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Buckling of a simple supported and cantilever nano‐rod and under action of self‐weight was modeled, taking into account the surface effect according to two models of surface elasticity – Gurtin–Murdoch and Steigmann–Ogden. The size effect under the buckling was studied by the Ritz method using two kinematic hypotheses, known as the rod theories of Euler–Bernoulli and Timoshenko. The simulation results were compared depending on the accepted surface elasticity model and the kinematic hypothesis. [ABSTRACT FROM AUTHOR]

The analytical solutions for buckling of closed and open cylindrical shells under different boundary conditions are challenging. A separation‐of‐variable method with closed‐form eigensolution under Donnell–Mushtari theory is proposed for eigenbuckling analysis in cylindrical shells. The modal function is adopted as the form W = eμαeλβ. It can be applied to the closed and open cylindrical shells with different boundary conditions, and the whole calculation process is explicit. The critical buckling capacities of short cylindrical shells are close under the simply supported or clamped boundary conditions. The predictions are in good agreement with those in literature and the finite element model. [ABSTRACT FROM AUTHOR]

Gridshell structures are characterized by an impressive strength-to-weight ratio, allowing their application in large-span roofing structures. However, their complex construction process and maintenance limited their widespread application. In recent years, the development of parametric and computational design tools has rekindled interest in this type of structure. Among these techniques, the Multibody Rope Approach (MRA) is a form-finding method based on the dynamic equilibrium of a system of masses (nodes) connected by ropes, which allows optimizing the structural shape starting from the dual geometry of the funicular network. To optimize the construction process, an improved version of the MRA, i-MRA, has been recently developed by the authors with the goal of uniforming the size of the structural components. To investigate the impact of the i-MRA method on the structural behavior of gridshell structures, the practical case of the design of a mosque roof is here analyzed. The comparison is carried out in terms of structural performance with respect to permanent and equivalent quasi-static loads. In addition, free-vibration natural-frequency shift is obtained by performing linear modal analysis. Finally, the global behavior with respect to buckling and elastic instability is assessed solving the relevant eigenvalue problem. The results demonstrate that for the roofing of the Dakar mosque, the structural configuration obtained through i-MRA is superior in terms of both construction efficiency and structural performance. The achieved shape exhibits a more uniform distribution of stresses induced by the applied loads together with very limited structural element typologies. [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]

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 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]

The woven structure made of naturally curved (in-plane) ribbons has smooth geometry and fewer geometric imperfections, but there is no study of its buckling mechanical properties under vertical loads. The aim of this paper is to investigate buckling mechanical properties of spherical woven structures. Three spherical woven structures with different ribbon types and six new spherical woven structures with different ribbon widths and thicknesses were designed and the quasi-static vertical compression tests were carried out. The buckling load of spherical woven structures were studied by nonlinear finite element and ring buckling theory. Results indicate that the failure mode of the spherical weave structure under vertical loading can be divided into two stages, where a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. Spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbon. Based on theoretical and finite element analysis, we propose a buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load. The formula is validated and has good agreement with the test results, which could help to design the stability of spherical weave structures with in-plane ribbons. [ABSTRACT FROM AUTHOR]

Recent massive earthquakes have raised concerns that megathrust earthquakes with magnitude 9 can occur in the near future. This article discusses the critical behavior of structures involving torsion caused by extreme ground motions. Unlike factors such as mass and stiffness eccentricity and accidental torsion in a structure that induce torsion, torsional buckling can occur in a moment-resisting frame (MRF) when all beam ends in the longitudinal and transverse directionsyield in the lower stories, even if the frame is well designed and its eccentricity is negligibly small. In this study, the theoretically predicted buckling load was presented and validated via numerical analyses. This article shows that excluding the P-Delta effect resulted not only in underestimated deformation but also in overlooked torsional buckling. This study suggests that a high-rise MRF designed in accordance with modern seismic design codes can suffer torsional collapse when the beam ends of the lower stories yield owing to extreme ground motion. Based on these findings, we recommend considering the P-Delta effect when examining the critical behavior of high-rise buildings so as not to overlook the brittle failure mode. [ABSTRACT FROM AUTHOR]

