Buckling Of Structures Research Articles

Buckling optimization of Double-Double (DD) laminates with gradual thickness tapering

Double-double (DD) laminates are promising replacements for conventional Quad laminates in aerospace applications because of their inherent design simplicity and, more importantly, the ease of tapering. However, the thickness thinning due to tapering will significantly increase the risk of buckling failure. In this paper, we proposed an implicit global & local model for thickness tapering optimization of DD laminates to maximize buckling resistance under the given weight constraint or weight reduction under buckling constraints. Firstly, a global model is established for buckling load calculation, with material properties calculated from homogenization of local laminates using the classical laminate theory. Then, nodal repeats of a four-plies DD sub-laminate are chosen as design variables to interpolate the tapered thickness profile. Sensitivities of structural responses are calculated semi-analytically to achieve efficient gradient-based optimization. Tapering spacing constraints between adjacent thicknesses are introduced to mitigate the potential delamination due to the stress concentrations caused by sharp thickness variation at the cost of a reduced optimization effect. Finally, typical numerical examples show that DD laminates with optimal gradual thickness tapering can remarkably increase the structural buckling resistance or the weight reduction.

Parametric Analysis of Critical Buckling in Composite Laminate Structures under Mechanical and Thermal Loads: A Finite Element and Machine Learning Approach.

This research focuses on investigating the buckling strength of thin-walled composite structures featuring various shapes of holes, laminates, and composite materials. A parametric study is conducted to optimize and identify the most suitable combination of material and structural parameters, ensuring the resilience of structure under both mechanical and thermal loads. Initially, a numerical approach employing the finite element method is used to design the C-section thin-walled composite structure. Later, various structural and material parameters like spacing ratio, opening ratio, hole shape, fiber orientation, and laminate sequence are systematically varied. Subsequently, simulation data from numerous cases are utilized to identify the best parameter combination using machine learning algorithms. Various ML techniques such as linear regression, lasso regression, decision tree, random forest, and gradient boosting are employed to assess their accuracy in comparison with finite element results. As a result, the simulation model showcases the variation in critical buckling load when altering the structural and material properties. Additionally, the machine learning models successfully predict the optimal critical buckling load under mechanical and thermal loading conditions. In summary, this paper delves into the study of the stability of C-section thin-walled composite structures with holes under mechanical and thermal loading conditions using finite element analysis and machine learning studies.

Stochastic Dynamic Buckling Analysis of Cylindrical Shell Structures Based on Isogeometric Analysis

In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis.

Impact Experiment and Buckling Criterion Analysis of Thin-Walled Cylindrical Shells

The impact test of tubular components is usually carried out by way of drop hammer impact. In fact, in many ships’ equipment, the form of load is often carried out by way of drop impact test. In this paper, the drop impact test is used to study the buckling of tubular structure under impact load, so as to make it closer to the impact form of components in actual ship structure. Firstly, the stress, strain, acceleration at each moment and the buckling deformation mode of the tubular member after the impact are obtained through the drop impact experiment, and then the impact process is analyzed. Secondly, the finite element method is used for numerical simulation of the impact process, and the accuracy of the finite element analysis results is verified by comparing with it. Thirdly, the finite element method proved to be effective and was used to simulate single and multiple drop impacts under more working conditions, and a large amount of data was obtained. Finally, according to the existing impact criteria based on the results of drop weight impact, it is applied to the drop impact process, and the accuracy of each impact criterion is analyzed and compared. This method makes up for the deficiency of the traditional experimental method of using falling weight to simulate impact, and provides a reference for the critical buckling condition of similar thin-walled cylindrical shells under impact.

