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In this research, experimental and theoretical results for bending and buckling of a five-layer sandwich plate with composite face sheets reinforced by carbon nanotubes (CNTs), carbon nanorods, graphene platelets (GPLs), or nitinol shape memory alloy (SMA) wire and foam core are studied. The equations of equilibrium for this sandwich plate based on RFSDT and the principle of minimum total potential energy are derived, and then, the transverse displacement and buckling load are obtained. Using the rule of mixture and the Halpin–Tsai equation, the mechanical properties of the reinforced composite face sheets are calculated and also, and the constitutive equations of the SMA are presented according to the Brinson model. As well as, the influence of various parameters including thickness ratio, aspect ratio, the volume fraction of CNTs, GPLs, and nitinol SMA wire, fiber placement angle, and temperature changes are investigated on transverse deformation and dimensionless critical buckling load. Finally, tensile and buckling experimental tests were performed according to the standard tests ASTM D 3039 and ASTM C 364, respectively. [ABSTRACT FROM AUTHOR]

In the current investigation, the novelty lies in the formulation of a novel four-node rectangular finite element with six degrees of freedom per node using the strain approach and first-order shear deformation theory, therefore, this is the first article to use this approach to analyze the static, free vibration, and buckling behaviors of functionally graded. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by a simple power law function. The notion of a neutral surface is presented to prevent membrane bending coupling. The displacement functions of the suggested element which possess higher-order expressions, is based on assumed functions of strain that satisfy both rigid body modes and compatibility equations. The performance of the developed element is verified and compared with the published results in the literature and excellent agreement is observed. The influence of the geometrical, material properties, and loading types with different boundary conditions on the bending, free vibration, and buckling analysis of FGM plate are also studied and discussed for the first time using the strain-based finite element formulation. [ABSTRACT FROM AUTHOR]

In this paper, the simple refined plate theory (S-RPT) is extended for the analysis of the bending and buckling behaviours of functionally graded graphene platelets reinforced composite (FG-GPLRC) plates supported by local elastic foundations under different boundaries. For the first time, an analytical method for determining the location of the local elastic foundation distribution by simple integration is extended to the analysis of the bending and buckling behaviour of plates. The method avoids complex calculations compared to previous methods for determining the position of the elastic foundation. Compared with other simplified plate theories, the displacement pattern of S-RPT is able to reflect the interrelationship between the gradient material properties and the displacement distribution along plate's thickness. The material properties of FG-GPLRC plates are affected by temperature. Using the static equilibrium method, the plate equilibrium equations are derived by directly integrating the three-dimensional elastic equations along the plate cross section. Galerkin's method is used to solve the governing equations. The accuracy of S-RPT under different boundary conditions and the accuracy of the analytical method for determining the location of the elastic foundation are verified by comparing the numerical results with the existing literature. Finally, the effects of different distribution patterns, weight fractions of GPLs, thickness ratios, aspect ratios, boundary conditions, temperature, elastic foundation distribution patterns, and elastic foundation parameters were investigated in detail. [ABSTRACT FROM AUTHOR]

This paper investigates stability and free vibration behaviours of bi-directional functionally graded material (BDFGM) curved sandwich beams. Simultaneous variation of material compositions along tangential and radial direction is considered. A three-node curved isoparametric beam element based on a 4-parameter global–local shear deformation theory is employed. The obtained results are verified with those from literature. Various parameters such as aspect ratio, deepness ratio, gradient indexes, boundary conditions are taken into account. Several results of BDFG curved beams are provided for benchmark purpose. [ABSTRACT FROM AUTHOR]

This study focuses on modeling ideal nonuniform standing beams and towers supporting a constant top mass. We also analyze their dynamical stability, as determining the design parameters influencing their shape and stability holds significant value for structural engineering. Initially, we employ a statical mechanics approach to balance the mechanical and gravitational forces. By solving an initial-value problem, we derive the cross-sectional areas of the columns. Our findings reveal that these areas, rather than the shapes, are the primary contributors to the engineering performance of the columns. Additionally, the top mass acts as a multiplying factor for the cross-sectional areas, and the density distribution along the column determines whether the top should be heavier or lighter. Furthermore, we demonstrate that exponential, parabolic, or linear cross-sections with significantly wider base profiles are crucial for accommodating heavier top loads. Moving on to the dynamical analysis, we consider two ideal tower configurations: FC and SC. Numerical and analytical results reveal that higher modes exhibit shorter amplitudes. FC modes necessitate higher design parameters to resist buckling phenomena, whereas SC modes show lower resistance to vibrational deflections. In terms of stability, a heavier top mass enhances the vertical beam's stability, while towers with parabolic bases are more susceptible to instabilities. [ABSTRACT FROM AUTHOR]

This paper deals with the determination of numerical and experimental buckling loads for circular plates. In the study, plates made of isotropic material and laminated composites were taken into consideration. For the experimental part of the study, a buckling apparatus for circular plates (BACIP) was designed and manufactured to apply radial compression on plates simply supported along the outer edge, which was the most important aspect of the study. Experimental buckling loads were determined by connecting this apparatus to a tension machine. ANSYS software based on the Finite Element Method (FEM) and the analytical buckling load formula found in textbooks were also used for the determination of the numerical and analytical buckling loads. The effects of parameters such as plate thickness, number of layers, cutout sizes, and so on on critical buckling loads were investigated within the scope of the work. Comparisons of analytical, theoretical and experimental buckling loads were presented in both graphical and tabular form. The results of the experimental and theoretical buckling were found to be comparatively compatible. [ABSTRACT FROM AUTHOR]

