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The collapsible tubular mast (CTM) can be compactly folded for transport and deployed in orbit to serve as a key structural element. Once deployed, the CTM is vulnerable to buckling under axial load and bending moments, compromising its load-bearing capacity. The intricate relationship between the CTM's cross-section and its buckling behavior poses a significant challenge for designers. This is due to the ultra-thin nature of the CTM, which gives rise to highly localized buckling modes rather than global ones. To overcome this challenge, we developed surrogate models using a neural network (NN) trained with data from finite element analysis (FEA). These NN-based surrogate models provide high computational accuracy in predicting nonlinear buckling loads under axial force and bending moments around the two principal axes of the CTM's cross-section, achieving R 2 values of 0.9906 , 0.9987 , and 0.9628 , respectively. These models also significantly improve computational efficiency, reducing prediction time to a fraction of a second compared to several minutes with FEA. Furthermore, the NN-based surrogate models enable the usage of the non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization (MOO) of the CTMs. These models can be integrated in the NSGA-II algorithm to evaluate the objective function of existing and new individuals until a set of 1000 non-dominated solutions, i.e., cross-sectional configurations optimizing buckling performance, is identified. The proposed approach enables the design of ultra-thin CTMs with optimized stability and structural integrity by promoting design decisions based on the quantitative information provided by the NN-based surrogate models. [ABSTRACT FROM AUTHOR]

To meet the complex and diverse demands for low-stress mechanical measurements of fabrics and other flexible materials, two integrated multidimensional force sensors with the same structure but different ranges were explored. They can support both rapid and precise low-noise, high-precision, low-cost, easy-to-use, reliable, and intelligent solutions for the complex measurement of fabric mechanics. Having analysed the mechanical relationship of the parallel beam theory, and considering the specific requirements of fabric measurement, a novel multi-dimensional force sensor is designed, capable of measuring tensile, shear, and buckling properties. Finite element analysis is used to simulate the mechanical performance of this sensor for fabric-loading/unloading measurement, and the sensitivity of the mechanical quantity transfer, the amount of sensor deformation, the stress distribution, and the degree of inter-dimensional coupling have been investigated and verified. The basis for subsequent digital processing is achieved by a low-offset, low-temperature-drift, low-power-consumption analogue front end, 24-bit ADC circuit, and signal conditioning electronics, suitable for the measurement of fabric mechanics under low stress, which is like the end-user requirements. The sensor information channel is supported by a host microcontroller with a DSP and a floating-point processing instruction set. Information processing is performed in time-sharing with the support of a multitasking real-time operating system. The purpose of designing this sensor is to facilitate the development of a new testing instrument, which will adopt the advances of current instruments whilst eliminating their shortcomings. [ABSTRACT FROM AUTHOR]

This study primarily focuses on the buckling behavior of wave-shaped pressure hulls subjected to uniform external pressure. The effect of slant angle on the buckling behavior of hulls was examined. The tested slant angles ranged from 0° to 30° and were increased at 1° increments. The buckling of smooth cylindrical pressure hulls and wave-shaped pressure hulls was investigated using numerical methods. A wave-shaped pressure hull was produced for experimental verification. The nonlinear numerical results aligned with the collected experimental data. The buckling load of the tested wave-shaped pressure hull was approximately 1.87 times that of the equivalent cylindrical pressure hull. Furthermore, a formula was developed to estimate the load-bearing capacity of the wave-shaped pressure hull. This formula, which has been experimentally validated, comprises a correction coefficient (obtained through numerical evaluation and regression analysis) and a classic semi-analytical formula for cylindrical pressure hulls. [ABSTRACT FROM AUTHOR]

This study investigates the structural behavior of a particular mechanical joint subjected to bending and perturbation and the selection of overlapping lengths for this CHS structure arrangement. We began this research by meticulously validating the methodology through a rigorous replication of a prior experimental study, establishing its reliability as a solid foundation. Subsequently, the process was applied to pile-in-pile (PIP) slip joints with varying overlapping lengths. The primary aim was to determine the optimal overlapping length, a critical parameter in this analysis, encompassing the evaluation of stiffness, bending capacities, and joint efficacy. These investigations reveal a clear correlation between increasing overlapping length and heightened joint stiffness. An optimal overlapping length that strikes a harmonious balance between stiffness, bending capacity, and joint efficiency was identified. These findings hold substantial promise for enhancing the joint design of tubular sections, particularly within the context of wind-turbine structures. Using this novel joint can be promising in increasing the efficiency and reliability of CHS structures in future construction and performance. [ABSTRACT FROM AUTHOR]

A new utilization of entropy in the context of buckling is presented. The novel concept of connecting the strain energy and entropy for a pin-ended strut is derived. The entropy of the buckling mode is extracted through a surrogate model by decomposing the strain energy into entropy and virtual temperature. This concept rationalizes the ranking of buckling modes based on their strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all the modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of the buckling modes that coincide with the measurement of the initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for a given energy roughly decreases with the inverse square of the mode index. For practical engineering, this study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics. [ABSTRACT FROM AUTHOR]

This study investigates the elastic buckling behavior of Functionally Graded Material (FGM) thin skew plates featuring a circular opening. FGMs, known for their unique property gradients, have gained prominence in structural engineering due to their mechanical performance and durability. Including a circular opening introduces a critical geometric consideration, influencing the structural stability and load-carrying capacity of FGM plates. The study examines the effects of the skew angle, plate's aspect ratio, opening position, and size on the critical buckling load, normalized buckling load, and various buckling failure modes through computer modeling and finite element analysis. The results offer valuable insights into the interplay between material heterogeneity, geometric configuration, and structural stability. For instance, the critical buckling load increases by 29%, 82%, and 194% with an increment in skew angle from 0° to 30°, 45°, and 60°, respectively. Moreover, as the opening shifts from the plate's edge closer to the center, the critical buckling load decreases by 26%. The critical buckling load is also dependent on the power index, as an increase in the power index from 0.2 to 5 reduced the buckling load by 1698 kN. This research contributes to the advancement of our understanding of FGM thin plates' behavior under skew loading conditions, with implications for the design and optimization of innovative structures. The findings presented provide a foundation for further exploration of advanced composite materials and their applications in structural engineering. [ABSTRACT FROM AUTHOR]