Probability model evolution laws and mechanisms of non-linear buckling capacity of single-layer spherical gridshells with topology-constrained initial imperfections

This research offers a detailed probability analysis of the non-linear buckling capacity (NBC) of single-layer gridshells (SLGs), impacted significantly by stochastic initial geometric imperfections during construction. Employing the constrained stochastic imperfection modal method, which adeptly incorporates topology constraints of actual initial imperfection scenarios. The key factors, such as the imperfection simulation method, imperfection amplitude, number of rings, and the rise-to-span ratio, are evaluated through systematic numerical analysis. The results reveal that the traditional random imperfection method cannot obtain the actual bimodal distribution of the NBC, and it can overestimate the maximum and minimum NBCs by 5.16 % and 52.49 %. Furthermore, the joint well-formedness is introduced to quantify the joint local stiffness, and it is found to have a highly intertwined correlation with the structural non-linear buckling mode. The evolution mechanism of probability models can be elucidated through the joint initial deviations leading to changes in joint well-formedness (i.e., local stiffness), based on which it is concluded that an imperfection amplitude of 1/1500 of the structural span should be recommended to be the imperfection amplitude acceptance limit to fully utilize the structural global buckling capacity; significant deviations in primary rib joints and inner ring joints markedly affect the NBC more than those in non-primary rib joints and outer ring joints. The aforementioned conclusions are essential for revising guidelines for permissible joint deviations and assessment methodologies for critical joints throughout the construction.

Thermal buckling of the concrete structures reinforced by nanocomposites: Introducing advanced deep neural networks for thermal buckling problem

The thermal buckling behavior of concrete annular sector plates reinforced with nanocomposites is investigated in this work. The thermal buckling issue is stated using mathematical modeling, taking into account the geometric linearity and material heterogeneity caused by the nanocomposite reinforcement. The governing differential equations that are obtained from the theoretical model are solved using the discrete singular convolution (DSC) technique. To generate accurate buckling load predictions, the DSC method’s great accuracy in handling complicated boundary conditions and discontinuities is used. Furthermore, using mathematical modeling to create extensive datasets, the research aims to train deep neural networks (DNNs) to anticipate thermal buckling reactions. These datasets provide a strong basis for DNN training as they include a wide range of factors, such as geometric configurations, loading situations, and material properties. By combining DNN predictions with DSC solutions, this unique technique for solving this difficult issue seeks to improve the accuracy and efficiency of thermal buckling analysis. The findings show how well sophisticated mathematical methods and machine learning models work together, opening the door to creative solutions for the design and analysis of concrete structures reinforced with nanocomposite under complicated stress.

Deployment behavior and mechanical property analysis of Kresling origami structure

Kresling origami, a representative variant of origami, exhibits several distinctive features such as multistable states, changeable stiffness, and compression-torsion coupling deformation. The first focus of this study involves examining the mechanical properties of origami structures, specifically, the equivalent modulus and critical buckling stress during the deployment process are evaluated. Subsequently, the collapsibility of the Kresling origami structure is explicated with regard to energy and strain. In the folding process, when the Kresling angle is 0.0135 rad, the maximum torque is 959 Nmm, and the structure will occur snap-through instability, which is the nonlinear critical buckling load of the failure. After that, the torque decreases rapidly, and then gradually increases slowly. The mechanical model is developed and subsequently evaluated in terms of its flexibility and adjustment of stiffness. The present study investigates the buckling modes and vibration properties of Kresling origami structures, as well as their combination structures. For the buckling of Kresling origami structure, the critical buckling load of Euler buckling is 0.023 N and that of local buckling is 0.67 N. In short, the critical buckling load of the column shell is greater than that of the Kresling origami structure, which is due to the small local stiffness of structure.

Surrogate modeling with non-stationary-noise based Gaussian process regression and K-Fold ANN for systems featuring uneven sensitivity distribution

