Search Results (116)

The main purposes of the present paper are to present the mathematical and algorithmic aspects of the ANM/FEM numerical model and to show how it is applied to analyze elastic and thermo-elastic nonlinear solid mechanical problems. ANM is a robust continuation method based on a perturbation technique for solving nonlinear problems dependent on a loading parameter. Historically, this technique has been successfully applied to problems in various fields of solid and fluid mechanics. This paper shows how ANM is used to solve nonlinear elastic and nonlinear thermo-elastic problems involving elastic behavior and geometrical nonlinearities. The implementation of ANM for FEM in the FreeFEM++ language is then presented. The FEM software development platform, called FreeFEM++, is structured to work with variational formulations and, therefore, is well adapted to implement ANM for instability problems in solid mechanics. In order to illustrate the great efficiency of FreeFEM++, scripts will be presented for computing the different steps of ANM continuation for solid elastic structures, considering simple geometries subjected to conservative loading. For the purpose of validation, the problem of a cantilever subjected to an applied force is presented. Next, the new numerical model is applied to study wrinkles appearing in a planar film/substrate system that is subjected to compressive surface forces at the lateral faces of the film. Finally, the model is applied to a spherical film/substrate system subjected to thermo-elastic shrinkage. In both cases, the ANM/FEM prediction method, together with a Newton–Riks correction (if needed), identifies the equilibrium paths efficiently, especially after the post-buckling regime. Full article

Composite materials have gained prominence in aerospace engineering due to their high strength-to-weight and stiffness-to-weight ratios. However, their susceptibility to interlaminar damage, particularly delamination, remains a significant concern, especially under compressive loads. This study presents a detailed numerical investigation into the buckling behavior and delamination propagation in flat and curved composite panels with centrally located circular delaminations. Four configurations were analyzed, differing by geometry (flat vs. curved) and delamination interface. The critical buckling load was first estimated through linear eigenvalue analysis, while post-buckling behavior and damage progression were studied using a nonlinear static analysis enhanced by the Smart-time XB (SMXB) tool. Numerical results, including out-of-plane displacements and delamination length evolution, were validated against experimental data from the literature. The findings confirm the accuracy of the adopted FEM approach and highlight the beneficial role of curvature in increasing buckling resistance and improving damage tolerance, offering valuable insights for the design of aerospace composite structures. Full article

This work aims to investigate the buckling and post-buckling behaviour of wood-based sandwich structures with and without a manufacturing defect, under compressive loading. The specimens were made by gluing birch veneers to a balsa wood core. The defect consisted of a central zone where glue was lacking between the skin and the core. A compression load was applied to the plate using the VERTEX test rig, with the plate placed on the upper surface of a rectangular box and bolted at its borders. The upper surface of the plate was monitored using optical and infrared cameras. The stereo digital image correlation method was used to capture the in-plane and out-of-plane deformations of the specimen, and to calculate the strains and stresses. The infrared camera enabled the failure scenario to be identified. The buckling behaviour of pristine specimens showed small local debonding in the post-buckling range, which was not detrimental to overall performance. In the presence of a manufacturing defect, the decrease in buckling load was only about 15%, but final failure occurred at lower compressive loads. Full article

Functionally graded materials (FGMs) have the potential to revolutionize the oil and gas transportation sector, due to their increased strengths and efficiencies as pipelines. Conventional pipelines frequently face serious problems such as extreme weather, pressure changes, corrosion, and stress-induced pipe bursts. By analyzing the mechanical and thermal performance of FGM-based pipes under various operating conditions, this study investigates the possibility of using them as a more reliable substitute. In the current study, the post-buckling and nonlinear vibration behaviors of pipes composed of FGMs transporting heavy crude oil were examined using a Timoshenko beam framework. The material properties of the FGM pipe were observed to change gradually across the thickness, following a power-law distribution, and were influenced by temperature variations. In this regard, two types of FGM pipes are considered: one with a metal-rich inner surface and ceramic-rich outer surface, and the other with a reverse configuration featuring metal on the outside and ceramic on the inside. The nonlinear governing equations (NGEs) describing the system’s nonlinear dynamic response were formulated by considering nonlinear strain terms through the von Kármán assumptions and employing Hamilton’s principle. These equations were then discretized using Galerkin’s method to facilitate the analytical investigation. The Runge–Kutta method was employed to address the nonlinear vibration problem. It is concluded that, compared with pipelines made from conventional materials, those constructed with FGMs exhibit enhanced thermal resistance and improved mechanical strength. Full article