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. [ABSTRACT FROM AUTHOR]

A parametric investigation of several unbraced steel frames with regular and irregular geometry subjected to elevated temperatures is carried out in this study to determine the most accurate procedure and buckling lengths to be considered during the structural design under a fire situation. In such conditions, the stiffness and strength of steel decrease considerably due to high temperatures, and uncertainty remains in the application of the fire design rules of Eurocode 3 Part 1-2 (EN 1993-1-2) for unbraced frames as no information is given regarding the treatment of the deformed geometry (the so-called second-order effects). More precisely, it is unclear in the norm whether the verification based on the buckling length concept could be used or if a second-order analysis to calculate the internal forces is sufficient to ensure the stability of the frame in case of fire. Based on the linear buckling analysis of the steel frames accounting for the temperature development during a fire, recommendations for the appropriate buckling lengths to be used are given. Finally, it is demonstrated that using the recommended buckling lengths together with the design rules of EN 1993-1-2 leads to results in favor of safety when compared to the results obtained with the finite element method. On the other hand, it is concluded that using second-order internal forces and the real length of the columns as the buckling length, as suggested for room temperature design, yielded results outside safety when compared with the finite element method, and this analysis and verification procedure should not be used for the case of fire. [ABSTRACT FROM AUTHOR]

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

A bimetallic steel bar (BSB) consisting of stainless-steel cladding and carbon steel substrate exhibits excellent corrosion resistance and good mechanical properties. The bimetallic structure of BSBs may affect their low-cycle fatigue performance, and current investigations on the above issue are limited. In this study, the low-cycle fatigue properties of bimetallic steel bars (BSBs) with inelastic buckling were investigated. Experiments and numerical studies were conducted to investigate the low-cycle fatigue capacity for BSBs, considering buckling. The buckling mode of BSBs is discussed. The hysteretic loops and energy properties of BSBs with various slenderness ratios (L/D) and fatigue strain amplitudes (εa) are investigated. With increases in the L/D and εa, the original symmetry for hysteresis loops disappears gradually, which is caused by the buckling. A predictive equation revealing the relation between the εa and fatigue life is suggested, which considers the effects of the L/D. A numerical modelling method is suggested to predict the hysteretic curves of BSBs. The effect of buckling on the stress and energy properties of BSBs is discussed through the numerical analysis of 44 models including the effects of the L/D, εa, and cladding ratios. The numerical analysis results illustrate that the hysteresis loops of BSBs with various εa values exhibit similar shapes. The increase in the cladding ratio reduces the peak stress and the dissipated energy properties of BSBs. The hysteresis loop energy density decreases by about 3% with an increase of 0.1 in the cladding ratio. It is recommended that the proportion of stainless steel inBSBs should be minimized once the corrosion resistance requirements are met. [ABSTRACT FROM AUTHOR]

The buckling failure of the afterburner cylinder is a serious safety concern for aero-engines. To tackle this issue, the buckling simulation analysis of the afterburner cylinder was carried out by using finite element method (FEM) software to obtain the buckling mode and critical buckling loads. It was found that the afterburner cylinder was susceptible to buckling when subjected to differential pressure or the compressive force of the rear flange. Buckling would occur when the differential pressure reached 0.4 times the atmospheric pressure or when the axial compressive force on the rear flange reached 222.8 kN. Buckling was also found at the front of the cylinder under the auxiliary mount load. Additionally, under various loads on the rear flange, buckling occurred in the rear section, with the buckling mode being closely related to the load characteristics. Based on the simulation results and structural design requirements, two structural improvements were proposed, including the wall-thickening scheme and the grid reinforcement scheme. FEM simulation analysis results showed that both schemes would improve the rigidity and stability of the afterburner cylinder. For the 0.3 mm increase in the wall thickness scheme, the critical buckling load increased by 17.86% to 66.4%; for the grid reinforcement scheme, the critical buckling load increased by 169% to 619%. Therefore, the grid reinforcement scheme had a stronger anti-buckling ability and was deemed the optimal solution. The findings of this paper could provide technical support for the structural design of large-sized and thin-walled components of aero-engines. [ABSTRACT FROM AUTHOR]

By experimental methods, 26 specimens were designed to conduct elastic and elastic–plastic buckling tests on cylindrical shells containing cracks. This study discusses the influence of factors such as the length–diameter ratio, the diameter–thickness ratio, the crack length, the inclination of the crack, etc., on the buckling load. Additionally, finite element models were established to compare with experimental results. For the PMMA cylindrical shell, the results showed that as the length–diameter ratio of the cylindrical shell increased, the buckling load first decreased and then increased. For the 6063 aluminum alloy cylindrical shell, with increasing length–diameter ratio, diameter–thickness ratio, and crack length of the cylindrical shell, the buckling load decreased accordingly. However, concerning the crack inclination, as the crack inclination increased, the buckling load increased accordingly. This indicates that the larger the crack inclination, the higher the load capacity of the cylindrical shell containing cracks. Through finite element simulations of cylindrical shells with cracks, it was found that through compressive mechanical properties, both elastic and elastic–plastic buckling loads yielded results that are closer to the experimental results. Additionally, the inclusion of contact effects in numerical simulations further improved the agreement with the experimental results, and the variation trend of the buckling load in the finite element simulation was consistent with the experimental results. The research findings provide valuable references for the assessment of load capacity in structures containing cracks. [ABSTRACT FROM AUTHOR]

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

A buckling defect will appear on the outer surface of the deformed ring during the constrained ring rolling (CRR) of an aluminum alloy thin-wall conical ring with inner high ribs (AATWCRIHR) if the geometrical dimension of the ribs does not match the wall thickness. To avoid the buckling defect, a quantitative method for characterizing the degree of the buckling defect is proposed using the area of the buckling profile. Then, an orthogonal experimental scheme was designed, taking the width of the middle rib, thickness of wall, and height of the middle rib as the design variables and defining the area of the buckling profile as the optimization objective. Subsequently, a quadratic polynomial response surface model was established by combining the optimization algorithm with the finite element method (FEM), and the geometrical dimension of the middle ribs of the deformed AATWCRIHR is optimized. Moreover, the optimal parameter combination to minimize the area of the buckling profile is obtained and verified using FE simulation. The results show that the AATWCRIHR after optimization does not generate the buckling defect during constrained ring rolling, and it is proven that the quantitative buckling defect representation method and the optimization design method based on the response surface model and the finite element simulation results are feasible for the constrained ring-rolling process of the AATWCRIHR. [ABSTRACT FROM AUTHOR]

