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The countersink depth accuracy is a remarkable quality index in modern aerospace industry, and it needs to be controlled quite accurately due to the extremely tight tolerances. However, the wide use of the thin-walled workpiece with low stiffness makes it difficult to achieve the required tolerance because of the complex deformation in the countersinking process. Focusing on the accurate control of countersink depth in the drilling of thin-walled workpiece, this paper provides a novel insight into the study on predicting of the feasible workpiece deformation and compensating for the countersink depth error through both theoretical and experimental analyses. An analytical model of workpiece deformation is first presented with the Fourier series approach in this study, and the finite element simulation is carried out to verify the model precision. Then a flexible cutting force model is developed to help to analyze the effect of deformation on the thrust force in the countersinking process. A novel approach of integrated iterative algorithm, that considers both the deformation and the cutting force, is established to calculate the final feasible deformation and make decision for the countersink depth error compensation, and the generalized convergence and adaptability of this iterative algorithm are investigated based on the calculus theory. Finally, the proposed integrated methodology is verified by multivariate simulations and experiments, and the results show that the countersink depth accuracy could be effectively guaranteed by countersinking with compensation based on this integrated methodology. The work in this paper enables us to understand the causes of poor countersink depth accuracy in the drilling of thin-walled workpiece and develop new countersinking techniques to satisfy the tight tolerance. [ABSTRACT FROM AUTHOR]

In this note I examine a number of statement made in Wadee and Yiatros (Z. Angew. Math. Phys. 61:565-577 ) in relation to my paper mentioned in the title. Most of the claims by Drs. Wadee and Yiatros are re-examined here in the proper context and it is shown that the results of the title paper are free of any errors. [ABSTRACT FROM AUTHOR]

With the rapid development of lithium-ion batteries, the electrode becomes more and more miniaturized. It is necessary to analyze the stress and axial force in the nanowire electrode. The main work of this paper is to analyze the stresses and buckling in homogeneous material nanowire electrodes and two kinds of composition-gradient (positive gradient and negative gradient) material nanowire electrodes of lithium-ion batteries. Comparing the diffusion-induced stresses (DISs) and buckling in three electrodes, we analyze the advantage of composition-gradient material electrodes on DISs and axial forces. The finite deformation theory and the stress-induced diffusion hypothesis are adopted to establish the constitutive equations, and the nonlinear influence of large deformation is considered. We conclude that ratios of length to radius and constraint conditions have great influence on the buckling of nanowire electrodes. The composition-gradient materials can reduce the stress and prevent the electrode from buckling. Under the same constraint condition, the positive gradient with smaller ratio of length to radius and smaller diffusion flux can delay buckling. When the ratio of length to radius are larger and the diffusion flux is larger, the negative gradient can delay buckling. The results can provide a theoretical guidance on the way of charging operation and the design of electrodes. [ABSTRACT FROM AUTHOR]

In this paper, a new model for porous structures in functionally graded plates (FGPs) is introduced that under significant differences in constitutive material properties and high porosity ratios, the difference in elasticity modulus of the suggested pattern reaches twice as many as the previous model. This study is based on the finite strip method, incorporating Eringen nonlocal elasticity and third-order shear deformation theory, to create standard and geometric stiffness matrices for mechanical and thermal buckling analyses of functionally graded porous nanoplates (FGPNPs). The procedure is founded on Lagrangian and Hermitian shape functions to account for significant shear deformation effects in thick plates, and all in-plane displacements are applied in the geometric matrix based on the virtual work principle. Various factors like boundary conditions, porosity distributions, temperature variations, and nonlocal parameter are investigated for their impact on the mechanical and thermal buckling loads of FGPNPs. The findings reveal the substantial influence of size effects on thick porous nanoplate evaluations. Mechanical analysis shows that O-, V-, X-shaped and uniform patterns exhibit the best performance against mechanical loads, respectively. Despite the material properties deteriorating with increased porosity ratios, thermal resistance is improved. The new uniform pattern performs the best under uniform loading, and V-shaped porous structures excel at strength against nonlinear loading. However, the X-shaped model exhibits the lowest thermal resistance in both conditions. [ABSTRACT FROM AUTHOR]

In this paper, the quantum effects of fine scaling on the buckling behavior of carbon nanotubes (CNTs) under axial loading are investigated. Molecular mechanics and quantum mechanics are respectively utilized to study the buckling behavior and to obtain the molecular mechanics coefficients of fine-scale nanotubes. The results of buckling behavior of CNTs with different chiralities with finite and infinite dimensions are given, and a comparison study is presented on them. The differences between finite and infinite nanotubes reflect the quantum effects of fine scaling on the buckling behavior. In addition, the results show that the dimensional changes highly affect the mechanical properties and the buckling behavior of CNTs to certain dimensions. Moreover, dimensional changes have a significant effect on the critical buckling strain. Beside, in addition to the structure dimensions, the arrangement of structural and boundary atoms have a major influence on the buckling behavior. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a third-order shear deformation theory to study the static buckling of FG sandwich nanobeams, where the core layer of the beam has hollows in the z direction, and the two sandwich types mentioned in this paper are the hardcore and softcore types. Methods: Based on nonlocal theory, the size effect is considered, and two different solutions, as an exact solution and an approximate solution for calculating the critical buckling load of nanobeams, are presented. Results: The results show the advantage of calculating for beams with many different boundary conditions, which is completely different from the conventional analytical solution (usually only for beams subjected to the simply supported boundary conditions), this is also the new point of this work. This work uses the weighted average operator and approache to come up with an expression for figuring out the critical buckling load of FG sandwich nanobeams as an approximation. The data has shown that both solutions in this work are reliable compared to published works. At the same time, this work also shows that, depending on the material distribution of the layers and boundary conditions, one can find the appropriate core layer thickness for the maximum load-carrying capacity of the nanobeam. Conclusion: The static buckling response of sandwich FGM nanobeams with a homogeneous and porous core layer is studied. The the weighted average operator and analytical approaches, in addition to the novel shear deformation theory, were used to perform the investigation, which is something new that can be found in this article. Both of the computation techniques that are presented in this paper are quite flexible, which enables them to be used for the purpose of assessing beams under a wide range of boundary conditions. [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]

The paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed section shaping in local buckling analysis problems. Furthermore, attention is paid to the impact of material characteristics on buckling stresses in a nonlinear domain. The objective of the paper is to propose a finite element method (FEM) model and a relevant numerical procedure in ABAQUS, complemented by an analytical one. It should be noted that the proposed FEM energetic technique makes it possible to compute accurately the critical buckling stresses. The suggested numerical method is intended to accurately follow the entire structural equilibrium path under an active load in elastic and inelastic ranges. The paper is also focused on correct modelling of interactions between sheets of cross section of a possible contact during buckling analysis. Furthermore, the FEM results are compared with the analytical solution. Numerical examples confirm the validity of the proposed FEM procedures and the closed-form analytical solutions. Finally, a brief research summary is presented and the results are discussed further on. [ABSTRACT FROM AUTHOR]

This paper investigates the failure load prediction of anisogrid cylindrical composite lattice structures under axial compression. The failure criterion to predict compressive failure load of lattice structure is developed by using the compression test results of representative subelement specimens including several unit cells. Compression tests of subelement using two different fixture jigs which generate different ratio of bending to compressive stress in the knot region of lattice structures were performed. The critical stress function is introduced from the compression test results and is utilized in failure criterion. The finite element analysis is used to calculate the failure load with the proposed failure criterion and also the buckling load for the full-sized cylindrical lattice structures. The compression failure loads for two different full-sized cylindrical lattice structures agreed well with the predicted failure loads by using the failure criterion proposed in this paper. The results of these studies indicate that the proposed failure criterion for the cylindrical composite lattice structures under compressive load in this work can be applied to the stress analysis and optimization problem in the preliminary design phase. [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]

In this paper, we study some comparisons of Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds. By introducing a new parameter, we provide some new relationships, which improve corresponding results of Ilias and Shouman in [Calc. Var. Partial Differential Equations, 2020, 59: Paper No. 127, 15 pp.] in some sense. [ABSTRACT FROM AUTHOR]

In this paper, the material length scale parameter of the modified couple stress theory for trabecular bones is studied. For this reason, experimental data for the buckling of single wet and dry trabeculae from the subchondral region of the human medial tibial plateau are used from the literature. A material length scale parameter is extracted using the modified couple stress theory-based buckling relation and the experimental results. This parameter can capture the size-dependent behavior of trabeculae and can be beneficial for micro-mechanical investigation of trabecular bones. In addition, this paper proposes a size-dependent length scale parameter for trabeculae to estimate the buckling behaviors of dry and wet trabeculae, more accurately. Therefore, this paper confirms that the softening (weakening) effects of the modified couple stress theory and size-dependent behavior of the material length scale parameter can be considered for some special cases, and additionally, a correct value for the length scale parameter of the trabecula is revealed. [ABSTRACT FROM AUTHOR]

Typically, structures fail due to buckling if loaded by compression. However, it is important to notice that-especially in lightweight structures-there are several situations in which instabilities, such as buckling or wrinkling, can be observed under tensile loads. In the present paper, a number of problems, dealing with buckling under tensile loads, are presented. Some solutions already contained in former papers of the author are reconsidered, compared to recent results, and extended. Further new results are presented. Bifurcation buckling under tensile loading of beams, plates (with and without cut-outs), rolled metal strips, thin cell walls of metal foams, and of thin metallic films on polymer substrates is treated in this paper. It is made clear that in all cases of buckling under tensile loads eventually compressive stresses are responsible for the loss of stability. Thus, one should carefully differentiate between "buckling under tension" and "buckling under tensile loads". Nonconservative loads as well as material instabilities under tension, such as necking, are not considered in this paper. [ABSTRACT FROM AUTHOR]