This study investigates the elastic buckling behavior of oblate hemi-ellipsoidal shells (OHES) subjected to non-uniform external hydrostatic pressure. The virtual work-energy of OHES consists of virtual strain energy due to membrane, bending, in-plane stress resultants, and virtual work of hydrostatic pressure. For buckling analysis, the geometric stiffness matrix is obtained from the strain energy due to in-plane stress resultants. A finite element procedure via a C1 continuity axisymmetric element is applied to solve the critical hydrostatic pressure from the eigenvalue buckling problem. The buckling pressure of the hemi-ellipsoidal dome subjected to uniform external pressure is verified with the previous research and FEM commercial software. Present results also indicate that the maximum in-plane stress of the hemi-ellipsoidal shell shapes are near the apex point as the axisymmetric buckling shape. In the case of hydrostatic pressure, the critical hydrostatic pressure of OHES is determined and are in good agreement when compared with the experimental results in published research. Furthermore, the shape ratio influences the difference in critical load results between uniform pressure and hydrostatic pressure, especially when the shape ratio is higher than 0.5 and the a / t ratio is less than or equal to 100. Seawater depth limitations in subsea engineering are also presented and found that the shell thickness and shape ratio are the major factors affecting critical seawater depth. [ABSTRACT FROM AUTHOR]

Jaya is a metaheuristic algorithm that uses a pair of random internal parameters to adjust its exploration and exploitation search behaviors. Such a random setting can negatively affect the search performance of the algorithm by causing inappropriate search behavior in some iterations. To tackle this issue, the present study deals with developing a new fuzzy decision-making mechanism for dynamic adjusting the trade-off between the exploration and exploitation search behaviors of the Jaya method. The new algorithm is named Fuzzy Reinforced Jaya (FRJ) method. The search capability of the FRJ is evaluated in solving a suite of unconstrained mathematical benchmarks and constrained mechanical and structural optimization problems with buckling and natural frequency constraints. Also, the relevant decision variables are selected from both continuous and discrete domains. To provide a deeper insight into the effect of the defined auxiliary fuzzy module, the performance of the algorithm is evaluated and discussed using normalized diversity concept and behavioral diagrams. Also, employing different statistical analyses (e.g., Q–Q diagrams, Wilcoxson and Friedman tests), the significance of the outcomes is evaluated. Also, the numeric achievements are compared with six other well-stablished techniques. Attained outcomes indicate that the proposed FRJ, as a self-adaptive and parameter-free method, provides superior and promising results in the terms of stability, accuracy, and computational cost in solving mathematical and structural optimization problems. [ABSTRACT FROM AUTHOR]

The post-buckling behavior of a hybrid functionally graded (FG) rectangular plate reinforced with carbon nanotubes (CNT) is presented. The mathematical model developed based on transverse displacement variation of second-order in third-order shear deformation theory, hence referred to as modified third-order shear deformation theory (MTSDT). Transverse shear stress is imposed zero on top and bottom surface of plate. 2D C0 finite element (FE) formulation model developed based on MTSDT. Inhouse MATLAB code developed of present FE formulation. The rectangular plates consist of matrix material, fiber, and CNT as reinforcement material. The grading of fiber material in the thickness direction ensured using a power–law distribution. The material characteristics of the hybrid FG plates predicted using the Halpin-Tsai equation and the rule of mixing technique. No shear correction factor is required due to realistic parabolic behavior considered in the present work. The comparison study results of the present model are in good agreement with the published work. After confirming the accuracy of the present model a parametric study was carried outd to check the influence of different parameters. [ABSTRACT FROM AUTHOR]

Most studies have focused on determining optimal dimensions of metal- or composite-based rectangular hollow sections (RHSs) by considering only the design requirement of strength. Different from those, an analytical procedure for the determination of optimal sectional dimensions of polymer-based RHS beams by accounting for both adequate-strength and local buckling for the first time has been presented in the context of this study. Analytical expressions which give the optimal sectional dimensions simultaneously satisfying the adequate-strength and local buckling conditions have been derived for two different loading configurations such as a pure major axis bending and a combined axial compression and major axis bending. The analytical procedure proposed in this study depends on the idea of preventing the polymer-based RHS from buckling prior to its compressive strength. This has been achieved by increasing the critical buckling stress of the RHS up to its compressive strength via optimizing its sectional dimensions. During the optimum design, different elastic and plastic material behaviors of polymers in tension and in compression have been taken into calculations. The results attained analytically have been validated against numerical predictions obtained from linear elastic eigenvalue buckling and postbuckling analyses implemented in Abaqus engineering finite element code. Thus, the analytical procedure reported in this study can be used as a benchmark in identifying the optimal dimensions of RHS members manufactured from polymers. Communicated by Davide Spinello. [ABSTRACT FROM AUTHOR]