This study presents a numerical investigation into the adhesion strength of micro fibrillar structures, incorporating statistical analysis and the effects of excessive pre–load leading to fibril buckling. Fibrils are modeled as soft cylinders using the Euler–Bernoulli beam theory, with buckling conditions described across three distinct states, each affecting the adhesive properties of the fibrils. Iterative simulations analyze how adhesion strength varies with pre–load, roughness, number of fibrils, and the work of adhesion. Roughness is modeled both in fibril heights and in the texture of a rigid counter surface, following a normal distribution with a single variance parameter. Results indicate that roughness and pre–load significantly influence adhesion strength, with excessive pre–load causing substantial buckling and a dramatic reduction in adhesion. This study also finds that adhesion strength decreases exponentially with increasing roughness, in line with theoretical expectations. The findings highlight the importance of buckling and roughness parameters in determining adhesion strength. This study offers valuable insights into the complex adhesive interactions of fibrillar structures, offering a scalable solution for rapid assessment of adhesion in various rough surface and loading scenarios. [ABSTRACT FROM AUTHOR]

The effects of initial small-scale material nonlinearity on the pre-yield and pre-buckling response of externally pressurized metallic (plane strain) perfect rings (very long cylindrical shells) is investigated. The cylindrically curved 16-node element, based on an assumed quadratic displacement field (in surface-parallel coordinates) and the assumption of linear distribution of displacements through thickness (LDT), is employed to obtain the discretized system equations. The effect of initial small-scale material nonlinearity (assumed hypo-elastic) on the deformation and stress in the pre-yield and pre-buckling regime of a very long relatively thin metallic cylindrical shell (plane strain ring) is numerically investigated. These numerical results demonstrate that the enhanced responses for metallic rings due to initial small-scale nonlinearity are significant enough to not miss attentions from designers and operators of submersibles alike. [ABSTRACT FROM AUTHOR]

This paper concerns the Eurocode 3 Part 1-3 (EN 1993-1-3) methods for calculating the distortional buckling (bifurcation) load of cold-formed steel-lipped channels subjected to axial force, major and minor axis bending. More specifically, the paper presents the results of a parametric study that assesses the accuracy of the simplified method in EN 1993-1-3, which relies on direct/iterative hand calculations and an approximate mechanical model, through comparison with "exact" numerical results, obtained using semi-analytical linearized buckling analyses based on Generalized Beam Theory, which are also allowed by the code. Isoline error maps are presented for a wide range of geometric and material parameters, covering common commercial profiles and corresponding to a dataset of more than 24,000 cases. These maps make it possible to identify the parameter ranges leading to an acceptable error and, even though they strongly depend on the loading, general remarks concerning the expected error pertaining to the simplified method are drawn. [ABSTRACT FROM AUTHOR]

The absence of analytical expressions in current codes for evaluating the critical moment for lateral–torsional buckling of cold-formed beams with omega-shaped sections presents a fundamental challenge when assessing their resistance to global buckling. In response to this challenge, a comparative study was conducted to explore various approaches for calculating the critical moment. This involved both analytical and numerical analyses, using different methods available in codes and computational tools. The analytical analysis followed the Effective Width Method, employing the expression proposed in ENV 1993-1-1:1992, which is commonly used for evaluating the critical lateral–torsional moment of hot-rolled profiles. Numerical analyses were then performed using the ABAQUS v6.13, GBTUL v2.0, and CUFSM v5.05 software packages. The ABAQUS model, validated with results obtained from an experimental campaign, serves as the reference model. Upon assessing the bending moment resistances according to European, Brazilian, and American standards, consistency was found among these standards. However, it became evident that using the analytical expression proposed for hot-rolled profiles is inadequate for evaluating the critical lateral–torsional moment of CFS omega-shaped profiles. Conversely, the agreement between the ABAQUS, GBTUL, and CUFSM results suggests their utility as reliable tools for estimating the elastic critical lateral–torsional buckling moment. [ABSTRACT FROM AUTHOR]

In steel structures, skew thin steel plates serve as panel zones in structures spanning large spaces (e.g., warehouses and gymnasiums). Considerable research has been conducted on the shear buckling of panels due to seismic loads acting on a structure. Conversely, under snow or wind loads, the panel zone may experience compressive and tensile stresses simultaneously from two directions. Considering the economic preference for thin steel plates, evaluating the elastic critical local buckling stresses in the panel zone under biaxial normal stress may provide essential information to structural engineers. In this study, an elastic buckling analysis based on the energy method is performed to clarify the impact of panel geometry and boundary conditions on the elastic local buckling stresses of skew panel zones. As confirmed from the results, the local buckling stresses calculated using the energy method were consistent with those determined using finite element analysis. The findings indicate that a skew angle of up to 30° marginally affects the elastic buckling stress under uniaxial stress. Consequently, engineer-friendly design formulas were developed based on these findings. Comparisons with previous research demonstrated that the buckling loads reported were generally higher than those determined by finite element analysis. The study also established the correlation of the buckling stresses under biaxial stresses, which implied that the skew angle posed minimal influence on buckling stress for skew plates under biaxial stress. Additionally, a method for evaluating this correlation was presented. Engineers can utilize the provided design equations to more efficiently and accurately calculate buckling loads, facilitating a safer and more economical design of structures with skew plates. [ABSTRACT FROM AUTHOR]