In the realm of aircraft design, there is a prevalent need for surrogate modeling techniques capable of efficiently and accurately modeling objects with high evaluation costs and uneven sensitivity distributions, such as those encountered in the nonlinear buckling of thin-walled structures and aerodynamics at transonic speeds. However, the non-stationary Gaussian Process Regression (GPR) model requires extensive hyperparameters or judicious assumptions, limiting its applications in such tasks, and the commonly used K-Fold methodology suffers from inherent instability. Addressing these issues, this paper proposes an active learning method for surrogate modeling in systems featuring uneven sensitivity distribution, integrating non-stationary-noise GPR and K-Fold Artificial Neural Network (ANN) methodology, namely NSN-GPR-KF. Instead of relying on a non-stationary kernel function, the algorithm regards noise as a non-stationary factor within a stationary GPR framework, with noise levels estimated via the K-Fold ANN methodology, allowing GPR to efficiently adapt to non-stationary systems while avoiding the aforementioned requirements for non-stationary GPR. Case validations, performed on two test functions with pronounced uneven spatial sensitivity, demonstrate that NSN-GPR-KF outperforms commonly used stationary GPR and pure K-Fold methodology. It synthesizes the exploration capabilities of GPR with the exploitation proficiency of the K-Fold methodology, achieving comparable global accuracy with reduced sample sizes—up to 26 % and 22 % less than the other two algorithms, respectively. The algorithm was successfully applied to predict the buckling load of thin-walled pipe beams, demonstrating accelerated convergence and approximately 25 % greater accuracy compared to pure K-Fold model. These results suggest that NSN-GPR-KF can serve as an efficient and precise modeling tool for engineering tasks with high evaluation costs and complex sensitivity distributions.

Tunnel rockbursts induced by dynamic disturbances: mechanism and mitigation

Rockbursts are characterized by violent rock fractures and pose a significant threat to hard-rock tunnels, potentially resulting in casualties and damage to excavation spaces. Globally recognized as one of the least understood and most feared challenges in underground excavations, rockbursts are often triggered by dynamic disturbances such as engineering activities or nearby vibrations. This study conceptualizes rockbursts as dynamic buckling or instability issues inherent in rock structures. It specifically investigates the mechanism of tunnel rockbursts induced by ambient blasting. The derivation of the governing equation of motion, which incorporates shear deformation and rotary inertia of the rock column, results in coupled Mathieu equations. By employing the proposed numerical method, the conditions triggering rockburst were established using instability diagrams. The study examines the effects of static components, dynamic loading, and frequency on a tunnel example, revealing that the amplitude and frequency of dynamic disturbances are critical in influencing the occurrence of tunnel rockbursts through perturbation effects and parametric resonance mechanisms. These insights offer valuable understanding into the mechanisms, mitigation, and control of tunnel rockbursts.

ZnS and CdS counterparts of biphenylene lattice: A density functional theory prediction

This study presents four novel inorganic structures based on the biphenylene network (BPN): planar BPN-ZnS (p-BPN-ZnS) and BPN-CdS (p-BPN-CdS) and buckled BPN-ZnS (b-BPN-ZnS) and BPN-CdS (b-BPN-CdS). Cohesive energy analyses reveal that structural buckling enhances stability, and a perturbation is necessary to obtain planar lattices. Phonon dispersion and ab initio molecular dynamics (AIMD) simulations demonstrated the dynamical and thermal stabilities. ZnS-based structures exhibited more pronounced charge accumulation and depletion than CdS. All evaluated structures are ultra-wideband gap semiconductors, with band gap energy values of 4.33, 5.34, 3.59, and 4.30 eV (at HSE06 level) for p-BPN-ZnS, b-BPN-ZnS, p-BPN-CdS, and b-BPN-CdS, respectively. p-BPN-ZnS demonstrated the highest Young modulus (Yx/Yy = 25.295/34.874 N/m), followed by p-BPN-CdS (Yx/Yy = 15.286/21.339 N/m). On the other hand, b-BPN-ZnS and b-BPN-CdS exhibit lower Young Modulus, Yx/Yy = 4.135/14.709 and 11.842/8.218 N/m, respectively. Notably, b-BPN-ZnS displayed a particular characteristic, a negative Poisson ratio (νx/νy = -0.008/-0.030), being an auxetic material. This report is expected to stimulate both theoretical and experimental researchers in the prediction and development of new inorganic materials based on the biphenylene network.