Traditional carbon fiber reinforced carbon matrix composites are mostly two-dimensional laminated structures with low interlayer properties. Z-fiber reinforcement technology can improve the properties of composites in the thickness direction. However, the low axial modulus of Z-fiber results in insufficient stiffness, and its implanting in large-thickness preforms is susceptible to buckling due to heavy resistance. The existing Z-fiber implantation techniques are challenging to realize the Z-direction reinforcement of large-thickness and high-density preforms. Therefore, this paper proposes a method of using hollow tubes to guide Z-fiber implantation into preforms and puts forward an improved solution for the issue of buckling during the insertion of hollow tube into the preform. A cutting edge was designed for the hollow tube, and a metal rod was utilized to provide support. The enhanced hollow tube was named "Z-fiber guiding needle." A mechanical model of the Z-fiber guiding needle inserted into the preform was established to optimize needle parameters. Then Abaqus software was used to study the strength and stiffness of the needle, as well as analyze its stability. Finally, experimentally verifies the Z-fiber guiding needle. The final results show that the strength, stiffness, and stability of the designed Z-fiber guiding needle can meet the requirements of implantation. This proves the designed method is correct and feasible, and provides a theoretical basis for the design of ultra-long needles used to guide Z-fiber implants into large-thickness, high-density composite material preforms. [ABSTRACT FROM AUTHOR]

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams. The analyses include three models for porosity distribution and two scenarios for thermal distribution. The material properties are assessed under two conditions, i.e., temperature dependence and temperature independence. The theoretical framework for the beams is based on the higher-order shear deformation theory, which incorporates shear deformations with higher-order polynomials. The governing equations are established from the Lagrange equations, and the beam displacement fields are approximated by the Chebyshev polynomials. Numerical simulations are performed to evaluate the effects of thermal load, slenderness, boundary condition (BC), and porosity distribution on the buckling and vibration behaviors of metal foam beams. The findings highlight the significant influence of temperature-dependent (TD) material properties on metal foam beams' buckling and vibration responses. [ABSTRACT FROM AUTHOR]

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [ABSTRACT FROM AUTHOR]

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This paper presents the analytical process of porous functionally graded graphene-reinforced truncated conical shells subjected to hydrostatic pressure and axial tension. Three types of graphene platelet (GPL) dispersion and three patterns of porous distribution were considered. A modified model, in which the volume fraction of the pores is regarded as the essential parameter, was built to evaluate the material properties. The static stability equations of the shells, coupled with the effect of the combined forces, were derived. The Galerkin integrate technique was employed to obtain the critical buckling hydrostatic pressure and axial tension. After the present method was validated, the influences of pores, GPLs, and shell geometrical characteristics were investigated in the parametric studies. The results show that the critical hydrostatic pressure and axial tension can be elevated by increasing the porous coefficient, semi-vertex, and length–thickness ratio. On the contrary, the critical pressure and tension are decreased with the rise of GPL mass fraction. [ABSTRACT FROM AUTHOR]

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication. The expression of the geometric stiffness matrix is derived, the finite element linear buckling analysis is conducted, and the sensitivity solution of the linear buckling factor is achieved. For a specific problem in linear buckling topology optimization, a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells. The aggregation function method is used to consider the high-order eigenvalues, so as to obtain continuous sensitivity information and refined structural design. With cyclic matrix programming, a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted. To maximize the buckling load, under the constraint of the given buckling load, two types of topological optimization columns are constructed. The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm. The vertex method and the matching point method are used to carry out an uncertainty propagation analysis, and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance. Finally, the differences in the structural topology optimization under different reliability degrees are illustrated by examples. [ABSTRACT FROM AUTHOR]

In the current research, we delve into the intricate realm of bifurcation analysis for Föppl–von Kármán plates, employing a precise numerical tool. This innovative numerical approach melds the power of spectral discretization with the prowess of a high-order continuation method-based Taylor series development (HODC). It is worth noting that combining the high-order continuation method with such discretization techniques offers an efficient path-following approach, complete with adaptive step lengths, capable of tackling a wide array of nonlinear problems. Despite the extensive applications of nonlinear elasticity, the spectral method remains relatively uncharted territory within this context. However, our deep-rooted understanding and expertise in the field drive us to embrace this method alongside high-order development continuation for bifurcation analysis of Föppl–von Kármán plates. The governing equations governing thin elastic plates experiencing significant elastic deflections manifest as a pair of coupled nonlinear differential equations, famously known as the von Kármán (vK) equations, presented in a strong form with two principal unknowns: deflection (w) and the Airy stress function (F). Leveraging Chebyshev decomposition matrices, we approximate these fourth-order elliptic nonlinear partial differential equations. Subsequently, we harness high-order development continuation techniques to morph these nonlinear systems into linear ones. Our rigorous evaluation and validation of this numerical approach's precision and performance come to fruition through a comprehensive buckling analysis encompassing multiple illustrative examples. [ABSTRACT FROM AUTHOR]