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

In order to evaluate the reliability of cracked cylindrical shell effectively and reasonably, study the load capacity of cracked structures and understand the failure modes of cracked structures, in this paper the finite element method is adopted for cylindrical shells with mixed mode crack. The finite element models of cylindrical shell with an inclined through crack under external pressure were established by finite element method, the elastic and elastic-plastic buckling loads were calculated. The influences of crack length (c), crack angle (θ), cylindrical shell length-radius ratio (L/R), radius-thickness ratio (R/T), boundary conditions on buckling load were explored. The analysis of cracked cylindrical shells with simple support on buckling load shows that the load bearing capacity of cracked cylindrical shells decreases with the increase of length- radius ratio, radius-thickness ratio and crack inclination angle. The increase of crack length can weaken the bearing capacity of cylindrical shell. The variation of elastic-plastic buckling load is consistent with that of elastic buckling load. Under the clamped support, the variation of buckling load is consistent with the buckling load of cracked cylindrical shell with simple support, and the buckling load of cracked cylindrical shell with clamped support is evidently higher than that of simple support. The post-buckling analysis further shows that the changes of crack inclination angle and crack length do not affect the variation modes of pre-buckling and post-buckling deformation of cracked cylindrical shells, but affect the load capacity. The relationship between buckling load of different boundary conditions (simply supported and clamp-supported) and geometrical parameters (length-radius ratio, radius-thickness ratio, crack length and crack Angle) was obtained by nonlinear regression. The results of solution can predict the buckling load of cylindrical shell with an inclined through crack. [ABSTRACT FROM AUTHOR]

Background: The diagnosis of anterior cruciate ligament (ACL) tear relies on clinical evaluation and magnetic resonance imaging (MRI). Direct and indirect signs of ACL tear have been described with MRI evaluation. Posterior cruciate ligament (PCL) buckling has been described as an indirect radiographic sign of an ACL tear. Purpose: The aim of the present study was to assess the variations in PCL buckling angles in patients with ACL tears and in patients with isolated lesions in the posterior horn of the medial meniscus. In addition, the influence of different patterns of medial meniscus tears in ACL-deficient knees was investigated. Finally, the influences of risk factors such as tibial slope, delay from injury to surgery, absence of medial meniscus tear, degree of Lachman and pivot shift testing were also assessed. Study design: This was a cohort study. Methods: A total of 154 patients (78 in the group with ACL tear and 76 in the control group) were assessed with MRI and lateral weight-bearing X-ray to assess PCL buckling angle and tibial slope by two independent observers. The presence of a medial meniscus bucket handle or ramp lesion of the medial meniscus was assessed and recorded at the time of surgery. Results: PCL buckling angle measurement was highly reliable, with an ICC of 0.866 and 0.894, respectively, in the study group and the control group for interobserver reliability. The intrarater reliability was found to be high in PCL buckling angle for the study group [ICC = 0.955] and the control group [ICC = 0.943]. The mean angle in patients with ACL tear was 110.7 ± 15.2° and 115.3 ± 16.2° (for the two examiners) and 111.4 ± 12° and 114 ± 14.5° (for the two examiners) in patients with an intact, healthy ACL. An association emerged between bucket handle tears of the medial meniscus (p = 0.010) and a decreased PCL buckling angle and between ramp lesions of the medial meniscus and increased PCL buckling angle both (p = 0.024). Conclusions: Good inter- and intraobserver reliability for the measurement of the PCL buckling angle was observed. Increased PCL buckling angle values were observed in patients with concomitant ACL and bucket handle tears of the medial meniscus, while decreased angle values were observed in those who had ACL tear and ramp lesion of the medial meniscus. No statistically significant difference in the PCL buckling angle emerged between patients with ACL tears and those who had a healthy, intact ACL. [ABSTRACT FROM AUTHOR]

In an experimental study of two-branched beams bent transversely about the major stiffness axis, the elastic critical load from the lateral-torsional buckling condition was determined. The tests were conducted on simply supported two-branch beam models with a built-up section consisting of two cold-formed channel members (2C) bolted back-to-back. The bolts were located at the mid-height of the built-up cross-section. Five groups of members differing in longitudinal bolt spacing were examined. The models were gravitationally loaded (using ballast) at the centre of the beam span. This approach eliminated the undesirable effect of the lateral support of the beam, e.g., by the actuator head. The critical load, measured by the concentrated transverse force (Pz,cr), was determined using the modified Southwell method. It has been experimentally shown that, in built-up beams, there is an influence of bolt spacing on the elastic critical load from the lateral-torsional buckling condition. The lowest critical load capacity and the most non-linear behaviour of the built-up member were observed in beams bolted with only three bolts (at the supports and in the middle of the span). However, the experimental results obtained in this study show that increasing the number of bolts above a certain level (in the case of the tested models, it was seven bolts) does not result in a further increase in the critical load, which is a surprising result. The obtained values were 15 to 23% lower than the critical load determined numerically by the finite element method (LTBeamN) for an analogous element with a uniform I-section. [ABSTRACT FROM AUTHOR]

The design of non-buckling interconnects with thick sections has gained important applications in stretchable inorganic electronics due to their simultaneous achievement of high stretchability, low resistance, and low heat generation. However, at the same time, such a design sharply increased the tensile stiffness, which is detrimental to the conformal fit and skin comfort. Introducing the fractal design into the non-buckling interconnects is a promising approach to greatly reduce the tensile stiffness while maintaining other excellent performances. Here, a hierarchical theory is proposed for the tensile stiffness of the non-buckling fractal-inspired interconnects with an arbitrary shape at each order, which is verified by the finite element analysis. The results show that the tensile stiffness of the non-buckling fractal-inspired interconnects decreases with the increase in either the height/span ratio or the number of fractal orders but is not highly correlated with the ratio of the two adjacent dimensions. When the ratio of the two adjacent dimensions and height/span ratio are fixed, the tensile stiffness of the serpentine fractal-inspired interconnect is smaller than that of sinusoidal and zigzag fractal-inspired interconnects. These findings are of great significance for the design of non-buckling fractal-inspired interconnects of stretchable inorganic electronics. [ABSTRACT FROM AUTHOR]