This paper presents a fiber element analysis model that simulates the structural responses of square steel‐reinforced concrete‐filled steel tubular (SRCFST) short columns under concentric compression including local buckling effects. The method of effective widths is utilized to model the gradual postlocal buckling of the steel tube walls of a SRCFST column loaded axially to failure. A new confinement model is developed for the concrete based on test results, considering the confinement induced by the embedded steel section. This confinement model is incorporated into the fiber model, and its accuracy is verified by experimental results. The accuracy of various confinement models proposed for concrete‐filled steel tubular (CFST) square columns in predicting the performance of SRCFST columns is evaluated. A parametric study is performed to investigate the performance of SRCFST columns with various parameters. The applicability of the design formulas specified in current standards for CFST columns to the design of SRCFST columns is examined. A formula is proposed to predict the strength of SRCFST short columns. The developed inelastic simulation model, confinement model, and design formula are found to yield performance predictions of SRCFST columns with good accuracy. [ABSTRACT FROM AUTHOR]

• Nonlinear torsional buckling of toroidal shell segments is presented using the Ritz energy method. • The corrugated core sandwich toroidal shell segments with FG-GRC coatings are considered. • The thermal forces are added to improve the homogeneous model for the corrugated core. • Ritz energy method, Donnell shells theory, and Pasternak's foundation model are applied. • Effects of corrugated core, material and geometrical parameters on the buckling behavior of shells are investigated. An investigation on the nonlinear torsional buckling of corrugated core sandwich toroidal shell segments with functionally graded graphene-reinforced composite (FG-GRC) laminated coatings in temperature change is mentioned in this paper using the Ritz energy method. The complex configuration of sandwich toroidal shell segments with double curvatures and the combination of the corrugated core and the FG-GRC coatings create the special behavior of structures. A homogenization model for corrugated structures and the extended Halpin-Tsai model can be applied to estimate the stiffnesses of shells. The effects of uniform temperature change are taken into account by supplementing the thermal forces into the total forces of shells. The Donnell shell theory and Pasternak's foundation model are used to establish the total potential energy of the structures. Ritz energy method is applied, and the closed condition and circumferential stress are taken into account, the postbuckling curve expressions of torsion-deflection and torsion-twist angle are obtained in explicit forms. The numerically obtained examples can show the significantly beneficial effects of FG-GRC laminated coatings and corrugated core on nonlinear buckling responses of structures. [ABSTRACT FROM AUTHOR]

Ensuring seismic resilience in earthquake-prone regions is imperative for structural safety. Fiber-Reinforced Concrete (FRC) columns hold promise for enhancing structural performance under seismic conditions. This study seeks to comprehensively evaluate their seismic behavior. The primary objective of this research is to assess and compare the seismic performance of various FRC column types, including polypropylene fibers (PFRC), steel fibers (SFRC), and hybrid combinations (HyFRC), in contrast to conventional reinforced concrete (RC) columns. To achieve this, the study employs eXtended Finite Element Method combined with Concrete Damage Plasticity (XFEM-CDP) in Abaqus to scrutinize static and dynamic responses. The nonlinear static pushover analysis unveiled a notable improvement in seismic resistance across all FRC types when compared to RC columns. Incremental dynamic analyses (IDA) are conducted using the selected suite of 10 near fault as-recorded ground motions to evaluate the inelastic seismic responses of different FRC bridge columns. XFEM-CDP simulations in Abaqus captured multiple aspects of FRC columns, such as concrete cracking, loss of stiffness and plastic behavior. Seismic fragility analysis of these FRC columns is conducted considering four damage states: a) longitudinal steel yielding, b) core concrete crushing, c) steel bar buckling, and d) longitudinal steel bar fracture. The results indicated that HyFRC columns exhibit the lowest damage vulnerability compared to PFRC and SFRC variants. [ABSTRACT FROM AUTHOR]