Interest in components with detailed structures increased with the progress in advanced manufacturing techniques. Parts with lattice elements can provide improved global buckling stability compared to solid structures of the same weight. However, thin features are prone to local buckling. We present a two-scale optimization approach that simultaneously improves the local and global stability of parametrized graded lattice structures. Elastic properties and local buckling behavior are upscaled via homogenization based on geometric exact beam theory. To reduce computational effort, we construct a worst-case model for the homogenized buckling load factor, which acts as a safeguard against local buckling. We briefly discuss advantages and limitations by means of numerical examples. [ABSTRACT FROM AUTHOR]

In this study, we employ density functional theory and the Siesta code to investigate the electronic and optical properties of beryllium oxide (BeO) zigzag nanotubes (n,0) with n = 6, 8, 10, 12, 14, 16. Our research aims to elucidate the characteristics of BeO nanotubes and their potential applications. Notably, we found that the bandgap energy of BeO nanotubes increases with diameter, indicating superior conductivity in smaller-diameter nanotubes. Our findings align closely with experimental data, particularly when using the GGA-WC functional. Additionally, we calculated nanotube buckling decrease with diameter, revealing its negligible impact on these structures. The static refractive index of BeO nanotubes remains consistent at approximately 1.1, with an optical absorption peak around 9 eV. Our research offers valuable insights into the electronic and optical properties of BeO nanotubes, which have implications for various applications. [ABSTRACT FROM AUTHOR]

Based on the shell and plate theory, this paper uses the divide-and-combine method (DCM) to derive an analytical out-of-plane compression buckling limit expression of the basic unit of the core layer of a grid beetle elytron plate (GBEP); the accuracy of expression and the mechanism of GBEP unit buckling are investigated through experiments and finite element (FE) simulation. The results show that: (1) the theoretical expression of the out-of-plane compression buckling limit of a GBEP unit obtained by DCM is applicable and is closer to the test results than the classical solution of the out-of-plane compressive buckling of a cylindrical shell and the theoretical result of Flügge. Based on this, a modified expression of the theoretical result of Flügge's compressive buckling limit load is proposed. (2) Given the significant differences between the theoretical values obtained in this paper and the experimental values, the out-of-plane compressive buckling resistance of the GBEP unit and its mechanism are investigated from the viewpoints of structural parameters η (the ratio of the radius of the trabeculae to the width of the element) and deformation process; the synergistic mechanism of the honeycomb-trabeculae structure is also studied. This paper contributes to improving the bionic system derived from the beetle's forewing. [ABSTRACT FROM AUTHOR]

Recent advancements in additive manufacturing (AM) have opened new possibilities for fabricating highly complex lattice structures with enhanced mechanical properties, particularly hybrid and functional gradient structures. Most of the conducted research focused on linear/longitudinal designs for both hybrid and functional gradient structures. This study focuses on designing and evaluating novel functionally graded radially hybridized structures, combining different unit cells from beam-based and surface-based structures. The research introduces a cylindrical/radial hybridization approach, incorporating three distinct unit cells: body-centered cubic (BCC), face-centered cubic (FCC), and octet from beam-based structures, and diamond, gyroid, and split-p from surface-based structures. Polylactic acid (PLA) was selected as the material, and fused filament fabrication (FFF) was employed for fabrication. Quasi-static compression tests were conducted to assess the influence of hybridization and functional gradience on compressive modulus, ultimate strength, specific energy absorption, and failure properties. Both experimental and numerical results demonstrated that functionally graded lattice structures, whether surface-based or beam-based, exhibited improved mechanical performance. The surface-based functionally graded lattice structures showed the highest compressive modulus (71%), ultimate strength (36%), and specific energy absorption (19%). On the other hand, the beam-based functionally graded structures displayed a higher compressive modulus (50%), ultimate strength (11%), and specific energy absorption (19%). However, it should be noted that the beam-based functionally graded structures exhibited a decrease in these properties due to factors such as unit cell size, volume fraction, and structural buckling. Overall, the findings highlight the superior mechanical properties of functionally graded lattice structures compared to hybrid lattice structures. [ABSTRACT FROM AUTHOR]

This paper proposes a three-dimensional (3D) Maltese cross metamaterial with negative Poisson's ratio (NPR) and negative thermal expansion (NTE) adopted as the core layers in sandwich plates, and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial. First, the NPR and NTE of the metamaterial are derived analytically based on energy conservation. The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method (FEM). Subsequently, the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton's principle with the consideration of the von Kármán nonlinearity. The differential quadrature (DQ) FEM (DQFEM) is utilized to obtain the numerical solutions. It is shown that NPR and NTE can enhance the global stiffness of sandwich structures. The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress, natural frequency, and critical buckling load. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