Size-dependent functionally graded material thin plate buckling and post-buckling problems are considered using the framework of the MCST (Modified Couple Stress Theory). Based on modified couple stress theory and power law, the post-buckling deflection and critical buckling load of simply supported functionally graded material thin plate are derived using Hamilton's minimum potential energy principle. The analysis compares the simulation results of linear buckling and nonlinear buckling. Innovatively, a power-law distribution with scale effects is considered. The influences of scale effect parameters l and power-law index parameters k on buckling displacement, load, and strain energy of plates have been investigated. In this article, it is found that the critical buckling displacement, critical buckling load, and buckling strain energy increase with increases in the power-law index parameters k. The membrane energy decreases as the power-law index parameter increases. If the upper and lower layers are swapped, the opposite result is obtained. In comparison, the scale effect parameter is more influential than the power-law exponent. The critical buckling displacement in the x-direction is not affected by scale effects. The critical buckling load, the membrane energy, and buckling strain energy increase as the scale effect parameter increases. Scale effects increase material stiffness compared with traditional theory, and the power-law index parameters affect FGM properties such as elastic modulus, Poisson's ratio, density, etc. Both scale effects parameters and power-law index parameters have important effects on the mechanical behavior of materials. [ABSTRACT FROM AUTHOR]

Transversely loaded beam grillages are quite often used in industrial construction. In order to produce a safe design of such structures, it is necessary to account for the lateral torsional buckling phenomenon, which reduces load-bearing capacity. To be able to calculate the relevant reduction factor, the elastic critical load must be determined. As regards the existing design practice for such structures, simplified conditions are assumed for the mutual restraint of the component beams. However, this approach does not correspond to reality. This study discusses the results of numerical investigations and analytical calculations concerning the effect of the elastic action of simple beam grillage (SBG) joints on the critical load, which results from the lateral torsional buckling (LTB) condition. The SBG was defined as a flat system of interconnected beams, unstiffened laterally and loaded perpendicularly to the grillage plane. The analysis covered H-shaped grillages with different span ratios of component beams, in which the main (coupling) beam was decisive for instability. The effectiveness of the use of closed-section stiffeners at the grillage joints was also investigated. The grillage elastic critical resistances (ECR) were determined for two variants of joint stiffening. The computations were performed by means of FEM numerical simulations. The spatial models were discretised with the following elements: (1) solid ones in Abaqus, (2) shell ones in ConSteel, and (3) thin-walled bars in ConSteel. The LTB critical moments of the weakest beam (critical beam), elastically restrained against warping and against lateral rotation (in the LTB plane), were computed using the analytical methods developed by the authors. To this end, the methods were proposed to determine the indexes of the critical beam elastic restraint in the adjacent stiffening beams. In the study, it was demonstrated that (1) taking into account the conditions of mutual elastic restraint and interaction of the component beams provides a more accurate assessment of the grillage ECR, (2) the use of closed-section stiffeners in the grillage joints increase the ECR compared with classic flat stiffeners, (3) the grillage ECR can be estimated based on the critical moment Mcr of the weakest beam (critical beam) when the conditions of its elastic restraint in joints are accounted for. [ABSTRACT FROM AUTHOR]

The formed-in-place pipe (FIPP) is a trenchless technology used for pipeline rehabilitation. It is a folded PVC pipe that expands through thermoforming to fit tightly inside the host pipe. However, the deficiencies during the construction of FIPP liners such as insufficient inflation, pipe misalignment and initial deformation will lead to elliptical deformation of the FIPP liner, which affects the load-bearing performance of the liner and makes it susceptible to buckling failure. In this paper, the buckling behavior of loosely fitted FIPP liners under uniform external pressure was investigated by the external pressure resistance test and finite element model. The pre- and post-buckling equilibrium paths verified the finite element model. The results indicated that the value of the dimension ratio will significantly reduce the critical buckling pressure. With the increasing value of liner major axis ratio to host pipe, the reduction effect on the critical buckling pressure caused by the increase in the ovality will diminish. Different values of liner major axis ratio to host pipe and ovality changed the range of the detached portion, which affected the critical buckling pressure. The parametric studies modified the design model from ASTM F1216, which was established to predict the critical buckling pressure of a loosely fitted FIPP liner and reduced the average difference rate from 23.43% to 5.52%. [ABSTRACT FROM AUTHOR]

This study aims to investigate the local elastic buckling behavior of simply-supported prismatic web plates under pure shear loading. Comprehensive finite element analysis is conducted to analyze the effects of various geometric parameters, such as tapering ratio, aspect ratio, and web slenderness, on the local elastic buckling behavior with simply-supported boundary conditions. An eigenvalue analysis is conducted to determine web plates' natural frequencies and corresponding shape modes with varying geometric parameters. Particular attention is given to the effect of the slenderness ratio, since current formulas do not consider the impact of the slenderness ratio on the elastic shear buckling coefficient. A sensitivity analysis is conducted to examine the importance of the web slenderness ratio for estimating the critical buckling coefficient of a prismatic plate under pure shear loading. Finally, a formula of the elastic local critical buckling coefficient for a simply-supported prismatic web considering the web slenderness effect is proposed, which can be used in international codes. [ABSTRACT FROM AUTHOR]

A thin-walled steel cylindrical shell is a common engineering structure that has an efficient load-carrying capacity. This structure is more easily subjected to partial axial compression loads in application, and buckling is the main failure mode. However, there are few available design methods for partial axially compressed steel cylindrical shells. Motivated by this, a design method called the localized perturbation load approach (LPLA) is proposed in this paper. The finite element framework for the application of LPLA is established. The location and number of perturbation loads are determined by considering the imperfection sensitivity and the buckling failure mode of partial axial compressed cylinders. A series of buckling experiments are carried out to validate the LPLA method. In addition, the reliability of LPLA for the design of cylindrical shells with different imperfection locations and dimensions is also verified. The results show that LPLA can give conservative and reliable lower-bound buckling loads. Therefore, LPLA can be used as a design method for thin-walled steel cylindrical shell structures under partial axial compression in actual engineering. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of an open hole on the stability of a compressed laminated composite plate. The study was carried out in two ways: using experimental tests and numerical analysis. As a result of the experiment, the buckling form and path of the plate were recorded. The form of buckling was determined using the ARAMIS non-contact measurement system. The critical load value was determined from the working path using the approximation method. The experimental results were verified by numerical analysis based on the finite element method. FEM investigations were carried out in terms of a linear eigenproblem analysis. This allowed the bifurcation load and the corresponding buckling form of the numerical model of the plate to be determined. Investigating the effect of the hole in the compressed plate at a critical state showed high agreement between the proposed test methods. No clear effect of the hole size on the buckling of the plate was observed. In contrast, a clear effect of the hole on the critical load value was determined. The maximum decrease in the critical load value was 14%. The same decrease was observed for the stiffness of the post-critical characteristics. It was shown that the [45|−45|90|0]s composite plate had more than three times lower strength compared to [0|−45|45|90]s and [0|90|0|90]s. The novelty of this article is the development of a research methodology based on new interdisciplinary research methods for describing the influence of the central hole on the stability of compressed composite plates. The ABAQUS system was used for the numerical analysis. [ABSTRACT FROM AUTHOR]