To establish a glide path, smaller files (up to size 0.15) with tapers of 2% are commonly used as pathfinding files. They pre-shape the root canal space before transitioning to larger taper endodontic instruments, aiming to prevent procedural errors. This study aimed to compare the design, metal wire composition, and mechanical characteristics of seven different ISO size 15 stainless-steel hand files (K-File and C-File+). Ninety-one new stainless-steel ISO 15 K-files were mechanically tested. All files were inspected for deformations before the assessment. Dental operating microscope, scanning electron microscope (SEM), and optical microscope analyses were conducted on four randomly selected instruments from each group, and two instruments per group underwent an energy-dispersive X-ray spectroscopy (EDS) analysis. Buckling mechanical tests were performed using an Instron universal testing machine, and microhardness was assessed using a Vickers hardness tester. The statistical analysis employed the nonparametric Mood's median test, with a significance level set at 0.05. The instrument design analysis unveiled variations in the active blade area length and the number of spirals, while maintaining consistent cross-sections and symmetrical blades. Distinct tip geometries and surface irregularities were observed. While the energy-dispersive X-ray spectroscopy confirmed similar compositions, the buckling strength and microhardness values exhibited variability across for all tested files. Notably, the Dentsply ReadySteel C-File+ recorded the highest buckling value (2.10 N), and the Dentsply ReadySteel K-File exhibited the lowest (1.00 N) (p < 0.05). Moreover, the Dentsply ReadySteel K-File recorded the highest microhardness value (703 HVN), while the SybronEndo Triple-Flex had the lowest (549 HVN) (p < 0.05). While similarities in cross-section design and metal wire composition were noted among the files, variations in the number of spirals and mechanical performance were also observed. Thus, all of these factors should be considered when selecting suitable files for an efficient root canal treatment. [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 Double-Double (DD) laminate family allows for simplification in the context of buckling analysis. Stacking-sequence discussions, known from conventional-laminate optimization, made from 0 ∘ , ± 45 ∘ , 90 ∘ plies, omit for DD. The recently presented DD-specific buckling relation is applied in this article to the 18-panel, 'horse-shoe' laminate blending reference case. The use case addresses the challenge of identifying a compatible group of laminates for differently loaded, adjacent regions, as it is a common scenario in wing covers and fuselage skins. The study demonstrates how the novel DD-laminate buckling relation simplifies the process of determining a buckling optimum for a group of laminates. The process of determining the optimum blended DD panel is presented. Its determined mass is compared with minimum masses, presented in earlier studies, which focus on stacking optimization and blending for more conventional ply orientations and laminate stacking conventions. [ABSTRACT FROM AUTHOR]

The buckling instability of cylindrical shells under axial compression has been one of the most renowned problems in structural engineering for several decades. Many pioneering works in the twentieth century have provided insights into understanding the shells' infamous imperfection sensitivity and led to reliability-based designs. However, a recent surge in numerical studies of the snaking phenomenon explores the development of a localized stable post-buckling mode in axially compressed cylindrical shells. Hitherto, none of the experimental studies report on the evolution of azimuthal snaking. In this work, experimental studies are carried out with the objective of revealing the snaking phenomenon. The axial compression experiments are performed on 3D-printed shells made of thermoplastic polyurethane (TPU). The work's novelty lies in the usage of TPU shells for slowing down the propagation of circumferential dimples and making it feasible to capture them using photogrammetry. Despite the match between the experimental and numerical mode shapes, the experiments reveal multiple routes for the snaking sequence. Furthermore, mode transitions such as reduction in circumferential wave number and transformation of symmetric mode into an asymmetric one are observed. These experimental results provide insights into the localized phenomenon of snaking and validate numerical solutions. [ABSTRACT FROM AUTHOR]

In this paper, buckling and nonlinear post-buckling behaviors of a bidirectional porous (BDP) beam are investigated under bidirectional hygrothermal environment. Euler–Bernoulli beam theory with the von Kármán nonlinearity is employed to derive the nonlinear variable coefficient governing differential equations based on Rayleigh quotient method. Analytical solutions of critical buckling load and load–deflection equilibrium path in post-buckling are deduced for the single directional varying (SDV) porous beam. The general numerical solutions for bidirectional varying (BDV) porous beam are obtained by differential quadrature finite element method (DQFEM) with Newton–Raphson iteration method based on the variation principle. The high accuracy of the present numerical method with higher computing efficiency is verified by comparison with published reports and the analytical results in this work. Parametric analysis on effects of the porosity bidirectional distributions, porosity coefficients, distributions of hygrothermal environment and boundary conditions on buckling load and post-buckling response is carried out to enhance the buckling and deformation resistances in design, manufacture and usage of porous structures. The results show that the bidirectional porosity pattern, linear and nonlinear hygrothermal distribution and boundary conditions play a significant role on buckling critical external load and critical hygrothermal increments, buckling form and post-buckling path. [ABSTRACT FROM AUTHOR]