Context: The discovery of graphene gave way to the search for new two-dimensional structures. In this regard, octa-graphene is a carbon allotrope consisting of 4- and 8-membered rings in a single planar sheet, drawing the research community's attention to study their inorganic analogs. Considering the promising properties of octa-graphene-like structures and the role of GaAs and GaP in semiconductor physics, this study aims to propose, for the first time, two novel inorganics buckled nanosheets based on the octa-graphene structure, the octa-GaAs and octa-GaP. This work investigated the structural, electronic, and vibrational properties of these novel octa-graphene-based materials. The octa-GaP and octa-GaAs have an indirect band gap transition with a valence band maximum between M and Г points and a conduction band minimum at Г point with energy of 3.05 eV and 2.56 eV, respectively. The QTAIMC analysis indicates that both structures have incipient covalent in their bonds. The vibrational analysis demonstrates the occurrence of ΓRaman = 6Ag + 6Bg and ΓRaman = 12A′ + 12B″ for octa-GaP and octa-GaAs, respectively. The symmetry reduction of octa-GaAs leads to activating inactive modes observed in the octa-GaP structure. The frontier crystalline orbitals are composed by Ga(px) and P(py and pz) orbitals for octa-GaP and Ga(px and py) and As(s, py, and pz) for octa-GaAs in the valence bands while in the conduction bands by Ga(py, pz, and s) for both compounds and P(px and pz) and As(py). The phonon bands demonstrate the absence of the negative frequency modes and the structural stability of these new nanosheets. This report aims to reveal the fundamental properties of both newfound materials for stimulating experimental research groups in the search for synthesis routes to obtain this structure. Methods: This work used the DFT/B3LYP approach implemented in the CRYSTAL17 computational package. Ga, As, and P atomic centers were described by triple-zeta valence with polarization (TZVP) basis set. The vibrational analysis was carried out via coupled-perturbed Hartree–Fock/Kohn Sham (CPHF/KS) method, and the chemical bonds were evaluated via the quantum theory of atoms in molecules and crystals (QTAIMC). [ABSTRACT FROM AUTHOR]

Background: The modelling of the sheet metal forming operations requires accurate and precise data of the material plastic behaviour along non-proportional strain paths. However, the buckling phenomenon severely limits the compressive strain range that could be used to deform thin metal sheets. Objective: The main aim of this paper was to propose an effective device, that enables to determine of accurate stress-strain characteristics of thin metal sheet specimens subjected to axial deformation without buckling and with a special emphasis on friction correction. Methods: In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of X10CrMoVNb9-1 (P91) power engineering steel, and DP500 and DP980 dual-phase steels, under compression loading. The fixture enables monitoring of the friction between the specimen and supporting blocks during the test, and thus the precise stress response of the material could be determined. Results: The effectiveness of the fixture was evaluated under tension–compression cyclic loading and during the compression tests in which high-strength thin metal sheets were successfully deformed up to 10% without specimen buckling. Furthermore, the successful determination of a friction force variation between supporting blocks and the specimen during tests enabled to determine an actual force acting on the specimen. Conclusions: The proposed testing fixture was successfully assessed during the compression and cyclic tension–compression of high-strength thin metal sheets as no buckling was observed. Its advantage lies in adapting to change its length with specimen elongation or shrinkage during a test. The friction force generated from a movement of both parts of the device could be effectively monitored by the special strain gauge system during testing and thus its impact on the stress-strain characteristics could be successfully eliminated. [ABSTRACT FROM AUTHOR]

Packing of slender objects into receptacles that are filled with a fluid is a ubiquitous process in biological systems and technological advances. Motivated by these applications, we study the quasi-static evolution of an extensible thin sheet that is confined between the two sides of a rectangular closed chamber. The two sides of the chamber, above and below the sheet, are filled with an ideal fluid. We derive an analytical model that accounts for the mutual interaction between the elastic deformation of the sheet and the pressure difference that it induces in the chamber. Our model reveals that the evolution of the system is governed by three dimensionless parameters: the normalized lateral displacement of the sheet, the slenderness of the sheet, and the bendo-gases parameter, that accounts for the ratio between the energy of the fluid and the bending energy of the sheet. We derive the state diagram of the system on this three-dimensional parameter space, and show that in addition to the flat configuration, the sheet exhibits three different branches of buckled solutions. We extract the details of the flat-to-buckle instability and derive approximated solutions to the height functions, and therefore the pressure drops, in each branch. Overall, our analysis sheds light on mechanical instabilities that emerge from the interaction between thin elastic bodies and a compressible fluid medium. [ABSTRACT FROM AUTHOR]

A hot stamping process of quenchable steel tubes using a mandrel reinforced with eco-friendly fibers was developed to produce ultra-high strength steel hollow parts having enhanced lightweighting and crashworthiness. High internal pressure was generated to improve the die quenchability and shape accuracy of the formed parts by the fiber reinforcement. Wood sawdust, shredded copy paper, and plant fiber made of recycled toilet paper were chosen as the fibers, and not only the strength was evaluated from a uniaxial compression test but also the melting behavior of the mandrel was examined. The influence of the fiber reinforcement on the shape accuracy and die quenchability of hot-stamped parts was investigated. The generated internal pressure with the fiber-reinforced ice mandrel was higher than that with the pure ice mandrel without the reinforcement, and thus, the shape accuracy and die quenchability of hot-stamped parts were significantly improved even for a comparatively small change in internal volume of tubes. [ABSTRACT FROM AUTHOR]

In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index (k), slenderness (L/h), porosity coefficient (e), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other. [ABSTRACT FROM AUTHOR]

Uncertainty is widely present in composite structures, and the probabilistic model is one of the most common ways to describe uncertainty. In some engineering problems, incomplete knowledge leads to uncertainty in the distribution parameters of probabilistic models. In this paper, the uncertainty of the distribution parameters is described by intervals, and the uncertainty analysis of a radome made by honeycomb sandwich composite is performed under imprecise probability. To reduce computational costs, a back propagation analysis neural network (BPA-NN) based on data from finite element analysis (FEA) is constructed. A variance-based global sensitivity analysis (GSA) is conducted to identify input variables that have a large influence on the output characteristics of the composite structure. A buckling failure model is established to evaluate the safety of the composite structure, and then GSA based on failure probability is carried out to identify input variables that have a large influence on the failure probability of the structure. The uncertainty analysis under imprecise probability in this paper provides a framework for the reliability assessment and design of composites. [ABSTRACT FROM AUTHOR]

