composite Wing in Non-Linear Regime

This study addresses the crucial role of post-buckling behavior analysis in the structural design of composite aeronautical structures. Traditional engineering practices tend to result in oversized composite components, increasing structural weight. EASA AMC 20-29’s Building Block Approach suggests phased testing, but its time and cost challenges necessitate a shift to high-fidelity post-buckling analyses, exemplified by MSC NASTRAN SOL 400. This approach, showcased in the analysis of the Next Generation Civil Tilt Rotor Technology Demonstrator’s wing (NGTCTR-TD), effectively de-risks static tests, contributing to a more efficient certification process. The study demonstrates how advanced simulations provide detailed insights into local buckling phenomena, allowing precise stress distribution analysis. These analyses eliminate the risk of structural failure, paving the way for safer, more efficient, and cost-effective airframe structures. Future developments aim to validate numerical analyses with experimental data, further emphasizing the reliability and benefits of high-fidelity simulations.

Post-Buckling Analysis of Arch and Serpentine Structures Under End-to-End Compression

Abstract Arch and serpentine structures are two fundamental structural forms with significant applications in various fields. When subjected to compressive loading at both ends, these structures undergo flexural-torsional post-buckling, resulting in complex deformation modes that are challenging to describe using basic functions (e.g., trigonometric functions and polynomial functions), posing significant challenges in finding analytical solutions. In this study, we propose a novel approach to address this issue. By representing the lateral displacement with a trigonometric series expansion and utilizing the equilibrium equation, the angular displacement is expressed in terms of special functions known as Mathieu functions. Furthermore, the energy method is employed to obtain analytical solutions for the flexural-torsional post-buckling deformation components. The theoretical findings are validated through experiments and finite element analysis. Based on the theoretical results, explicit analytical expressions for the maximum principal strain and the bending-torsion ratio of the structures are derived, offering valuable insights for the design of arch and serpentine structures in practical applications.