Purpose: This paper uses analytical methods to analyze the buckling behavior of sandwich nanobeams composed of three layers of material, with the central layer including a hollow hole. This study is the first instance of using such analytical techniques for investigating the buckling response of these specific FGM (functionally graded material) nanobeams. Methods: The calculation formulas have been derived using a novel third-order shear deformation theory. The equilibrium equation of the nanobeam is formulated based on the notion of virtual work. Analytical solutions have been used to get the precise answer for the ultimate load of the beam. Empirical evidence has substantiated the dependability of this particular approach. Results: This feature complicates the response of the beam and gives rise to several fascinating phenomena, including the idea of the virtual critical load which allows for the evaluation of the loss of the critical load. This research also looks at how the buckling behavior of the beam is affected by some geometric elements, material characteristics, hollow features of the intermediate layer, and viscous resistance-related parameters. Conclusion: Based on the findings of this investigation, several inferences can be inferred. The third-order theory employed in this investigation exhibits commendable reliability in the computation of the buckling issue pertaining to sandwich beams experiencing substantial deformations. The presence of a viscoelastic foundation has a significant impact on the critical buckling load of the beam, resulting in the inclusion of both real and fictitious components. The critical buckling load is influenced by various factors, including the core thickness, foundation parameters, material composition ratio, and the number of hollows, nonlocal characteristics, and core layer material. These factors not only impact the actual magnitude of the critical buckling load, but also affect the rate at which it is lost. The findings of this study hold considerable importance for engineers in their calculations and designs of similar structures within the field of engineering. Moreover, this serves as the foundation for other forthcoming study avenues that can serve as valuable sources of reference. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a novel shear deformation theory to study the static bending and buckling of nanoplates subjected to flexomagnetic influence. This is done using the revolutionary shear strain theory and establishing finite element formulations based on the finite element technique. Methods: This study uses a finite element method to solve the nanoplate bending and buckling problem while taking into consideration the flexoelectromagnetic effect. Results: The investigation's novel aspects are summarized: since the flexomagnetic effect makes the plate stiffer, the maximum deflection is lowered when this effect is included. This effect also has varying influences on the plate under various boundary conditions, particularly the maximum position of the deflection, stress, Hz, and Bz responses. The thinner the plate thickness, the more pronounced the flexomagnetic effect. The flexomagnetic effect causes the thickness distribution of the stress components, Hz, and Bz to diverge from that of conventional structures (where this effect is disregarded), particularly for plates with CFFF boundary conditions. The longer the length of the compression zone increases, the lower the critical buckling load of the plate. The greater the stiffness of the elastic foundation, the better the plate can withstand compressive loads. Conclusion: The findings of this work provide a significant scientific foundation for the computation and development of nanoplates with magnetic properties. To design a structure that meets the necessary criteria, it is crucial to carefully choose geometric characteristics, boundary conditions, and stiffness parameters of the elastic foundation. According to this study, potential areas for additional research include investigating the impact of the flexomagnetic effect on nanoplates including fractures, optimizing nanostructures that exhibit flexomagnetic effects, and calculating the influence of flexomagnetic effects and temperature on nanostructures. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical investigation on the buckling behaviour of corroded cold-formed steel (CFS) channel section columns under axial compression. 7 stub columns and 7 medium long columns were accelerated corrosion by the outdoor periodic spray test. Prior to compression tests, the mass, residual thickness, surface morphology and initial geometric imperfection of the corroded CFS columns were measured. The failure modes, load–strain curves and load–axial displacement curves obtained from axial compression tests were discussed. Based on the corrosion morphology, the non-linear finite element (FE) model for the corroded CFS columns was then developed. Finally, the calculation method for corroded CFS channel section columns was proposed. The results indicated that with the increasing mass loss rate, the irregularity of residual thickness increased rapidly at first, and then increased slowly due to uniform corrosion. The failure mode of the corroded specimens may change from distortional buckling to local buckling as the mass loss rate increased. With the increase in mass loss rate, the buckling critical load, ultimate load, post-buckling strength and axial displacement corresponding to ultimate load decreased. The failure positions of distortional buckling and local buckling were mainly related to the corrosion degree of the flange and web, respectively. The FE results were compared against the experiment results showing a good match in terms of both the ultimate strength and failure modes. [ABSTRACT FROM AUTHOR]

Functionally graded (FG) sandwich plates have been spotlighted as an advanced composite structure so that the vast amount of research efforts have paid on the study of their thermo-mechanical behaviors. Among them, the thermal buckling has emerged as an important research subject because it is directly related to the safety of structural system. In this situation, this paper examines the thermal buckling behavior of ceramic-metal FG sandwich plates with a homogeneous core and two FGM face sheets. The thermal buckling problem is formulated according to 3-D thermo-elasticity and approximated by making use of a (1,1,0) hierarchical model and 2-D natural element method (NEM). The NEM-based numerical method was compared with the reference methods, from which its reliability was verified. In addition, the critical buckling temperatures (CBTs) of ceramic-metal FG sandwich plates subject to uniform, linear and nonlinear temperature loads are parametrically examined. The parametric experiments informed that the CBT is strongly influenced by the width/thickness, core thickness and aspect ratios, the ceramic and nonlinearity indices, and the boundary condition type. [ABSTRACT FROM AUTHOR]

This paper exposes full analytical solutions of a plane, quasi-static but large transformation of a Timoshenko beam. The problem is first re-formulated in the form of a Cauchy initial value problem where load (force and moment) is prescribed at one end and kinematics (translation, rotation) at the other one. With such formalism, solutions are explicit for any load and existence, and unicity and regularity of the solution of the problem are proven. Therefore, analytical post-buckling solutions were found with different regimes driven explicitly by two invariants of the problem. The paper presents how these solutions of a Cauchy initial value problem may help tackle (i) boundary problems, where physical quantities (of load, position or section orientation) are prescribed at both ends and (ii) problems of quasi-static instabilities. In particular, several problems of bifurcation are explicitly formulated in case of buckling or catastrophe. [ABSTRACT FROM AUTHOR]

Purpose: This paper is devoted to the development of a novel four-node quadrilateral finite element for mechanical buckling and free vibration responses of functionally graded material plates. Methods: This element which possesses five essential degrees of freedom per node is formulated within the framework of the strain approach and the first-order shear deformation theory. The element displacement functions contain higher-order terms that satisfy the rigid body modes and they are based on assumed strains satisfying compatibility equations. Material properties of the plate are assumed to be graded across the thickness direction using a simple power-law distribution of the volume fractions constituents. The concept of the neutral plane is introduced to avoid the membrane-bending coupling. Results: The performance of the suggested element is evaluated through various numerical tests and the obtained results are compared with available solutions from the literature. These tests are conducted on functionally graded plates with various shapes, boundary conditions, side-to-thickness ratios, several values of gradient index n and under different types of in-plane loading. Conclusion: The present element results have proved excellent accuracy and efficiency in predicting free vibration and buckling of functionally graded plates and they show that this element is free from any shear locking. [ABSTRACT FROM AUTHOR]