Rail transport is expected to become a key component in the development of a long-term sustainable transport system. The planning, construction, operation, and maintenance of railway infrastructure are crucial in this effort. Hence, it is essential to ascertain that the railway infrastructure withstands and is adapted to extreme weather conditions and climate change. This study focuses on evaluating climate adaptation measures for lateral track buckling in Sweden. Through a literature review and interview with an expert at Swedish Transport Administration, it is highlighted that the maintenance status of railway infrastructure plays a significant role in the occurrence of lateral track buckling. According to the expert, inadequate track maintenance is the primary cause of lateral track buckling rather than weather variables like air temperature. The interview also clarifies that the chain of events related to the handling of track buckling is mainly initiated by the observation of a discrete lateral irregularity by a train driver, whereupon the train dispatcher at the traffic management center stops traffic until the location in the track has been inspected by a track entrepreneur. During the inspection, up to half of the observed cases of track buckling turn out to be false. [ABSTRACT FROM AUTHOR]

The local buckling behavior of welded square box section columns subjected to pure compression is investigated. Local buckling represents a crucial failure mode in thin-walled structures, exerting a significant impact on their overall stability and load bearing capacity. The primary objective of this research is to perform an extensive literature review considering the theoretical background of buckling phenomena and encompassing key findings and methodologies reported in previous studies. Additionally, the development and validation of a novel numerical model is presented, capable of accurately predicting the ultimate buckling capacity. Two different calculation methods are applied in the present study: (i) a numerical model using equivalent geometric imperfections to cover the residual stresses and out-of-straightness of plates, (ii) realistic geometric imperfections combined with an assumed residual stress pattern which has an experimental-based background. The objective of the numerical investigation is to investigate the accuracy of the numerical model by using different residual stress and imperfection patterns taken from the international literature. Many test results are collected from the international literature, to which the computational results are compared, and the effect of the residual stresses and geometric imperfections are analyzed. Based on the numerical analysis, the accuracy of the imperfection models is assessed and the imperfection model leading to the most accurate resistance is determined. The calculated buckling capacities are also compared to analytical design approaches, in which accuracy is also analyzed and evaluated. The current investigation proved the buckling curve developed by Schillo gives the most accurate results to the numerically calculated buckling resistance. [ABSTRACT FROM AUTHOR]

The local buckling of I-section beams is investigated with the flange–web interactions taken into account. Using numerical results employing the finite element method and a semi-analytical method, the flange–web interactions of I-sections and their effects on the buckling stresses are explored and discussed. Simple approximate solutions for the buckling coefficients of the web and compressive flange are developed using the energy method, and they are refined using the numerical results. Using the simple solutions for buckling coefficients, the limits for the width-to-thickness ratio of the compressive flange and web of I-section beams are then proposed. Comparisons with the results of existing solutions and provisions in design codes imply that the proposed solutions are superior in predicting the limits for width-to-thickness ratios, and they are capable of accounting for the flange–web interactions at the local buckling of I-section beams. [ABSTRACT FROM AUTHOR]

The design and development of a wing for a completely brand-new aircraft represents, in aeronautics, one of the highest challenges from an engineering point of view. The present work describes a novel methodology devoted to execute numeric simulation in a non-linear post-buckling regime to verify the composite wing compliance under the design load conditions. The procedure was developed as part of a wing design and research activity and was motivated by the need to have more realistic results, without standard conservatisms like the no-buckling up to ultimate load, to be of use for achieving further weight savings. To carry this out, it was obviously necessary to ensure that the structural integrity was also guaranteed in the post-buckling regime, above the limit load, and therefore in a highly non-linear regime. The present work illustrates a numerical approach based on non-linear finite element analysis which uses the inertia relief option in order to have a more realistic representation of the structural response of the wing in its real context. All that represents a novelty since, at present, the commercial FE codes allow us to use the inertia relief option exclusively for linear analysis. Obviously, the approach can be applied to any other structural component with similar needs. The obtained results show that the differences between linear and non-linear regime are not negligible and, above all, that it is possible to design a wing (or other structural components) considering, at the same time, the large deformation due to the post-buckling regime, the material non-linearities due to the failures and any other non-linearities in order to achieve the challenging weight requirement of the new aircraft generation. [ABSTRACT FROM AUTHOR]

This article compares the results of estimating the buckling capacity of steel spherical shells using simple engineering formulas with the results of selected experimental studies that have been conducted over the past 70 years. It is worth noting that these studies were conducted by research centers from all over the world, and the tested coatings differed in material, manufacturing method, radius R, and thickness t. The test methods, procedures, and measurement tools were also different. The convergence of the results obtained between the proposed simple engineering approach, which is based on the provisions of EN-1993-1-6 and the recommendations in EDR5th, and the experimental studies is satisfactory, and in many cases the results obtained are almost identical. Therefore, it is possible to practically apply the developed algorithms for estimating the buckling capacity of steel spherical shells without worrying too much about the capacity reserve. [ABSTRACT FROM AUTHOR]