Peridynamics is a non-local continuum theory which accounts for long-range internal force/moment interactions. Peridynamic equations of motion are integro-differential equations, and only few analytical solutions to these equations are available. The aim of this paper is to formulate governing equations for buckling of beams and to derive analytical solutions for critical buckling loads based on the nonlinear peridynamic beam theory. For three types of boundary conditions, explicit expressions for the buckling loads are presented. The results are compared with the classical results for buckling loads. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the current approach. The results show that with an increase of the horizon size the critical buckling load slightly decreases for the fixed overall stiffness of the beam. [ABSTRACT FROM AUTHOR]

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell's shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior. [ABSTRACT FROM AUTHOR]

The general theory of slender structure buckling by Grabovsky and Truskinovsky (Cont. Mech. Thermodyn. 19(3–4):211-243, 2007), (later extended in J. Nonlinear Sci. 26(1):83–119, 2016 by Grabovsky and the author), predicts that the critical buckling load of a thin shell under dead loading is closely related to the Korn's constant (in Korn's first inequality) of the shell under the Dirichlet boundary conditions resulting from the loading program. It is known that under zero Dirichlet boundary conditions on the thin part of the boundary of positive, negative, and zero (one principal curvature vanishing, and one apart from zero) Gaussian curvature shells, the optimal Korn constant in Korn's first inequality scales like the thickness to the power of −1, − 4 / 3 , and − 3 / 2 respectively. In this work we analyse the scaling of the optimal constant in Korn's first inequality for elliptic shells that contain a finite number of points where both principal curvatures vanish. We prove that the presence of at least one such point on the shell leads to the scaling drop from the thickness to the power of −1 to the thickness to the power of − 3 / 2 . To our best knowledge, this is the first result in the direction for constant-sign curvature shells, that do not contain a developable region. In addition, under the assumption that a suitable trivial branch exists, we prove that in fact the buckling deformation of such shells under dead loading, should be localized at the vanishing curvature points, as the shell thickness h goes to zero. [ABSTRACT FROM AUTHOR]

Based on three-dimensional theory of elasticity, static bending, free vibration and buckling behaviors of functionally graded carbon nanotube-reinforced composite plates are investigated with the isogeometric analysis (IGA). The carbon nanotubes are supposed to be distributed uniformly and graded functionally along the plate thickness. The refined rule of mixtures is applied to predict the effective material properties. Based on the IGA, the displacement field of the plate is expressed by three-dimensional NURBS basis functions. The Hamilton's principle is used to obtain the formulations for the static bending, free vibration and buckling analysis. The convergence study is performed and the accuracy of the present approach is validated by comparing the numerical results with the published literature. In addition, the effects of CNTs volume fractions, CNTs distributions, geometrical parameters and boundary conditions on the static bending, free vibration and buckling analysis of the functionally graded carbon nanotube-reinforced composite plates are investigated. [ABSTRACT FROM AUTHOR]

This paper presents a novel optimization strategy using Design of Experiments and SunFlower optimization algorithm in order to achieve the better drop-off location in composites tubes used in applications to lower limb prosthesis. The main difficulty in using drop-offs is related to finding an ideal location to the drop-offs that provides higher structural performance. Furthermore, in a single structure there are a variety of possibilities for drop-off location. The statistical approach combines 4 design variables related to drop-off location and 1 categorical variable, which is responsible for providing the type of employed fiber in the tubular structure that can be hybrid manufactured with carbon (CFRP) and glass (GFRP) or not (only CFRP). Based on combinations between the design and categorical variables, numerical analyses using the Finite Element Method were carried out to provide the response variables with regard to structural behavior, such as failure index, nonlinear buckling load, mass and first natural frequency. Two different types of experiments were executed in the design of experiments, the factorial design which identified the significance and curvature of response variables. In the second experiment, the Response Surface Methodology revealed the main effects, the significance of design variables and their interactions considering only the response variables that showed significance. Finally, a multiobjective optimization strategy was elaborated to indicate the better drop-off location using the SunFlower algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the behavior of a medical guidewire within a vessel with a specific focus on its buckling, commonly known as tip load. The guidewire is simulated as a variable section microshaft embedded in an elastic environment, and a comprehensive buckling analysis is carried out based on the modified couple stress theory (MCST). The fundamental frequency is determined by applying Hamilton’s principle and Rayleigh’s method. A formula for calculating the buckling force is subsequently introduced. Numerical simulations were conducted to analyze the impact of the material properties, tapered tip length, core thickness, slenderness ratio, and material length scale parameter on the tip load and penetration force. Furthermore, a comparative study was carried out to validate the proposed formulation. The findings derived from this research can provide valuable insights for the optimization and exploration of various parameters related to medical guidewires. The findings indicate that coronary guidewires with lengths exceeding 10 cm exhibit minimal variations in tip load, whereas those with lengths below this threshold experience a substantial decrease of 65–75% in both tip load and penetration force when the length is doubled. In addition, nitinol guidewires demonstrate greater flexibility, with their tip load being nearly 75% lower than that of stainless steel guidewires of equivalent dimensions. Moreover, there is a notable increase in penetration force with an expanding radius, with tapered tips resulting in an approximate 20–30% increase in penetration force. [ABSTRACT FROM AUTHOR]