Hierarchical buckling is a novel phenomenon observed in elastic fibers subjected to transverse confinement; however, the deformation mechanisms and modal transitions of this unique phenomenon remain to be elucidated. This paper investigates the hierarchical buckling of elastic fibers with elliptical (circular) cross-sections under transverse confinement through analytical derivations and numerical simulations. Various magnitudes of hierarchical buckling of fibers are observed with the variation of the controlled elastic matrix stiffness. An analytical solution is first derived for the fiber's buckling phenomenon, and the hierarchical buckling is accomplished through the superposition of buckling at various modes. The theoretical results are validated against the finite element simulations with good agreement. It is demonstrated from the parametric results that the hierarchical buckling phenomenon is primarily influenced by the stiffness of the external transverse confinement (matrix), which is defined as a dimensionless parameter. It is thus illustrated from the computational results that the buckling of elastic fibers within a solid or fluid matrix can be controlled and customized. The present work provides theoretical guidance for the application of elastic fibers in stretchable conductor fibers and flexible electronic devices. [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]

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young's modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson's ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates. [ABSTRACT FROM AUTHOR]

Introduction: Preventive control is a critical feature in autonomous technology to ensure safe system operations. One application where safety is most important is robot-assisted needle interventions. During incisions into a tissue, adverse events such as mechanical buckling of the needle shaft and tissue displacements can occur on encounter with stiff membranes causing potential damage to the organ. Methods: To prevent these events before they occur, we propose a new control subroutine that autonomously chooses a) a reactive mechanism to stop the insertion procedure when a needle buckling or a severe tissue displacement event is predicted and b) an adaptive mechanism to continue the insertion procedure through needle steering control when a mild tissue displacement is detected. The subroutine is developed using a model-free control technique due to the nonlinearities of the unknown needle-tissue dynamics. First, an improved version of the model-free adaptive control (IMFAC) is developed by computing a fast time-varying partial pseudo derivative analytically from the dynamic linearization equation to enhance output convergence and robustness against external disturbances. Results and Discussion: Comparing IMFAC and MFAC algorithms on simulated nonlinear systems in MATLAB, IMFAC shows 20% faster output convergence against arbitrary disturbances. Next, IMFAC is integrated with event prediction algorithms from prior work to prevent adverse events during needle insertions in real time. Needle insertions in gelatin tissues with known environments show successful prevention of needle buckling and tissue displacement events. Needle insertions in biological tissues with unknown environments are performed using live fluoroscopic imaging as ground truth to verify timely prevention of adverse events. Finally, statistical ANOVA analysis on all insertion data shows the robustness of the prevention algorithm to various needles and tissue environments. Overall, the success rate of preventing adverse events in needle insertions through adaptive and reactive control was 95%, which is important toward achieving safety in robotic needle interventions. [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]

The quest for safe lower bounds to the elastic buckling of axially loaded circular cylindrical shells has exercised researchers for the past 100 years. Recent work bringing together the capabilities of nonlinear numerical simulation, interpreted within the context of extended linear classical theory, has come close to achieving this goal of defining safe lower bounds. This paper briefly summarizes some of the important predictions emerging from previous work and presents new simulation results that confirm these earlier predictions. In particular, we show that for a specified maximum amplitude of the most sensitive, eigenmode-based geometric imperfections, normalized with respect to the shell thickness, lower bounds to the buckling loads remain constant beyond a well-defined value of the Batdorf parameter. Furthermore, we demonstrate how this convenient means of presenting the imperfection-sensitive buckling loads can be reinterpreted to develop practical design curves which provide safe, but not overly conservative, design loads for monocoque cylinders with a given maximum permitted tolerance of geometric imperfection. Hence, once the allowable manufacturing tolerance is specified during design or is measured post-manufacturing, the greatest expected knockdown factor for a shell of any geometry is defined. With the recent research interest in localized imperfections, we also attempt to reconcile their relation to the more classical, periodic, and eigenmode-based imperfections. Overall, this paper provides analytical and computational arguments that motivate a shift in focus in defect-tolerant design of thin-walled cylinders--away from the knockdown experienced for a specific geometric imperfection and towards the worst possible knockdown expected for a specified manufacturing tolerance. [ABSTRACT FROM AUTHOR]