Thin-walled parts are critical structural components in the aircraft industry. However, because thin-walled parts have low stiffness, it is impossible to eliminate the elastic deformation generated by cutting force during the machining process, resulting in poor machining accuracy. In this paper, the simulation and surface roughness prediction model of thin-walled necks with ribbed constrained at both ends were constructed to understand the deformation mechanism and processing quality of thin-walled necks. The deformation mechanism of thin-walled necks with thin rib structures was revealed, and the deformation mode of the "S" shape to the "V" shape of fine boring thin-walled parts was analyzed. Then, the temperature field and the residual stress of the thin-walled neck with the spindle speed, feed, and depth of cut were revealed. Finally, the surface roughness prediction model for thin-walled parts is established using multiple regression functions. This study provides a theoretical foundation and technical assistance for managing the boring quality of thin-walled items by deeply understanding the machining deformation and cutting process mechanism. [ABSTRACT FROM AUTHOR]

In this paper, we present a robust and accurate finite element model based on the higher-order shear deformation theory for buckling analysis of porous functionally graded sandwich plates resting on Winkler–Pasternak elastic foundations. An FG sandwich plate including isotropic core and FGM skins is considered here and the power-law distribution is employed to estimate the constituents' volume. The discrete form results in an eigenvalue problem whose solutions are the critical buckling load. The finite element solution is carried out using the quadrilateral element with eight nodes and nine degrees of freedom per node. A parametric study is performed to investigate several effects such as the plate's width-to-thickness ratio, Winkler and Pasternak modulus parameters, regular-linear and irregular-nonlinear loading types, power-law index, coefficient and distributions porosities as well as boundary conditions. Good agreement is achieved with the review results of the literature. [ABSTRACT FROM AUTHOR]

Mechanical buckling response of bidirectional functionally graded (BDFG) imperfect sandwich plates by using a quasi-3D solution is studied in this paper. The formulation used in the present study includes indeterminate integral terms and involves only four unknown functions. The material properties of the sandwich plates change in the axial and thickness direction as well as the porosity following a defined distribution law. Imperfect BDFG sandwich plates are considered to be submitted to a variety of in-plane compressive loads, such as uniform, linear and exponential. The equations of motion are obtained from the virtual work principle and the critical buckling loads are computed for plates with different boundary conditions. The results of the current formulation are checked with those available in the literature where good agreement is found. Finally, the parametric study of the in-plane mechanical buckling are carried out, including the porosity, plate geometric parameters, boundary conditions and grading indexes. The results reveal that these parameters have a great influence on the buckling response of BDFG porous sandwich plates. These results can serve as reference solutions for future investigations. [ABSTRACT FROM AUTHOR]

In high-pressure and high-temperature gas wells, tubing string buckling behavior is a significant engineering problem to be addressed. To solve this problem, a finite element model of tubing string buckling with geometric nonlinearity and contact nonlinearity is established, and the buckling behavior of tubing string in the whole wellbore section is simulated. The effects of axial compression, connector and wellbore diameter on tubing string buckling are studied. It is found that a variety of complex buckling forms may co-exist in the same wellbore and that with the increase of axial compression load, the lateral displacement of tubing string increases gradually, and the buckling state of tubing string gradually intensifies. Under the same axial compression load, buckling is relieved when the effect of the connector is considered, indicating that the connector has the effect of delaying the buckling and promoting the transfer of axial force. Wellbore diameter has a great influence on the buckling critical load and the buckling behavior of tubing string. The work presented in this paper can provide a technological basis for tubing string buckling behavior analysis in high pressure and high temperature gas wells. [ABSTRACT FROM AUTHOR]

In this paper, dynamic buckling analysis of composite cylindrical panels under two separately suddenly applied loads (axial compression and lateral external pressure) is investigated. Abaqus/Explicit operator has been used to monitor time responses of the structure under various magnitudes of loads in order to determine the critical dynamic buckling loads based on the Budiansky–Roth criterion. The effect of boundary conditions and loading duration is studied thoroughly in this work. [ABSTRACT FROM AUTHOR]

A new analytical approach to the nonlinear buckling and postbuckling analyses of functionally graded graphene-reinforced composite laminated cylindrical shells stiffened by functionally graded graphene-reinforced composite laminated stiffeners under external pressure taking into account the elastic foundation effect in a uniformly distributed thermal environment is presented in this paper. An improved smeared stiffener technique is developed for anisotropic stiffeners, and a special design for ring and stringer functionally graded graphene-reinforced composite laminated stiffeners is presented and successfully applied in this paper. The governing equations for the cylindrical shells are established by using the Donnell shell theory with the geometrical nonlinearity term in the von Kármán sense with the shell-foundation interaction formulated by the Pasternak elastic foundation model. A three-term solution form is chosen for the deflection, the stress function is introduced, and the Galerkin method is used to establish the nonlinear postbuckling relation. The numerical results validate the effects of the stiffeners, volume fraction of graphene, type of graphene distribution of the shell skin and stiffeners with different geometrical parameters, elastic foundation moduli, and uniformly distributed temperature changes on the nonlinear buckling and postbuckling behaviors of stiffened cylindrical shells. [ABSTRACT FROM AUTHOR]