This study conducts buckling and free vibration analyses of multi-directional functionally graded sandwich plates subjected to various boundary conditions. Two scenarios are considered: a functionally graded (FG) skin with a homogeneous hard core, and an FG skin with a homogeneous soft core. Utilizing refined plate models, which incorporate a parabolic distribution of transverse shear stresses while ensuring zero shear stresses on both the upper and lower surfaces, equations of motion are derived using Hamilton's principle. Analytical solutions for the buckling and free vibration analyses of multi-directional FG sandwich plates under diverse boundary conditions are developed and presented. The obtained results are validated against the existing literature for both the buckling and free vibration analyses. The composition of metal–ceramic-based FG materials varies longitudinally and transversely, following a power law. Various types of sandwich plates are considered, accounting for plate symmetry and layer thicknesses. This investigation explores the influence of several parameters on buckling and free vibration behaviors. [ABSTRACT FROM AUTHOR]

A beam model for thermal buckling analysis of a bimetallic box beam is presented. The Euler–Bernoulli–Vlasov beam theory is employed considering large rotations but small strains. The nonlinear stability analysis is performed using an updated Lagrangian formulation. In order to account for the thermal effects of temperature-dependent (TD) and temperature-independent (TID) materials, a uniform temperature rise through beam wall thickness is considered. The numerical results for thin-walled box beams are presented to investigate the effects of different boundary conditions, beam lengths and material thickness ratios on the critical buckling temperature and post-buckling responses. The effectiveness and accuracy of the proposed model are verified by means of comparison with a shell model. It is revealed that all of the abovementioned effects are invaluable for buckling analysis of thin-walled beams under thermal load. Moreover, it is shown that the TD solutions give lower values than the TID one, emphasizing the importance of TD materials in beams. [ABSTRACT FROM AUTHOR]

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

For large ships and offshore vessels, structural safety is verified through whole-ship analysis using commercial software. In the case of general oil tankers, classification rules for structural strength evaluation are uniformly applied. Structural strength evaluation is mainly divided into the cargo hold, fore-end, and aft-end parts. For the structural design of a cargo ship, it is important to calculate the design load and determine the thickness and size of the structural member. Structural FEA (Finite Element Analysis) is performed on only the cargo hold range as recommended by the CSR (Common Structure Rule). There is no FE analysis recommendation for either the aft- or the fore-end area. Therefore, structural safety is carried out based on existing design experience and engineer judgment. With previous approaches, it is difficult to clarify the safety of the aft-end part according to external loads such as hull girder load and local pressure. Recently, local buckling damage cases have investigated the aft-end of the shuttle tanker. Although this is a good example, it can be recognized that it is necessary to improve the accuracy of prediction when estimating the structural safety at the aft-end part. In this study, a novel FE-based evaluation methodology about buckling damage is proposed. In order to conduct a structural strength verification based on FE analysis modeling, reasonable solutions for load conditions, boundary conditions, modeling methods, and evaluation criteria are presented. This result is expected to be helpful in examining the structural strength of the aft-end part of similar carriers in the future. [ABSTRACT FROM AUTHOR]

The buckling behavior of rectangular thin plates, which are supported at their four corner points with four edges free, is a matter of great concern in the field of plate and shell mechanics. Nevertheless, the complexities arising from the boundary conditions and governing equations present a formidable obstacle to the attainment of analytical solutions for these problems. Despite the availability of various approximate/numerical methods for addressing these challenges, the literature lacks accurate analytic solutions. In this study, we employ the symplectic superposition method, a recently developed method, to effectively analyze the buckling problem of rectangular thin plates analytically. These plates have four supported corners and four free edges. To achieve this, the problem is divided into two sub-problems and solve them separately using variable separation and symplectic eigen expansion, leading to analytical solutions. Finally, we obtain the resolution to the initial issue by superposing the sub-problems. The current solution method can be regarded as a logical, analytical, and rational approach as it begins with the basic governing equation and is systematically derived without assuming the forms of the solutions. To examine various aspect ratios and in-plane load ratios of rectangular thin plates, which are supported at their four corner points with four edges free, we provide numerical examples that demonstrate the buckling loads and typical buckling mode shapes. [ABSTRACT FROM AUTHOR]

Although a crane is exposed to a wide range of loads, there is a growing need for a lighter, more slender design. As a result, double girder cranes are becoming single girder cranes, aiming to make the steel structure as light as possible. The optimization potential of the classic design as a hollow-box girder is approaching its end. In order to meet today's requirements, a new design was developed, which combines beams with curved panels into a new cross-section to be used as the crane's main girder. Compound cross-sections pose a challenge for the mechanical engineer as there are usually no comparative data available and designing using numerical methods is complex. For this reason, a scaled model was abstracted for which a load determination will be carried out in 2024. This article deals with the finite element calculations for the design of the test specimen. A global numerical analysis was used to determine the buckling load, and several imperfection patterns were investigated. The results revealed that the buckling loads are similar to each other. This finding may lead to the conclusion that the most damaging imperfection pattern has yet to be found, which supports the need for an accompanying series of tests. [ABSTRACT FROM AUTHOR]

Submarine pipelines are prone to developing flaws, such as ellipticity and depression during the manufacture, burying, and use processes. The local buckling characteristics of submarine pipelines with initial imperfection must be studied since the initial imperfection have an impact on local pipeline buckling. In this study, the local buckling of submarine pipelines with varying depression depths and ellipticity is simulated using the finite element program ABAQUS, and defect sensitivity of submarine pipelines with varying shape ellipticity, varying depression depths, and varying pipe radius-thickness ratios is examined. Meanwhile, research is being conducted on the combined load buckling of a submarine pipeline with initial imperfection caused by bending, axial force, and external hydrostatic pressure. The results indicated that the critical external pressure of the pipeline is sensitive to the imperfection, although the buckling propagation pressure is not. The buckling morphology is influenced by the shape and size of the imperfection. Additionally, the ability to withstand external hydrostatic pressure of the pipeline reduces after it has been bent. [ABSTRACT FROM AUTHOR]