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

Piezoelectric nanobeams are important components in micro-nano electromechanical systems. They are often used as mechanical structures such as wireless sensors, biological probes and transistors. And their mechanical performance is a very important research topic. Based on the theory of surface elasticity and the "core–shell" model, post-buckling behavior of porous piezoelectric nanobeams is analyzed using the first-order shear deformation beam theory, where the surface effect is introduced by employing the surface energy model. The governing equations and boundary conditions of post-buckling of porous piezoelectric nanobeams under mechanical loading were derived by introducing the concept of median surface in physics and the principle of minimum potential energy. The influence of surface effect on post-buckling configuration, post-buckling path, amount of induced charge and critical load of porous piezoelectric nanobeams with different external constraints and porosities were discussed. The results show that considering surface effects, the effective elastic modulus and critical load of porous piezoelectric nanobeams will be increased, and the post-buckling configuration, post-buckling path and amount of induced charge will be reduced. Meanwhile, the mechanical properties of porous piezoelectric nanobeams can be effectively improved by appropriate pore distribution. These findings can be used as a theoretical basis for the accurate design and manufacture of micro-nano mechanical and electronic devices. [ABSTRACT FROM AUTHOR]

A detailed assessment is made here of a recently proposed buckling model for a drillstring that remains in conformal contact with an axially toroidal borehole. Suitable rescaling of the relevant equations allows us to identify a particular regime of interest, which is subsequently explored in depth with a multiple-scale asymptotic strategy. In particular, the localisation phenomena previously reported in the literature are placed on firm ground and explained with the help of a small number of analytical formulae. Two new sets of qualitatively different solutions are also identified and discussed in detail. Our asymptotic predictions of the critical loads are shown to be in very good agreement with the direct numerical simulations of the corresponding linear bifurcation problem. [ABSTRACT FROM AUTHOR]

Buckling of slender members due to gravity loading or thermal effects is influenced by the member's geometric imperfections, boundary conditions, and intermediate lateral supports. When assessing the capacity of such members, these parameters are often unknown (e.g., the rotational stiffness of end connections in a truss or the lateral support provided by the ties to a rail track), and conservative assumptions must be made resulting in conservative assessments. Distributed fiber optic sensors (DFOS) can potentially be used to determine these parameters with greater accuracy using strain measurements along the length of a member. A series of buckling experiments was conducted on a slender member instrumented with DFOS subjected to axial load with varying levels of lateral restraint or to increasing temperature. The distributed strain data were then used to evaluate the geometric imperfections, boundary conditions, and lateral support stiffness. These inputs were used to create a finite-element model to estimate the ultimate load response of the member using data acquired at service loads. [ABSTRACT FROM AUTHOR]

Large infrastructure projects can efficiently use large diameter bars as longitudinal reinforcement in reinforced concrete elements. In earthquake-prone zones, critical regions of these elements must be detailed for ductility and hysteretic energy dissipation. Longitudinal bars in these regions are expected to sustain large-amplitude strain cyclic reversals before bar fracture occurs, in a mode of failure defining the collapse prevention limit state. To date, no successful large strain-amplitude cyclic loading testing has been reported on large-diameter reinforcing bars to observe the large-strain amplitude fatigue life of such bars, which often involves plastic bar buckling. This paper describes a test program designed to determine the plastic buckling/straightening fatigue life of ASTM A706 Grade 60 No. 18 bars (Ø57 mm) reinforcing bars subjected to cycles of reversed plastic strains. The design and implementation of the loading apparatus, critical for the gripping of the bars, the metallurgical characterization of the bars, and several key test results are discussed in the paper. Finally, the paper discusses a general unidimensional fatigue damage index precursor to bar fracture following a few plastic buckling and straightening cycles. [ABSTRACT FROM AUTHOR]