Sandwich structures are widely used in aerospace, marine and other engineering industries. This paper is focused on the post-buckling and free vibration of the sandwich beam theoretically in thermal environments with simply supported and clamped boundary conditions. Firstly, nonlinear governing equations of the sandwich beam are obtained based on the principle of virtual work and natural frequencies are derived by linear equations. Secondly, buckling temperatures together with corresponding modes are addressed. Thirdly, the new equilibrium position of the sandwich beam is obtained after it loses the stability. Finally, free vibration analysis of a post-buckling sandwich beam is derived when the temperature exceeds the critical temperature. It is observed that the maximum deformation of the sandwich beam suddenly increases sharply once it loses the stability. The natural frequencies of a sandwich beam decrease with the increment of temperature, but the first-order natural frequency increases as the temperature rises once the temperature exceeds the critical buckling temperature. The theory of this paper will provide a theoretical support for the numerical method and engineering design. [ABSTRACT FROM AUTHOR]

This paper presents the results of experimental investigation on the stability of orthotropic cylindrical shells of different lengths weakened by regular circular holes located in one zone along the guide cell under torque loading. The buckling modes of shells are described. The critical buckling loads as a function of the number of holes are analyzed. [ABSTRACT FROM AUTHOR]

The present paper provides an analysis to obtain the critical buckling load and vibration frequencies of the sandwich cylindrical panel with functionally graded (FG) face sheets and FG porous core resting on an elastic foundation, subjected to mechanical load and in thermal environments. The panel is formulated within the framework of the nonlocal strain gradient theory for shell model and classical shell theory. Based on Hamilton's principle and Galerkin's method, the effects of nonlocal and strain gradient parameters, materials and geometrical characteristics, porosity, temperature and elastic foundation on buckling load, fundamental frequencies, and dynamic response of the panel are considered. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the topology optimization of columns exposed to a loss of stability. The idea is to replace a conventional maximization of a buckling load by a locally formulated topology optimization problem based on compliance minimization. In order to do this, the standard instability analysis of a compressed column is performed first and the buckling mode is determined. Then the compressive loading is replaced by a transverse one which is selected so as to generate a bending moment, the distribution of which coincides with the one representing the considered buckling mode. Minimization of compliance is performed for the bent structure and optimal topology is generated. Finally, the critical load for the optimal column is calculated. The selected numerical results obtained with the use of the above technique, under the assumption that the buckling load is unimodal, are presented. The above approach allows generating optimal topologies using Cellular Automata (CA) method, which by nature requires local formulation of the design problem. [ABSTRACT FROM AUTHOR]

Due to the poor rigidity of thin-walled parts, vibration (chatter) is extremely easy to occur during the cutting process, affecting the precision, surface quality, and efficiency of part processing. The chatter in milling thin-walled workpieces becomes a more complex, nonlinear, and unstable signal as the dynamics of thin-walled workpieces change with time and position. To realize chatter detection, a method using ensemble empirical mode decomposition (EEMD) and nonlinear dimensionless indicators is proposed in this paper. Firstly, the EEMD is adopted to decompose the raw signal because it is suited for nonlinear and nonstationary signal. Subsequently, the correlation analysis is used to obtain chatter-related intrinsic mode function (IMF) components. When chatter occurs in the milling, time series complexity is changed and energy is transferred to the chatter bands. Therefore, the nonlinear sample entropy (SE) and energy entropy (EE) of IMFs can be extracted as two indicators. Then, principal component analysis (PCA) is adopted to further reduce the feature vector dimension. After that, an improved support vector machine (SVM) is developed to identify the chatter. Among them, genetic algorithm (GA) and grid explore (GE) are used to explore the best parameters of the SVM. In addition, off-line chatter prediction is employed to determine the cutting status under different machining parameters used in the experiments. At last, the cutting force signals are performed to verify the proposed method. The results show the proposed method using SE and EE can effectively detect the chatter, which provides an option for chatter detection. [ABSTRACT FROM AUTHOR]

A generalized variational principle and a parameterized generalized variational principle are obtained for large deformation analysis of circular cylinders by the semi-inverse method; all known variational principles in the literature are special cases of the obtained parameterized functional. In this approach, a trial functional is constructed with an energy-like integral involving an unknown function, which is identified step by step. The present paper provides a quite straightforward but rigorous tool to the construction of a variational principle for the shell or plate buckling. [ABSTRACT FROM AUTHOR]

This paper investigates the buckling of isotropic plates with circular cutout subjected to non-uniform in-plane loading. The buckling load is calculated in two steps. In the first step, the prebuckling stress distribution is computed. The existence of cutout causes the solution of stress distribution to be nontrivial. In this paper, a novel analytical method is presented for calculating the stress distribution. This method is based on expansion of the stress function in polar coordinates and using a boundary integral to satisfy the boundary conditions at plate edges. In the second step, the obtained stress distribution is used to calculate the buckling load from the Ritz method. In this method, The displacement field is defined according to the first order shear deformation theory and the characteristic beam functions are used for approximation. The effect of cutout size, plate's aspect ratio, different uniaxial and biaxial loading profiles, i.e. constant, parabolic and cosine loading and different boundary conditions on the buckling load is studied. [ABSTRACT FROM AUTHOR]