At the initial stage of design, the structural strength and stability of the load-bearing structural members of the aircraft are mainly considered. In this paper, the structural strength and stability of a support of aircraft assembly are analyzed. First, structural strength analysis, under the design load of 30.151 KN, and numerical analysis shows that, in the stress concentration area, the stress peak value is 571.9 Mpa. The experimental value of the strain sensor S6 position is compared with the numerical results, and the error is within 2.5%, which verifies the validity of the numerical model and the structural strength to meet the design requirements. Second, structural stability adopts the method of buckling analysis. Linear buckling analysis shows that the first six order buckling modes and critical loads. The first order critical load is 464.9 KN. Risk arc length method is used in the nonlinear buckling analysis. Considering the geometric imperfection of the support, 1% and 10% initial imperfection values are used. Nonlinear buckling critical load values—without imperfection and considering the initial imperfection—are obtained, which are 110.6 KN, 108.4 KN, and 106.2 KN, respectively. There is little difference between the three values, indicating that the geometric imperfection of the support is not obvious to the nonlinear buckling, and they have structural stability. In the case of no imperfection, the maximum deformation of the main area reaches 21.4 mm, and the support enters the instability state. This paper comprehensively discusses the results of structural strength and structural stability analysis, which can provide reference for the design and optimization of bearing components. [ABSTRACT FROM AUTHOR]

Flexible pipe is one of the most important types of equipment applied in the deep-water development of oil and gas and deep-sea metal mining. The carcass of an unbonded flexible pipe with a typical interlocked structure prevents buckling failure under external hydrostatic pressure. The process and principle of carcass layer deformation are described, and a three-dimensional finite element model with solid-shell elements is developed to simulate the cold forming process of a metal strap subjected to a series of rollers. The deflection and deformation behavior in the bend-rolling and interlocking process are investigated, and the residual stress due to deformation is calculated. Taking the carcass layer of a 4-inch internal diameter flexible pipe as an example, a three-dimensional finite element model of the carcass layer loaded with external hydrostatic pressure is developed. The buckling collapse of the carcass layer is evaluated considering different initial imperfections, including residual stress. The results show that the critical pressure can be 60% less than under ideal conditions when the geometric imperfection, material nonlinearity and residual stress due to deformation are considered, which indicates that the effect of residual stress on buckling collapse cannot be ignored. The numerical model and results provide an efficient method and basis for nonlinear buckling analysis and a collapse-resistant unbonded flexible pipe design for industry. [ABSTRACT FROM AUTHOR]

The present research aims at determining the axial buckling load of stiffened multilayer cylindrical shell panels made of functionally graded graphene-reinforced composites (FG-GPL RCs). Rings and stringers are applied as stiffening tools for shell panels, whose elastic properties are determined according to the Halpin–Tsai relations. The virtual work principle and finite element approach are implemented here, according to a first-order shear deformation theory (FSDT) and Lekhnitskii smeared stiffener approach, in order to determine the governing equations of the stability problem. Four different dispersions of nanofillers are assumed in the thickness direction, including the FG-X, FG-A, FG-O, and UD distributions. A large systematic investigation considers the effect of different geometric and material parameters on the buckling loads and mode shapes of the stiffened FG-GPL RC cylindrical shell panel, primarily the dispersion and weight fractions of the nanofiller, the number of rings and stringers, and the boundary conditions, with useful insights for design purposes. [ABSTRACT FROM AUTHOR]

Composite laminated structural panels are widely used in various industries such as aerospace and machinery because of their light weight, large specific stiffness, and strong fatigue resistance. As a typical engineering structure, the composite stiffened plate is designed to enhance the bearing capacity of the laminated plate. In this study, composite stiffened panels reinforced by carbon and/or E-glass fibres are modelled by finite element analysis (FEA) using Ansys. Nonlinear structural analysis is employed to find the critical buckling load. Three different skin layups, i.e., [45°/−45°/90°/0°]S, [90°/0°/90°/0°]S, and [60°/−30°/90°/0°]S, are studied. For each ply angle combination, different ply material combinations are studied. The cost and weight of each combination formed by applying different ply materials to the skin and stiffeners are studied. The results show that hybrid reinforcement in the stiffened panels reduces costs and maintains high buckling loads. Carbon/epoxy composites as the outer layers also reduce costs and maintain acceptable buckling loads without compromising the overall performance. Customized composite designs in terms of cost and weight can be achieved while maintaining critical buckling loads. [ABSTRACT FROM AUTHOR]

This paper examines the accuracy and effectiveness of various beam theories in predicting the critical buckling loads and fundamental frequencies of functionally graded porous (FGP) beams whose material properties change continuously across the thickness. The beam theories considered are classical beam theory (CBT), first-order shear deformation beam theory (FSDBT), third-order shear deformation beam theory (TSDBT), and the broken-line hypothesis-based shear deformation beam theory (BSDBT). Governing equations for those beam theories are formulated by using the Hamilton's principle and are then solved by means of the generalised differential quadrature method. Finite element simulation solutions are provided as reference results to assess the predictions of those beam theories. Comprehensive numerical results are presented to evaluate the influences of the porosity distribution and coefficient, slenderness ratio, and boundary condition on the difference between theoretical predictions and simulation results. It is found that the differences significantly increase as the porosity coefficient rises, and this effect becomes more noticeable for the rigid beam with a smaller slenderness ratio. Nonetheless, the results produced by the BSDBT are always the closest to simulation ones. The findings in this paper will contribute to the establishment of more refined theories for the mechanical analysis of FGP structures.

Semiconductor chips on a substrate have a wide range of applications in electronic devices. However, environmental temperature changes may cause mechanical buckling of the chips, resulting in an urgent demand to develop analytical models to study this issue with high efficiency and accuracy such that safety designs can be sought. In this paper, the thermal buckling of chips on a substrate is considered as that of plates on a Winkler elastic foundation and is studied by the symplectic superposition method (SSM) within the symplectic space-based Hamiltonian system. The solution procedure starts by converting the original problem into two subproblems, which are solved by using the separation of variables and the symplectic eigenvector expansion. Through the equivalence between the original problem and the superposition of subproblems, the final analytical thermal buckling solutions are obtained. The SSM does not require any assumptions of solution forms, which is a distinctive advantage compared with traditional analytical methods. Comprehensive numerical results by the SSM for both buckling temperatures and mode shapes are presented and are well validated through comparison with those using the finite element method. With the solutions obtained, the effects of the moduli of elastic foundations and geometric parameters on critical buckling temperatures and buckling mode shapes are investigated. [ABSTRACT FROM AUTHOR]