Understanding the role of interface in deformation behavior of additively manufactured bimetallic structures of pure metals

Directed energy deposition (DED)-based additive manufacturing (AM) was employed to fabricate three distinct bimetallic compositions to understand the role interface for the deformation behavior of bimetallic structures under compressive loading. Commercially pure titanium (CP Ti) with a hexagonal closed packed (HCP) structure, nickel (Ni) with a face-centered cubic (FCC), and tantalum (Ta) with a body-centered cubic (BCC) structure were selected to understand the deformation behavior within the pure metals and damage accumulation at the bimetallic interface. By incorporating the combination of these materials, such as Ni–Ti, Ni–Ta, and Ta–Ti, we aimed to manufacture layered-base polycrystalline composite structures with FCC-HCP, FCC-BCC, and BCC-HCP crystal unit cells, respectively. In Ni–Ti and Ni–Ta bimetallic structures, it was determined that deformation is controlled by the Ni region, where the highest deflection occurs when Ni bulges out and makes lateral stress at the interface, resulting in crack initiation, propagation, and failure of the structure. Structural edges were found to experience the highest deformation, prompting grain inclination towards the <111> crystal orientation, resulting in a favorable orientation for dislocation slip and a higher Taylor factor. However, strong interfacial bonding and similar Young's modulus between Ta and Ti altered the deformation mechanisms to twinning formation in the Ti region and observed buckling of the entire structure without significant failure at the interface.

Research on Structural Collapse of a Containership under Combined Bending–Torsion by Oblique Waves

Large waves cause a great number of collapsed-ship accidents, resulting in the loss of many lives and properties. It has been found that most of these collapses are caused by encountering oblique waves. As a result, the ship structure experiences a complex collapse under combined bending and torsion. This paper utilizes a numerical hydroelasto-plastic approach, coupling CFD (Computational Fluid Dynamics) with the nonlinear FEM (Finite-Element Method), to study the structural collapse of a containership in oblique waves. First, a 4600 TEU containership was selected to study its collapse mechanism under oblique waves. Second, a hydroelasto-plastic numerical coupling of CFD and nonlinear FEM is used to co-calculate the wave loads and structural collapse of containership. The hydrodynamic model is constructed and used to solve wave loads in the CFD solver, and a nonlinear FEM model of containership with finer meshes is also modeled to solve the structural collapses, including plasticity and buckling. Third, several oblique-wave cases involving heading angles of 120°, 135°, 150°, and 180° are determined and calculated. Typical cases are discussed for time-domain stress histories and collapsed courses. Finally, the influence of oblique-wave parameters on structural collapse is discussed, and the collapse mechanism of containerships under the action of oblique waves is obtained, which provides a new understanding of ship structure design.

On matched asymptotic expansion solutions of a bucklewave propagation problem

AbstractIn the present paper, the method of matched asymptotic expansions is used to derive approximate analytical solutions to a model problem related to bucklewave propagation in undersea pipelines. The model problem, introduced by Chater, Hutchinson and Neale (in: Collapse – The Buckling of Structures in Theory and Practice (Thompson, J.M.T., Hunt, G.W., eds.) Cambridge Univ. Press, Cambridge, 1983), consists of a linear elastic beam resting on a nonlinear elastic foundation, with inclusion of axial tension and inertia, related to a propagating buckle. When tension dominates over inertia, it is found that the asymptotic solution describing a propagating buckle has the character of nonoscillatory motion. When tension and inertia forces are of equal magnitude, or when inertia forces dominate over tension, the solutions are found to be oscillatory, but still localized around the bucklewave front. Finally, it is shown that when the propagation speed of the buckle exceeds a critical value, a spatial instability sets in, with exponentially growing amplitude of the beam deflection.