In concentrically braced frames, braces-to-adjacent member connections are suitable locations for the dissipation of seismic energy. If the implementation of dissipative connections does not compromise the global lateral stiffness of the structure, the compression braces can then be protected from buckling, while the structural ductility is increased and the action effects reduced. Furthermore, an efficient use of dissipative connections allows reducing the cost of post-earthquake interventions. In this paper, an innovative dissipative connection for braced frames is proposed, consisting of a steel plate bent to a U shape and connecting the brace to the adjacent column. In this connection, energy dissipation is obtained through the inelastic flexural deformation that takes place in the plate. This paper presents experimental results on the isolated U-connection and on single-storey concentrically braced frame (real scale) including the U-connection. Besides considering several variations on the geometry of the U-shape plate, the tests considered both monotonic and cyclic loading. The results highlight the efficiency of the U-connection to dissipate the energy input through inelastic deformations. On the other hand, the cyclic tests show however that the connection is potentially sensitive to fatigue, as the deformation capacity is significantly reduced with repeated loading and increasing stress amplitude, requiring thus specific attention in practical design situations. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the investigation of the nonlinear torsional buckling and postbuckling of sandwich functionally graded cylindrical shells with the von Karman large deflection nonlinearities under thermal effect by an analytical method. The shell skin is reinforced by stringer, circular ring and spiral stiffeners, the material properties of shell skin and stiffeners are assumed to vary continuously through the thickness. The very large effect of spiral stiffeners on the buckling load-carrying capacity of a cylindrical shell in comparison with orthogonal stiffeners is clearly proved in numerical investigations. Based on the Donnell shell theory and the improved smeared stiffener technique for both thermal and mechanical terms of spiral stiffeners, the equilibrium equations of the shell are established in this paper. By using the Galerkin method, the postbuckling curves and critical buckling loads are obtained. The effects of temperature change, stiffeners, material and dimensional parameters on the nonlinear torsional buckling and postbuckling of shell are numerically analyzed. [ABSTRACT FROM AUTHOR]

This paper investigates the size-dependent vibration and buckling behavior of nanoplates described by the nonlocal Kirchhoff model analytically. The nonlocal and local constitutive relations, governing equations and boundary conditions are comprehensively discussed. A shifted governing equation in terms of local stress resultants with associated local boundary conditions is chosen in the current work. The direct separation of variables method is formulated based on the Hamiltonian dual form of the governing differential equation to address the eigenvalue problems of nonlocal rectangular plates with each edge either simply supported or clamped. The closed-form eigen-solutions are acquired for the first time for the cases where two adjacent clamped edges exist. The validity and accuracy of the present approach are verified by comparison with published analytical and numerical results. Parametric studies are performed to investigate the influences of nonlocal parameter and boundary conditions on the size-dependency of natural frequencies and critical buckling loads of nanoplates. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the nonlinear buckling behavior of carbon nanotube-reinforced (CNT-reinforced) cylindrical shells with the CNT-reinforced stiffeners under external pressure taking into account the effects of uniform temperature rise. A new design of stiffener system is proposed for CNT-reinforced cylindrical shells with five cases of the CNT distribution law for shell and stiffeners. A modified homogenization technique for CNT-reinforced stiffeners is developed and presented. Based on the Donnell shell theory and the von Kármán nonlinearity assumption, the Galerkin method is applied with the solution of deflection approximated in threeterm form, the critical buckling, and load-deflection postbuckling curves can be achieved in explicit expressions. Effects of the CNT-reinforced stiffeners, the thermal temperature, and the CNT-reinforced parameters on the external pressure buckling responses are numerically indicated and validated. [ABSTRACT FROM AUTHOR]

The paper aims to develop a unified modeling to analyze the free vibrations and buckling of laterally functionally graded material columns. The columns of rectangular cross-section, in which the mass density and Young's modulus vary along the depth as a power-law function, were considered. The differential equation governing a mode shape of a deformed column was derived with the relevant boundary conditions, including the effect of rotatory inertia. The computation results for the natural frequencies and buckling load were compared well with those available in the open scientific literature. The effects of geometrical and material properties on natural frequencies and buckling loads with the mode shapes are highlighted. [ABSTRACT FROM AUTHOR]

Purpose: Buckling problem has important practical value in the field of engineering. The purpose of this paper is to study the dimensionless critical buckling load of coupled bending-torsional buckling of wind turbine tower on elastic foundation. Method: Based on the principle of minimum potential energy and the Euler–Bernoulli column theory, the buckling differential equations of the wind turbine tower are derived. The differential quadrature method (DQM) is used to obtain the coupled bending-torsional dimensionless critical buckling load of the inhomogeneous tower with variable cross section under elastic boundary condition. Results and Conclusions: The effects of warp, elastic support, cross-section variety, wall thickness, eccentricity on the coupled bending-torsional dimensionless critical buckling loads of tower are analyzed. The numerical results show that DQM is efficient and accurate for solving coupled buckling differential equations. The dimensionless critical buckling load of wind turbine tower increases with the increase of the wall thickness and foundation stiffness. The eccentricity has little effect on the dimensionless critical buckling load of the wind turbine tower when the eccentricity is small. However, the dimensionless critical buckling load of the wind turbine tower becomes significantly smaller with the increase of the eccentricity when the eccentricity is large. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical buckling analysis of sandwich plates with functionally graded CNT-reinforced composite (FG-CNTRC) layers. The core is isotropic metallic material while two face-sheets are made of polymer reinforced with CNTs. For an accurate and effective buckling analysis of advanced sandwich structures, a new numerical method is developed by making use of hierarchical models and 2-D natural element method (NEM). The hierarchical models are based on 3-D elasticity theory, in which the displacement field is interpolated as a product of 2-D in-plane unknown functions and 1-D assumed thickness monomials. The model level is adjusted by controlling the maximum orders of thickness monomials, and the 2-D in-plane functions are approximated by NEM. The numerical method is compared with the advanced plate theories, from which the numerical accuracy has been justified. Using the proposed natural element hierarchical models (NEHM), the buckling load parameters of FG-CNTRC sandwich plates are parametrically investigated. Through the parametric numerical experiments, the effects of major design parameters were profoundly investigated, and which provide the useful guideline for the buckling-resisting design of FG-CNTRC sandwich plates. [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]