In recent years, there has been increasing use of thin-walled structures with a plate thickness of 6-10 mm in the construction of cruise ships. As one of the important processes of cruise ship construction, hybrid laser-arc welding, combining the advantages of laser welding and arc welding, is increasingly applied in thin-walled cruise ships with the objective of reducing panel deformation. However, due to the weak stiffness of the thin-walled structure with a continuous weld length of 4-16 m, complex welding deformation, e.g., buckling deformation, will be prone to occur. This paper analyzed the deformation behavior of large-scale thin-walled cruise ship structures with the change of weld length, structural width, and plate thickness in the hybrid laser-arc welding process. The buckling mode induced by the welding deformation is predicted based on the combination method of thermal elastic-plastic and inherent strain, as well as experimental verification. By analyzing the deformation behavior with the weld length of 5-15 m, when the continuous weld length exceeds 7.5 m during butt welding of large thin-walled cruise ship structures, the welding deformation mode will change from bending deformation to buckling deformation, while the maximum deformation will be reduced by about 50%. Compared with the buckling mode of the traditional thick-walled structures, with the decrease of plate thickness, the buckling mode of large ship structures will change from wave buckling deformation of the whole structure to wave buckling at the edge of structures. [ABSTRACT FROM AUTHOR]

Buckling restrained brace is an important structure for improving the seismic resistance of structures. Conducting research on new types of buckling restrained brace can improve the seismic performance and reliability of buckling resistant support. Four different types of buckling restrained braces specimens were designed and manufactured: cross-shaped square steel pipe members, cross-shaped round steel pipe members, cross-shaped carbon fiber members, and in-line carbon fiber members. By conducting quasi-static tests, the force displacement hysteresis curves, skeleton curves, stiffness degradation, equivalent viscous damping coefficient, and energy dissipation ratio of four different types of buckling restrained brace were analyzed. The research results showed that all four buckling restrained brace specimens have good hysteresis performance. The load-bearing capacity and energy consumption performance of the three specimens of square steel pipe, round steel pipe and carbon fiber with the same core unit are the same, but the inline type is worse than the cross type. The core unit specimen with a width of 80 mm is about 60% higher in bearing capacity and energy consumption than a specimen with a width of 50 mm. The core unit of some specimens undergoes multi-wave buckling. For carbon fiber specimens, the CFRP is prone to breakage due to the lateral thrust of the restraining unit. Therefore, steel hoop or stirrup should be added to the end to improve the restraint effect when designing and manufacturing. [ABSTRACT FROM AUTHOR]

Attractive large-scale glazing is currently an architectural trend. However, achieving adequate stiffness for larger glazing spans requires the use of complex cross-sections, generally aluminium sections of considerable height. Members with openwork webs are sometimes used in order to achieve increased load-bearing capacity and stiffness with reduced weight. The disadvantage is that this solution takes up a lot of space inside the building. A recently patented diagonalless member attempts to solve the above-mentioned problems. The member is fully demountable and allows glass units to be installed in the space between the chords. It consists of two chords spaced apart by metal sleeves with bolts passed through them. In this study, preliminary qualitative experimental tests were carried out to determine the behaviour of the member under load and to identify zones sensitive to local deformation. On this basis, numerical models (bar and 3D solid models, including contact interactions) were created and tested. Subsequently, the optimum sleeve spacing was determined, the effect of rotational and translational stiffness reduction at the nodes was investigated, and stress concentration zones and forms of stability loss were identified. A new form of local loss of stability of the chord facewall was identified, the so-called sliding push effect of the chord walls on the sleeve (within the larger openings). This is a completely different type of chord facewall failure from that found in known tubular welded joints. The research programme focused on identifying the phenomena occurring in the new member in order to provide a basis for further, more advanced analyses. [ABSTRACT FROM AUTHOR]

Buckling phenomenon is a common failure mode for composite materials under the effect of compressive loading which is mainly investigated in two stages as pre – buckling and post – buckling. At the pre – buckling phase, the deformations take place temporarily in elastic range. However, load carrying capacity of a member can be increased by regarding the post – buckling process. Therefore, it is important to determine the final and maximum load carrying ability of the structure. Since, at the end of the post – buckling, the body cannot carry load and crippling failure takes place. In this review article, crippling behavior of the composite structures is investigated. After describing the crippling phenomenon, this study mainly investigates both experimental and theoretical points of views. In this scope, affecting parameters such as stacking sequence, geometrical properties and boundary conditions are determined. Then, the improved theoretical approaches are stated. The compatibilities of the test results are assessed with theoretical studies. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of friction on the buckling behavior of a thin, shallow, elastic spherical shell under uniform external pressure based on an axisymmetric model of the finite element method. The study examines a combination of different geometric parameters with three different types of boundary conditions: clamped, hinged, and frictional ends with a wide range of friction coefficients. Friction has a significant influence on the buckling response of the spherical shell for all geometric parameters. In general, the critical pressure decreases as the friction coefficient or geometric parameter decreases. The buckling behavior of the frictional end with small friction coefficients presents an obvious difference compared to the results of high coefficients. For certain geometric parameters, the buckling mode of the spherical shell is transited because of changing the friction coefficient. A buckling map that describes the dependence of critical pressure on both friction coefficient and geometric parameter combined with buckling mode is generated. This map can be applied to the design of the spherical shell against buckling. [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]