A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity. By introducing the local thickness defects function of the micro-beam, the variable coefficient differential equations of the buckling problem are obtained with the variational principle. Combining the eigensolution series of the complete micro-beam with the Galerkin method, we obtain the critical load and buckling modes of the micro-beam with defects. The results show that the depth and location of the defect are the main factors affecting the critical load, and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam. The effect of defect location on buckling is related to the axial gradient of the rotation angle, and defects should be avoided at the maximum axial gradient of the rotation angle. The model and method are also applicable to the static deformation and vibration of the micro-beam. [ABSTRACT FROM AUTHOR]

One of the major drawbacks of material extrusion additive manufacturing (AM) is hot-end clogging. This study aims to answer the question, "How clogging happens and what thermal conditions lead to clogging during filament-based material extrusion?" Answering this question requires a clear understanding of temperature distribution inside the liquefier. However, this could not be achieved only through experimental measurements. Therefore, numerical simulations were also carried out by developing a 3D finite volume model of the hot-end. The results obtained from numerical simulations show good agreement with experimental measurements. They also give us a detailed picture of the temperature gradient near the nozzle. A series of experiments were performed to determine at what thermal conditions clogging occurs, and some criteria for avoiding clogging were presented. The temperature distribution of those thermal conditions that leads to clogging is then investigated numerically to analyze the clogging mechanism. As the results show, overheating the heat barrier increases the length of the filament, whose temperature is above the glass transition temperature. As this length exceeds a critical value, the filament buckles under the extruder motor force, and consequently clogging occurs. [ABSTRACT FROM AUTHOR]

Cantilever nanobeams subjected to the axial pressure are considered under the assumption that the material behaviour can be modelled with the help of the nonlocal theory of elasticity. The nanobeams and nanocolumns under consideration have rectangular cross section with piecewise constant dimensions and are weakened by crack-like defects at the re-entrant corners of the steps. The critical buckling loads of stepped nanobeams are calculated and the sensitivity of critical loads with respect to crack parameters is studied. Results show the significant effect of crack parameters on the stability of stepped nanobeams. The numerical results are presented with the aid of MATLAB tools and are found to be in a close agreement with the available work in the literature. [ABSTRACT FROM AUTHOR]

We developed and obtained close-form solutions for the buckling growth rate of microtubule (MT) bundles using the Timoshenko beam theory. We took into consideration the surface effects and the Poisson's ratio of the microtubules surrounded by neighbouring filaments in the viscous cytosol. We developed the motion equation by using the modified couple stress theory (MCST) which will take into account the small-scale effects of the microtubules. We then proceeded by studying the effects of various parameters on the buckling growth rate of microtubule bundles. Our results show that the internal material length scale parameter has a decreasing effect on the buckling growth rate of the microtubule bundle. And as microtubule added in the bundle increases, the buckling growth rate reduces further due to the effects of the surrounding microtubule-associated proteins (MAPs). On the contrary, the Poisson's ratio has an increasing effect on the value of the buckling growth rate of the microtubule bundle. We also investigated the effects of other parameters such as surface energy on the buckling growth rates of microtubule bundles and showed the validity of our model by comparing our results with those obtained by previous researchers. [ABSTRACT FROM AUTHOR]

To prevent accidents in minimally invasive surgeries, force limiters have been developed for forceps grippers. When a force limiter is in use, if the absolute value of its spring constant is reduced, the risk of damage to the organs decreases. This paper proposes the use of a leaf spring buckling mechanism as a force limiter for forceps. The results obtained indicate that the spring constant of a buckled leaf spring is lower than that of a normal coil spring. Furthermore, the use of a leaf spring allows the independent adjustment of its thickness and width, based on the stress and force values. This enables an easy calibration of the threshold value. In the experiments, the spring constant of the buckled leaf spring was 1.5 × 10 - 1 N/mm, which is half of that of a normal coil spring. After calibrating the gripping force, it was confirmed that the force limiter reduced the extent of damage to the dummy organs in the ex vivo experiments. [ABSTRACT FROM AUTHOR]

Background: Accurate predictions of thin sheet material springback during forming processes are of great interest in the forming industry. However, thin sheets are susceptible to buckling under shear loading. Objective: The present research aims at improving the so-called Arcan setup for testing thin (1-5 mm) sheet samples with large gauge areas (i.e., width about 21 mm) by introducing anti-buckling devices to mitigate sample buckling. Method: Three monotonic and one cyclic shear tests were carried out on 1 mm thick C60 high carbon steel. Results: The use of the proposed anti-buckling device resulted in the suppression of sample buckling. Numerical analyses of the experiment where buckling was eliminated revealed predominant shear stress states in the gauge area (i.e., stress triaxiality = 0), which highlights minor influences of the anti-buckling device on the sample stress state. Conclusion: To suppress buckling, the use of anti-buckling devices was essential. Moreover, the friction coefficient between the sample and the proposed devices was calibrated ( μ = 0.33 ) in addition to kinematic hardening parameters. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of imperfect pipes conveying fluid in the pre-buckling and post-buckling states are investigated. In this paper, the novel motion equation of fluid-conveying imperfect pipe supported at both ends is derived by considering the geometric imperfection and the geometric nonlinearity induced by mid-plane stretching. The imperfect configurations are chosen as the first bucked modes of pined–pined and clamped–clamped pipes. The exactly analytical solutions for static response are obtained due to the fluid flow. In the linear vibration analysis, the equation is discretized by the Galerkin method and solved as a linear eigenvalues problem. Excellent agreement is observed between the present solution and the available literature. Compared with the supercritical pitchfork bifurcation of the perfect pipe conveying fluid, the results show that the cusp bifurcation occurs in the imperfect pipe when increasing the flow velocity. In the post-buckling state, there are three equilibrium configurations composed of two asymmetry stable branches and an unstable branch. The critical velocity firstly increases and then decreases when the imperfect amplitude increases. The numerical results indicate that initial imperfect amplitude and flow velocity have a complex influence on the natural frequency of the imperfect pipe. The first natural frequency increases when the initial imperfect amplitude increases. The three branches of the imperfect pipe in the post-buckling state provide more interesting and essential dynamic behaviors. [ABSTRACT FROM AUTHOR]