The fuselage serves as the primary component of commercial aircraft. The strength reliability of fuselage panels is therefore crucial for commercial aircraft. In the present study, a finite element (FE)-based modeling approach has been developed to predict the post-buckling behavior of curved fuselage panels under combined axial compression and in-plane shear loads at different shear-to-compression ratios. The intra-laminar damage was replicated using a progressive damage model driven by the Hashin’s failure criteria, while the skin−stiffener debonding was modeled using the cohesive zone model. Failure tests were performed using a bespoke Fuselage Panel Test System (FPTS), enabling comparison between experiments and simulations. The predicted buckling loads and ultimate failure loads are in good agreement with those obtained from experiments, which verify the predictive capability of the FE model. The failure load of the panels was found to be at least 30% higher than the initial buckling loads for all loading cases, indicating significant post-buckling load-carrying capacity. Under these four loading conditions studied, the load transfer mechanisms of curved panels were examined. All specimens experienced local skin buckling and subsequent global buckling, resulting in skin−stiffener debonding followed by fracture of the stiffeners, which was the dominant failure mechanism for the panel studied. Full article

Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field effect. CNTs dispersion across the shell thickness follows a power law, with five distribution types developed. The modified couple stress theory is applied to incorporate the small-size effect using a single material parameter. Furthermore, the Knudsen number is used to address the small-size effect on the microfluid. The external force between the magnetic fluid and microshell is modeled by applying the Navier–Stokes equation depending on the fluid velocity. Nonlinear motion equations of the present model are derived using Hamilton’s principle, containing the Lorentz magnetic force. According to the Galerkin method, the equations of motion are transformed into an algebraic system to be solved, determining the post-buckling paths. Numerical results indicate that the presence of the magnetic field, CNT reinforcement, and fluid flow improves the load-bearing performance of the cylindrical microshells. Also, many new parametric effects on the post-buckling curves of the FG-CNT microshells have been discovered, including the shell geometry, magnetic field direction, length scale parameter, Knudsen number, and CNT distribution types. Full article

Stiffened panels are extensively used in aerospace applications, particularly in wing and fuselage sections, due to their favorable strength-to-weight ratio under in-plane loading conditions. This research employs the commercial finite element software Ansys-19 to analysis the critical buckling and ultimate collapse load of an aluminum stiffened panel having a dimension of 1244 mm (Length) × 957 mm (width) × 3.5 mm (thickness), with three stiffener blades located 280 mm away from each other. Both the critical buckling load and post-buckling ultimate failure load of the panel are validated against the experimental data found in the available literature, where the edges towards the length are clamped and simply supported, and the other two edges are free. For nonlinear buckling analysis, a plasticity power law is adopted with a small geometric imperfection of 0.4% at the middle of the panel. After the numerical validation, the investigation is further carried out considering four different lateral pressures, specifically 0.013 MPa, 0.065 MPa, 0.085 MPa, and 0.13 MPa, along with the compressive loading boundary conditions. It was found that even though the pressure application of 0.013 MPa did not significantly impact the critical buckling load of the panel, the ultimate collapse load was reduced by 18.5%. In general, the ultimate collapse load of the panel was severely affected by the presence of lateral pressure while edge compressing. Three opening shapes—namely, square, circular, and rectangular/hemispherical—were also investigated to understand the behavior of the panel with openings. It was found that the openings significantly affected the critical buckling load and ultimate collapse load of the stiffened panel, with the lateral pressure also contributing to this effect. Finally, in critical areas with higher lateral pressure load, a titanium panel can be a good alternative to the aluminum panel since it can provide almost twice to thrice better buckling stability and ultimate collapse load to the panels with a weight nearly 1.6 times higher than aluminum. These findings highlight the significance of precision manufacturing, particularly in improving and optimizing the structural efficiency of stiffened panels in aerospace industries. Full article