This paper investigates the performance of several meta-heuristic algorithms, including Particle Swarm Optimisation (PSO), different variants of Differential Evolution (DE), Biogeography-Based Optimisation (BBO), Cultural Algorithm (CA), Optics-Inspired Optimisation (OIO), and League Championship Algorithm (LCA), for optimum layup of laminated composite plates. The study provides detailed Pseudo codes for different algorithms. The buckling capacity maximisation of a 64-layer laminated composite plate under various load scenarios has been considered as the benchmark problem, in which the design variables are the stacking sequences of layers. A Deep Statistical Comparison (DSC) method is employed to rank the performance of different algorithms. The DSC uses a nonparametric two-sample Kolmogorov-Smirnov test to conduct the performance comparisons between the algorithms. The overall performance rankings obtained from the DSC suggest that the LCA, OIO, and PSO algorithms perform remarkably better in comparison to other algorithms. The comparisons provide some interesting conclusions on the performance of different algorithms. [ABSTRACT FROM AUTHOR]

Pre-stresses or axial loadings induced by deformations of adjacent structures, edge constraints or mounting inaccuracies and elastic supporting components attached to one side of the sandwich structures may affect the aerothermoelastic stability, which is an important subject in the design of supersonic aircraft. Therefore, the nonlinear flutter and thermal buckling behavior of composite lattice sandwich beams with translational springs under axial loading in supersonic airflow is investigated in this paper. In the structural modeling, the von Kármán large-deflection theory is applied to establish the stain–displacement relations. The aerodynamic pressure is evaluated by the supersonic piston theory. The differential equations of motion are obtained by Hamilton's principle and the assumed mode method. The highlight of this study is that a new approach for limit cycle oscillation (LCO) suppression and thermal buckling elimination without changing the stiffness of the lattice sandwich structure is proposed by utilizing the axial loading and translational springs. The structural natural frequencies are obtained and compared with reference results in the literature. The influences of the axial loading and the translational springs on the nonlinear supersonic flutter and thermal buckling properties of the sandwich beams are analyzed. Numerical results indicate that the present method is effective for nonlinear flutter suppression, and the thermal buckling effect can be completely eliminated by adjusting the axial loading of the sandwich beams. [ABSTRACT FROM AUTHOR]

Predicting the critical buckling loads of functionally graded material (FGM) plates using an analytical method requires solving complex equations with various modes of deformation to determine the minimum loads. The approach is too complex for application in engineering practice. In this paper, a data-driven model using the artificial neural network (ANN) is proposed for the critical buckling load of FGM plates, as an alternative tool for practicing engineers. A database is first developed for randomly selected inputs using an analytical solution based on first-order shear deformation theory for simply supported FGM plates. The database is then divided into a training dataset with 80% of the data and a testing dataset with 20% of the data for developing and validating, respectively, the ANN model. The ANN model developed using six hidden layers with 32 nodes in each layer is found to match the data with a coefficient of determination of 99.95%. Using the ANN model, the stochastic characteristic of the critical buckling load is examined with respect to randomness of the input parameters. The study reveals that along with the dimensional parameters, the critical buckling load is significantly affected by the randomness of the volume fraction ratio and ratio of the modulus of elasticity of the ceramic and the metal. [ABSTRACT FROM AUTHOR]

It might seem amazing: Cutting a hole in a plate can increase the buckling strength! It is the objective of this paper to present and clarify this astounding phenomenon. In lightweight design, typically thin-walled structures are used. Therefore, buckling must be considered as a possible failure mode. One might assume that removing material, and thus, reducing stiffness must result in a reduction of the buckling strength. However, perhaps surprisingly, it can be shown that introduction of cutouts, placed appropriately, can under certain conjunctures increase buckling loads. At the same time, the structural mass is reduced. Thus, the paper presents a measure, which can be used for fulfillment of a requirement in lightweight design in a twofold manner: increase in buckling strength by reduction of mass! In addition to describing a nice theoretical peculiarity, it might be of more importance from the engineering point of view that the presented methodology may help designers of lightweight structures, e.g., for aerospace applications, to place openings, which are required for some reasons in a plate being part of the construction, at such positions, at which the plate's buckling resistance is just slightly or not at all reduced or even increased, and to avoid placing holes in unfavorable areas. Based on the Rayleigh–Ritz method in terms of the Rayleigh quotient, criteria and procedures are derived which can be used to find beneficial positions for cutouts and such ones, at which cutouts should not be placed. [ABSTRACT FROM AUTHOR]

Buckling load estimation of continua modeled by finite element (FE) should be based on non-linear equilibrium. When such equilibrium is obtained by incremental solutions and when sensitivity analysis as well as iterative redesigns are included, the computational demands are large especially due to optimization. Therefore, examples presented in the literature relate to few design variables and/or few degrees of freedom. In the present paper a non-incremental analysis is suggested, and a simple sensitivity analysis as well as recursive redesign is proposed. The implicit geometrical non-linear analysis, based on Green-Lagrange strains, apply the secant stiffness matrix as well as the tangent stiffness matrix, both determined for the equilibrium corresponding to a given reference load, obtained by the Newton-Raphson method. For the formulated eigenvalue problem, which solution gives the estimated buckling load, the tangent stiffness matrix is of major importance. In contrast to formulations based on incremental solutions, the tangent stiffness matrix is here divided into two matrices, the stress stiffness matrix that is linear depending on stresses and the remaining part of the tangent stiffness matrix. Examples verify the effectiveness of the proposed procedure. [ABSTRACT FROM AUTHOR]