In this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters. [ABSTRACT FROM AUTHOR]

A unified plate model predicting the buckling behaviors is proposed by incorporating both surface and size effects into the general third-order plate theory (GTPT). From the minimum potential energy principle, the governing equations are implemented with presenting the corresponding boundary conditions. Analytic buckling loads for rectangular nanoplates are obtained by considering different boundary conditions. The surface effects, size effects and geometric sizes of nanoplates on the plate instability loads are discussed by using four types of single crystalline metallic nano-materials, gold, silver, copper and nickel. The study reveals that the GTPT is more accurate in predicting the buckling behaviors of nanoplates than the Reddy's plate theory when surface effects are considered due to the fact that the GTPT can freely satisfy the strain condition on plate surfaces. Further discussion shows that the nonlocal strain gradient GTPT predicts a higher critical buckling load of a nanoplate with increasing high order scale parameter while a lower critical buckling load with increasing nonlocal parameter than the classical GTPT. Moreover, it is found that the increasing in length-to-thickness ratios of the nanoplates enhances the influence of surface effects on the critical buckling loads. A nanoplate with significant surface stresses and the effects on dimensionless critical buckling load factor [ABSTRACT FROM AUTHOR]

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire. [ABSTRACT FROM AUTHOR]

Large-scale landsliding is an extremely important geological process in shaping landscapes in the Tibetan Plateau. In this research, an ancient river-damming landslide with an estimated debris volume of 4.9 × 107 m3, located in the upper Jinsha River, SE Tibetan Plateau, was studied. The landslide once formed a dam over 60 m high and blocked the river. Lacustrine sediments, composed of silty clay with particle sizes of 0.002–0.25 mm, are intermittently distributed along both banks, extending about 6.5 km upstream. The OSL dating indicates that the lacustrine sediments have an age of 2.6 ± 0.2 ka. Detailed field investigation and theoretical analysis was performed to investigate the characteristics, potential cause and mechanism of the landslide. The results suggest that the landslide was most likely triggered by buckling of planar rock slabs under gravity. It may start as a translational sliding along the weak interlayer composed of mica schist at the upper part of the slope and then formed buckles by curving amphibolite rock beds near the slope toe. The hillslope has still been affected by gravitational deformations, with geomorphology characterized by tension cracks, buckle folds, and small landslide scars distributed on the slope surface, suggesting that the evolution of the river valley caused by buckling deformation has not achieved equilibrium. [ABSTRACT FROM AUTHOR]

The present paper aims at studying the effect of geometric parameters and moisture content on the mechanical performances of 3D-printed isogrid structures in short carbon fiber-reinforced polyamide (namely Carbon PA). Four different geometric isogrid configurations were manufactured, both in the undried and dried condition. The dried isogrid structures were obtained by removing the moisture from the samples through a heating at 120 °C for 4 h. To measure the quantity of removed moisture, samples were weighted before and after the drying process. Tensile tests on standard specimens and buckling tests on isogrid panels were performed. Undried samples were tested immediately after 3D printing. It was observed that the dried samples are characterized by both Young modulus and ultimate tensile strength values higher than those provided by the undried samples. Similar results were obtained by the compression tests since, for a given geometric isogrid configuration, an increase in the maximum load of the dried structure was detected as compared to the undried one. Such discrepancy tends to increase as the structure with the lowest thickness value investigated is considered. Finally, scanning electron microscopy was carried out in order to analyze the fractured samples and to obtain high magnification three-dimensional topography of fractured surfaces after testing. [ABSTRACT FROM AUTHOR]

The potential for spontaneous failure of quarry pit floors by various buckling modes has increasingly become a concern because of the potential impacts on safety, the environment, and mining operations. The most notable and concerning form of buckling failure is referred to as a "pop up" which is a nearly-instantaneous and violent event similar to a rock burst. A means to evaluate potential risk from this hazard within a rational engineering framework is required to aid with licensing and operations decisions. A first step in understanding the likelihood of buckling event occurrence under various conditions is the review of a thorough compilation of past observed in situ events. The objective of this study is the development of a database of observed cases to provide insight into the various buckling failure modes and associated geotechnical conditions. Although available documented historic case study details vary significantly, the collected data, as a whole, is of value. All available, information on the geological environment, rock type, mechanical properties, in situ stresses, and buckle dimensions are documented within the database. The database has been analyzed and revealed trends relating buckling orientation and in situ stress orientation/magnitude. In addition, the database has been used to develop a categorization of the main buckling-related failure modes which is presented along with a summary of their associated typical analysis methods. [ABSTRACT FROM AUTHOR]