Corrosion in steel girder ends, progressing from localized thinning of the web and the lower flange to severe perforation in severe cases, can significantly affect structural integrity. This study evaluates the effects of severe corrosion, including web–lower flange disconnection and transverse flange perforation combined with web damage, on the residual shear strength of steel girder end web panels through experimental and numerical methods. Results indicate that when only the web is affected, post-buckling strength starts to decline by corrosion damaging the plastic hinge on the tension flange, disrupting the tension field action. Conversely, in cases involving simultaneous web and lower flange damage, localized yielding at fracture points near the flange damage leads to the abrupt rotation of the tension field inclination angle, causing an earlier and more pronounced decline in post-buckling strength compared to web-only damage scenarios. Full article

Shapes and topologies of lattice materials have been extensively studied, yet very few studies have dealt with shapes inspired by ancient mathematicians, such as the Platonic solids discovered by Plato in 360 BC or the mathematical behavior of the unexplored “semi-regular” solids of Pacioli (1445–1517). Using the finite element analysis method, the buckling and post-buckling behavior of Platonic and Paciolian cells subjected to a compressive load were analyzed. In these solids, the energy absorbed per unit mass is an increasing function with the number of faces, similar to porosity, which reaches a maximum value for solids comprised of 90–100 surfaces. Full article

An asymptotic analytical method is proposed to study the thermal post-buckling behaviors of fiber-reinforced composite (FRC)-laminated beams with geometric imperfections employing a modified zig-zag beam model. The beam model satisfied the discontinuity of the shear deformation at the interlayer interfaces and the stress boundary conditions on the upper and lower surfaces. Each imperfection was assumed to possess the same shape as the buckling mode, and the in-plane boundary conditions were presumed to be immovable. A two-step perturbation method was used to solve the nonlinear governing equations and obtain the equilibrium path. Subsequently, the initial defect sensitivity of the post-buckling behaviors was analyzed. The existence of the bifurcation-type equilibrium path for perfect beams is discussed in depth. Load–deflection curves for beams with various boundary conditions and ply modes were plotted to illustrate these findings. The effects of the slenderness ratio, elastic modulus ratio, thermal expansion coefficient ratio, ply modes, and supported boundaries on the buckling and post-buckling behaviors were also investigated. The numerical results indicate that the slenderness ratio significantly influences the critical buckling temperature, with thicker beams exhibiting higher buckling resistance. The elastic modulus ratio also plays a crucial role, with higher ratios leading to increased buckling strength. Additionally, the thermal expansion coefficient ratio affects the post-buckling load-bearing capacity, with lower ratios resulting in greater stability. Full article

The corner element is the most basic constitutive element of multi-cellular thin-walled structures; however, scenarios for using relevant theories are limited. To improve this situation, this research investigated the effect of boundary conditions on the compression performance of corner elements with different angles. The deformation laws of corner elements were also explored. The approach was based on experiments and the finite element method. The result shows the outwardly extending plates on both sides yield first, the central twisted wire region then destabilizes and exits the working state, and the plate enters the post-buckling phase. A more relaxed boundary and larger angle can make it easier for the corner elements to trigger the symmetric deformation mode. Moreover, a mechanical model for simplified computation is proposed to predict the initial peak crushing force. The research can provide a reference for studying the compression performance of energy-absorbing elements in engineering. Full article