Stretchability dependency on stiffness of soft elastomer encapsulation for polyimide-supported copper serpentine interconnects

For conventional flexible printed circuit board widely used in industry, jointing islands of electric components with polyimide-supported copper serpentine interconnects is an effective approach to ensure circuit stretchability. The stretchability of the interconnects varies significantly due to the soft elastomer encapsulating the interconnect, as the encapsulation essentially constrains the lateral buckling of the serpentine structure during stretching. Previous studies have indicated that thin encapsulation with a low Young’s modulus is required to maximize stretchability. However, extremely low modulus and thinness lead to the elimination of the encapsulation function, and the design criteria for maximizing stretchability while maintaining adequate modulus and thickness are still unclear. This study investigates the dependence of stretchability on encapsulation stiffness, an index that simultaneously considers modulus and thickness. The interconnects with core–shell and single-elastomer encapsulations, each with a different stiffness, were prepared. The relationships between the elongation to failure of the interconnect and the tensile and bending stiffness of the encapsulation were investigated through experiments and finite element method calculations. The results indicate that the tensile stiffness is a more useful index in encapsulation design than the bending stiffness because the elongation to failure monotonically decreases as the tensile stiffness increases. The results also indicate that the required tensile stiffness to maximize interconnect stretchability, essentially making the interconnect almost freely deformable, ranges from 5 to 34 N m−1 when the interconnects use an 18 μm thick copper and 50 μm thick polyimide.

Modified couple stress and artificial intelligence examination of nonlinear buckling in porous variable thickness cylinder micro sport structures

This investigation focuses on the nonlinear behavior of porosity-dependent functionally graded (FG) truncated conical small-scale structures. The modified coupled stress theory, as well as the energy method, are applied to generate the nonlinear partial differential equations (PDEs) related to buckling analysis of simply supported nonuniform micro-cylindrical structures. The material dispersion is gradually changed along the length of the structures between the Nickel and concrete, while the porosity voids are scattered in the radial direction, and the external radius of the structure decreases along the length direction via nonlinear mathematic equations applicable in sports structures. The PDEs are numerically solved via the generalized differential quadrature method (GDQM) coupled with the numerical iterative technique. In this particular context, the aim is to predict nonlinear results using a newly developed methodology that employs artificial neural networks (ANNs). The predictions generated by this approach will be compared against previously obtained data and validated to ensure their accuracy and reliability. The ANN methodology is expected to provide a more robust and comprehensive framework for predicting nonlinear results, which would be helpful in a variety of settings, from scientific research to engineering applications.

Mechanics of Pure Bending and Eccentric Buckling in High-Strain Composite Structures.

To maximize the capabilities of nano- and micro-class satellites, which are limited by their size, weight, and power, advancements in deployable mechanisms with a high deployable surface area to packaging volume ratio are necessary. Without progress in understanding the mechanics of high-strain materials and structures, the development of compact deployable mechanisms for this class of satellites would be difficult. This paper presents fabrication, experimental testing, and progressive failure modeling to study the deformation of an ultra-thin composite beam. The research study examines the deformation modes of a post-deployed boom under repetitive pure bending loads using a four-point bending setup and bending collapse failure under eccentric buckling. The material and fabrication challenges for ultra-thin, high-stiffness (UTHS) composite boom are discussed in detail. The continuum damage mechanics (CDM) model for the beam is calibrated using experimental coupon testing and was used for a finite element explicit analysis of the boom. It is shown that UTHS can sustain a bending radius of 14 mm without significant fiber and matrix damage. The finite element model accurately predicts the localized transverse fiber damage under eccentric buckling and buckling stiffness of 15.6 N/mm. The results of the bending simulation were found to closely match the experimental results, indicating that the simulation accurately shows deformation stages and predicts damage to the material. The findings of this research provide a better understanding of the structure characteristics with the progressive damage model of the UTHS boom, which can be used for designing a complex deployable payload for nano-micro-class satellites.

Numerical and experimental analysis of inelastic and rate-dependent buckling of thin injection-moulded high-density polyethylene structure

Semi-crystalline polymers is an important group of materials that is used in a vast array of products. In this study, the rate-dependent properties of high-density polyethylene (HDPE) are investigated, both experimentally and theoretically. Experimental compression testing of a three-dimensional HDPE structure is performed and analysed numerically by use of the finite element method. In addition, an Eulerian constitutive material model for isotropic, semi-crystalline polymers is proposed. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, pressure-dependence of inelastic deformations, and damage. The proposed material model was implemented in Abaqus as a VUMAT, which is an explicit implementation. The material model was calibrated by use of uniaxial tensile tests performed on HDPE dog-bone shaped samples, and the model was further explored by applying the VUMAT implementation to the compression tests of the HDPE structure. The simulation model was able to reproduce the experimental results well, both the uniaxial tests and the compression tests. In particular, the friction present in the compression tests seems to play an important role in determining the buckling mode of the structure.