In the process of thermal recovery of heavy oil, the casing in oil production wells is subjected to complex stress conditions, which may cause potential damage and affect the lifecycle of the casing. The factors influencing the casing instability and the mechanism of the process in thermal production wells need to be comprehensively researched, particularly in the case where oil extraction is accompanied by sand production. In this paper, the authors have applied the three-dimensional finite element method to simulate the casing instability characteristics in the sand production section of a thermal recovery well. We have also analyzed the effect of sand production, perforation parameters, and the casing strength parameters on the axial and circumferential instability of the casing. The results show that sand production can cause a significant decrease in the lateral support of the casing and greatly reduce the buckling resistance of the casing in a thermal horizontal well. With increase in perforation diameter and perforation density, the critical buckling load of the casing decreases. On the other hand, the buckling load is less affected by the perforation phase. When the combination of the perforation density and perforation phase angle results in a bigger number of perforation holes in the row, it can significantly reduce the casing collapse strength and increase the risk of circumferential instability. The research results provide a theoretical basis in the design of casing in horizontal sections of thermal production wells. [ABSTRACT FROM AUTHOR]

In this paper, the vibration and buckling behavior of a functionally graded piezoelectric porous cylindrical microshell under thermo-electro-mechanical loads are explored on the basis of modified couple stress theory and higher-order shear deformation theory. First, the model of a functionally graded piezoelectric porous cylindrical microshell composed of piezoelectric materials with gradient change in the thickness direction was described. Second, the governing equations of the microshell were derived by Hamilton's principle and Maxwell equation. Third, the modal frequency and buckling equations of the microshell with simply supported ends were obtained on the basis of harmonic trigonometric functions. Finally, the effects of parameters on the modal frequency and buckling behavior were carried out by case studies. The results show that the modal frequency of the microshell can be adjusted by changing the porosity volume fraction, power index, applied voltage, axial load and geometric dimensions. It is also found that the vibration of the microshell is suppressed by positive voltage and axial compression but is strengthened by negative voltage and axial tension, and the material length scale parameter increases stiffness. In addition, the effects of applied voltage and axial load on the buckling behavior are larger than those of temperature. Results can be used to guide the design and application of piezoelectric devices. [ABSTRACT FROM AUTHOR]

The wrinkle pattern exhibited upon stretching a rectangular sheet has attracted considerable interest in the "extreme mechanics" community. Nevertheless, key aspects of this notable phenomenon remain elusive. Specifically—what is the origin of the compressive stress underlying the instability of the planar state? what is the nature of the ensuing bifurcation? how does the shape evolve from a critical, near-threshold regime to a fully developed pattern of parallel wrinkles that permeate most of the sheet? In this paper we address some of these questions through numerical simulations and analytic study of the planar state in Hookean sheets. We show that transverse compression is a boundary effect, which originates from the relative extension of the clamped edges with respect to the transversely contracted, compression-free bulk of the sheet, and draw analogy between this edge-induced compression and Moffatt vortices in viscous, cavity-driven flow. Next, we address the instability of the planar state and show that it gives rise to a buckling pattern, localized near the clamped edges, which evolves—upon increasing the tensile load—to wrinkles that invade the uncompressed portion of the sheet. Crucially, we show that the key aspects of the process—from the formation of transversely compressed zones, to the consequent instability of the planar state and the emergence of a wrinkle pattern—can be understood within a Hookean framework, where the only origin of nonlinear response is geometric, rather than a non-Hookean stress–strain relation. [ABSTRACT FROM AUTHOR]

Wood-fibre conformation affects paper properties in various paper-product categories, such as packaging, printing, and absorbents. Qualitative investigations suggest that capillary forces play a crucial role in determining the fibre conformation upon drying. To quantify this process, we theoretically and experimentally investigate deformation of a circular tube under capillary pressure. Fibre pit holes, which impose a significant capillary pressure while drying, are modelled as circular holes in a tube. The calculations are undertaken by coupling the analytical solution for buckling a circular tube to numerical solutions of the Young-Laplace equation. This elasto-capillary model elucidates the influences of wetting angle, tube-wall flexibility, and hole size on the tube deformation. In experiments, flexible silicon-rubber tubes with a hole in the wall are filled with liquid, and the internal pressure is measured while withdrawing this fluid, thus mimicking evaporation during the drying of wood fibres. The results prove that capillarity can collapse the fibre lumen, either partially or completely, depending principally on the fibre-wall flexibility. [ABSTRACT FROM AUTHOR]

This paper deals with the determination of approximate solutions for a model of column buckling using two efficient and powerful methods called He's variational approach and variational iteration algorithm-II. These methods are used to find analytical approximate solution of nonlinear dynamic equation of a model for the column buckling. First and second order approximate solutions of the equation of the system are achieved. To validate the solutions, the analytical results have been compared with those resulted from Runge-Kutta 4th order method. A good agreement of the approximate frequencies and periodic solutions with the numerical results and the exact solution shows that the present methods can be easily extended to other nonlinear oscillation problems in engineering. The accuracy and convenience of the proposed methods are also revealed in comparisons with the other solution techniques. [ABSTRACT FROM AUTHOR]