Based on the first-order shear deformation theory (FSDT) and moving least-squares approximation (MLS), a new meshfree method that considers the effects of geometric nonlinearity and the pre- and post-buckling behaviors of curved beams is proposed. An incremental equilibrium equation is established with the Updated Lagrangian (UL) formulation under the von Karman deflection theory. The proposed method is applied to several numerical examples, and the results are compared with those from previous studies to demonstrate its convergence and accuracy. The pre- and post-buckling behaviors of the curved beam with different parameters, such as vector span ratios, bending forms, inclusion angles, boundary conditions, slenderness ratios, and axial shear stiffness ratios, are also investigated. The effects of the parameters on the buckling response are demonstrated. The proposed method can be extended to the study of double nonlinearities of curved beams in the future. This extension will provide a more scientific reference basis for the structural selection of curved girder structures in practical engineering. Full article

Steel jacking pipes are potentially prone to buckling instability, a phenomenon that has received limited attention in hard rock formations. This study reports on the field monitoring of a water pipeline project in Zhongshan City, where the circumferential and hoop strains of steel pipe segments jacked in hard rocks were recorded. The buckling deformation observed during steel pipe jacking, as well as the critical buckling load, was analyzed with the aid of numerical simulations using finite element software. The initial defect for the post-buckling analysis of the steel pipe was selected as the first-order buckling mode. Field monitoring revealed that the loading conditions experienced by the steel pipe segments during the jacking process are complex, leading to significant deformation. Throughout the monitoring process, axial stress at each measurement point underwent tensile-compressive transitions. Numerical results showed the actual critical buckling load increases with wall thickness at a constant length-to-diameter ratio, which is significant for short pipes. For pipes with the same wall thickness and outer diameter, the actual critical buckling load of long pipes is significantly lower than that of short pipes. Additionally, initial defects were found to significantly reduce the actual critical buckling load of the steel pipe. Furthermore, the actual critical buckling load of long pipes is much lower than their yield load, whereas, for short pipes, the critical buckling load is limited by their yield load. Measures for managing buckling deformation of steel pipes in situ were also reported. The findings on critical buckling load and the countermeasures for managing buckling in situ would be valuable for the design and construction stages of similar projects employing pipe-jacking technology in hard rock formations. Full article

Delamination is a common type of damage in composite laminates that can significantly affect the integrity and stability of structural components. This study investigates the post-buckling behavior of carbon fiber-reinforced epoxy composite laminates with embedded delamination under quasi-static compression. Experimental tests were conducted using an electronic universal material testing machine to measure deformation and load-bearing capacity in the post-buckling stage. The specimens, prepared from T300 carbon fiber and TDE-85 epoxy resin prepreg, were subjected to axial compressive loads with delamination simulated by embedding Teflon films. Finite element analysis (FEA) was performed using ABAQUS software, incorporating a four-part model to simulate delaminated structures, with results validated against experimental data through comprehensive convergence analysis. The findings reveal that increasing delamination depth and length decrease overall stiffness, leading to an earlier onset of buckling. Structural instability was observed to vary with the size of delamination, while the post-buckling deformation mode consistently exhibited a half-wave pattern. This research underscores the critical impact of delamination on the structural integrity and load-bearing performance of composite laminates, providing essential insights for developing more effective design strategies and reliability assessments in engineering applications. Full article

A phase-field crack model is developed for numerical analysis of thermal buckling and postbuckling behavior of a functionally graded (FG) graphene platelet-reinforced composite (FG-GPLRC) plate with a central crack. The inclined central crack is represented according to a stable, effective phase-field formulation (PFF) by introducing a virtual crack rotation. The problem is formulated using first-order shear deformation theory (SDT) incorporated with von Kármán geometric nonlinearity. And it is approximated by combining regular Laplace interpolation functions and crack-tip singular functions in the framework of the 2D extended natural element method (XNEM). Troublesome shear locking is suppressed by applying the concept of the MITC (mixed-interpolated tensorial components)3+ shell element to the present numerical method. The results demonstrate the effectiveness of this method in accurately predicting the critical buckling temperature rise (CBTR) and the thermal postbuckling path. In addition, the parametric results reveal that the CBTR and postbuckling path of the FG-GPLRC plate are distinct from those of the FG carbon nanotube-reinforced composite (FG-CNTRC) plate and remarkably affected by the parameters associated with the crack and graphene platelet (GPL). Full article