Considering the size discreteness of commercially available metal plates and the intrinsic buckling strength vulnerability of slender silo, this paper proposed a methodology, which integrated the nonlinear implicit dynamic Finite Element Method (FEM), Particle Swarm Optimization (PSO) algorithm and MATLAB programming, to optimize the wall-thickness layout for stepped thin-walled cylindrical silo, with the objective of minimizing silo mass while ensuring its structural stability. Taking into account both practicality and reliability, silo discharge loads were amplified 1.6 times to try to reflect the comprehensive effectiveness of negative and positive factors on slender silo buckling strength. When evaluating the fitness of PSO method, nonlinear implicit dynamic FEM results, such as kinetic energy history data plots, total energy history data plots, etc., were used to intuitively determine whether silo buckled or not. In essence, the optimal wall-thickness layout problem of a stepped silo is an NP-hard combinational optimization problem. The discrete thicknesses of rolled metal plates set an unavoidable constraint on stepped silo size optimization, which implies that there are only a few specific thickness values could be selected. In addition, the data of plate width are also discrete and one width value might correspond to several thickness data. For reasons for saving the potential cutting costs, the heights of most silo segments should be an integral multiple of the corresponding plate width value as far as possible, while the overall height of the silo should be kept still. To realize this goal, numerical processing techniques, such as generating a random number from a uniformly distributed set of discrete positive integers, linear normalization and linear interpolation, etc., were applied in this study. [ABSTRACT FROM AUTHOR]

This paper presents three-dimensional solutions for the buckling of variable angle tow (VAT) composite laminated plates. The p-version finite element with hierarchical basis functions is adopted to determine the buckling of VAT composite laminates with different parameters. Inter-element compatibility is achieved by matching the generalized displacements at the vertices, edges, and faces shared by neighboring elements. The buckling loads of symmetrical and anti-symmetrical laminates with various boundary conditions are obtained. A convergence study is performed and the accuracy of the method is confirmed by comparing the numerical results with those in the literatures. The verified results indicate that the present 3D p-FEM method is accurate for the buckling analysis of VAT composite laminated plates, and that these three-dimensional results may serve as a benchmark for future studies. [ABSTRACT FROM AUTHOR]

The instability of functionally graded material (FGM) structures is one of major threats to their service safety in widely engineering applications. This paper aims to clarify a long-standing controversy on the type of thermal instability of simply-supported FGM beams. Firstbased on the Euler-Bernoulli beam theory and von Kármán geometric nonlinearitya nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang's two-variable method is formulated. Secondan approximate analytic solution to the nonlinear integro-differential boundary value problem with a thermal-induced inhomogeneous force boundary condition is obtained by using a semi-inverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finallybased on the free energy theoremit is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermorethe nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures. [ABSTRACT FROM AUTHOR]

This study aims to examine the effect of the diameter, number, and location of the circular cutout on the free vibration response and buckling loads of the laminated composites. Eigen-buckling and free vibrations analyses are performed for the laminated composite plates by using the finite element software ANSYS. Numerical results obtained by the finite element method are compared to the experimental ones. In the numerical analyses, the effect of the delamination around the cutout on the buckling load and the natural frequency is also examined. The critical buckling load and first natural frequency values obtained by both numerical and experimental studies are used to create a prediction model using the artificial neural networks. The Levenberg–Marquardt backpropagation algorithm is used as the training method. It is observed that both the number and location of the cutout affect the critical buckling load and first natural frequency values. Numerical and experimental results are presented together with the ANN prediction results. [ABSTRACT FROM AUTHOR]

In this paper, the buckling and free vibration of a Mindlin plate with a side crack are presented considering a uniaxial in-plane compressive or tensile load. The side crack is through the thickness of the plate. In the Ritz method, a series of corner functions are incorporated into the admissible functions which consist of the modified characteristic functions. With this treatment, one can describe the singularity in stress near the tip of the crack as well as the discontinuities in both displacement and bending rotations across the crack. The buckling loads and natural frequencies are solved through eigenvalue problems considering the existence of the crack. The effects of location, length and orientation of the crack on the buckling and free vibration of the loaded plate are demonstrated. The coupling effect of the crack and the in-plane load on the vibrational characteristics of the plate is analyzed with varying parameters. It is shown that the influences of the tensile and compressive preloads are enhanced by the crack, and the tensile preload can cause the low-order frequency to increase with the growing crack. [ABSTRACT FROM AUTHOR]

The present work aims at studying the effect of geometric parameters of isogrid structures on their buckling behavior. To this purpose, isogrid structures in polyamide reinforced with short carbon fibers, with different rib widths, rib thicknesses, and cell heights, were additively manufactured using the fused deposition modeling technology; then, they were subjected to compression test until the occurrence of buckling. It was observed that isogrid structures can undergo to different failure modes, local and global buckling, depending on the values of geometrical parameters. Furthermore, the geometrical parameters that lead to the highest strength are different to those providing the highest specific strength. However, the specific strength of the 3D printed composite material is higher than those of 1XXX and 3XXX aluminum alloys. Rib thickness was characterized by the highest effect on both strength and specific strength while the cell height results in the lowest contribution. Finally, optical and scanning electron microscopies were carried out in order to analyze the fractured ribs and to obtain high magnification three-dimensional topography of fractured surfaces after buckling. The effect of moisture content on polyamide reinforced composites and the comparison between 3D printed and traditionally produced isogrid structures will be investigated in future researches. [ABSTRACT FROM AUTHOR]