Pilot study of lattice endoprosthesis buckling by compression in-situ using X-ray tomography

Take into account additive manufacturing while design lattice implant can improve load-bearing properties and decrease construction weight. The usage of lattice structure and biomaterials makes it possible to solve the main problem of arthroplasty – preservation of the implant after surgery in the patient's body. Unfortunately, nowadays biomaterials do not have the necessary strength capacity. In spite of this, a lot of researches are directed towards to develop new design methods or improve the existing ones. There are number of articles focused on in-situ testing and quality control of lattice structures. The study is devoted to investigate the buckling of lattice structures under uniaxial compression with synchronous X-ray computed tomography scanning. In the article an experimental study of lattice structures of two kinds has been carried out. Edges of hexagonal bipyramid were a basic cell of the samples. The distribution of basic cells in the first type of construction was uniform, and was non-uniform in the second type. The studied samples were manufactured by laser stereolithography method. The lattice structures were loaded step-by-step with a longitudinal compressive load. The loading of the specimens was carried out in cooperation with their scanning by X-ray computed tomography. As a result, the displacement fields of structures at each step of loading were obtained. The general and local buckling of lattice structures was revealed. The general buckling occurred at the second loading step for each type of structure. Local buckling was observed at the third loading step. The influence of the architecture of the lattice structures on the buckling process was revealed. The effect of interruption of the buckling process was observed in the specimen with non-uniform distribution of basic cells. And because of that the structure continued to work in compression. In other words, the lattice architecture "dampened " the bending components of the displacement vector.

Novel buckled graphenylene-like InN and its strain engineering effects

This paper reveals the structural, electronic and mechanical properties of a novel inorganic graphenylene based on indium nitride (IGP-InN). The IGP-InN was characterized via density functional theory (DFT) simulations. The phonon dispersion shows the dynamic stability of IGP-InN, and molecular dynamics simulations confirm its thermal stability up to 700 K. Besides the electronic properties, the indirect band gap transition with energy (Egap) of 2.49 eV makes IGP-InN suitable for optoelectronic applications under UV–visible. Also, the Egap tunability with mechanical strain was analyzed, with a decrease of 1.19 eV in the Egap for tensile strains. The structural buckling plays an important role, with a transition to a planar structure for tensile strains. This work reveals a new class of 2D materials, buckled inorganic graphenylenes, and provides valuable insights into designing and optimizing graphenylene-like materials.

Study on buckling behavior of multilayer pyramid lattice structures

Three-dimensional lattice structures with high specific strength, specific stiffness and low apparent density, are widely employed across multiple engineering fields. Under uniaxial compressive loading, the lattice structure may experience local buckling or global buckling. This paper conducted a systematic parametric study of the various factors affecting the buckling behavior of multilayer pyramid lattice structures to investigate the mechanism of the two main instability modes, local and global buckling. It was found that the critical buckling load increases with the increase in the size of the unit cell and decreases with the increase in the total height of the structure for the same relative density. As the relative density increases, the buckling resistance of the lattice structure increases. It is possible to examine various buckling modes by varying the geometrical properties of the pyramid unit cell (slenderness ratio, rod inclination angle, cross-sectional size of strut connection parts). Finally, numerical simulations were performed to calculate the yield strength and buckling strength of the lattice structure under uniaxial compression load, in order to estimate the threshold relative density for structural buckling and yield failure. The results demonstrated that buckling failure should be considered for aluminum alloy pyramid lattice when the relative density is below 4.07%. This study provides design criteria for lattice structures dominated by buckling and offers ideas for improving the buckling capacity of truss-type lattice structures.