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]

In this study, we investigated toroidal shell wrinkling in free hydroforming. We specifically focused on toroidal shells with a regular hexagonal cross-section. Membrane theory was used to examine the distribution of stress and yield load in both preform and toroidal shells. The wrinkling moment was then predicted using an empirical formula of shell buckling. In addition, the wrinkling state was investigated using a general statics method, and the free hydroforming of toroidal shells was simulated using the Riks method. Subsequently, nonlinear buckling and equilibrium paths were analyzed. A toroidal preform was manufactured, and free hydroforming experiments were conducted. Overall, the experimental results confirmed the accuracy of the theoretical predictions and numerical simulations. This indicates that the prediction method used in the study was effective. We also found that wrinkling occurs during hydroforming in the inner region of toroidal shells due to compressive stress. Consequently, we improved the structure of the toroidal shells and performed analytical calculations and numerical simulations for the analysis. Our results indicate that wrinkling can be eliminated by increasing the number of segments on the inner side of toroidal preforms, thereby improving the quality of toroidal shells. [ABSTRACT FROM AUTHOR]

This study investigates the influence of friction on the buckling behavior of thin, elastic, spherical shells under uniform external pressure. The study spans a range of geometric parameters, from shallow shells to hemispheres. Three different end-edge boundary conditions - clamped, hinged, and frictional ends - are considered across a wide range of friction coefficients using an axisymmetric model and nonlinear buckling analysis. The spherical shell becomes increasingly susceptible to buckling when the friction coefficient falls below the converged friction coefficient. A formula is developed to estimate this converged friction coefficient for each geometric parameter. Furthermore, a boundary separating the effects of friction on critical pressure into distinct regions is established, and equations predicting critical pressure within each region are provided. The study also finds that friction influences the buckling mode transition in the shells. Due to significant changes in the theta angle of the no-bending point with increasing geometric parameter and friction coefficient, buckling mode transitions occur at lower friction coefficients in wider spherical shells. These findings provide valuable insights into the intricate interplay between geometric parameter, friction, and buckling behavior in shells. In practical applications, this study can be used to assess and enhance the safety and reliability of spherical shells. [ABSTRACT FROM AUTHOR]

The paper analyzes the influence of cutouts on the buckling of shallow shells with double curvature. Based on the Timoshenko-Reissner hypothesis, a mathematical model is presented that considers transverse shifts, material orthotropy, geometric nonlinearity and structural weakening by cutouts. Cutouts are specified discretely by single columnar functions. The computational algorithm is based on the Ritz method and the Newton method. The implementation of the algorithm is carried out in the Maple 2022 software package. To study the buckling, the Lyapunov criterion is adopted. Calculations of the buckling of flat shells of double curvature with square cuts, graphs of the dependence of deflections on loads and deflection fields are given. Accounting for the structural cutouts leads to a decrease in the critical load. At the same time, for the considered problems, it is found that the decrease in the critical load does not exceed 25 % for the cutout volume not exceeding 10 % of the shell volume. [ABSTRACT FROM AUTHOR]

This paper is devoted to a thin-walled sandwich plate with an individual functionally graded core. The nonlinear shear deformation theory of a straight normal line is applied. A system of three differential equations of equilibrium of this plate is obtained, based on the principle of stationary potential energy, which is reduced to two differential equations and solved analytically. The critical load of the rectangular sandwich plate is determined. A detailed analytical study is carried out for selected exemplary plates. Moreover, a numerical FEM model of this plate is developed. The results of these calculations are compared with each other. [ABSTRACT FROM AUTHOR]

In practical engineering, a thin-walled cylindrical shell structure is more easily subjected to localized axial compression loads caused by external adjacent structures or devices. However, until now there are few studies to reveal the buckling behavior of cylindrical shells under such nonuniform loading conditions based on initial imperfection sensitivity. Therefore, buckling analysis of cylindrical shell under localized axial compression loads is investigated in this paper. Based on the buckling test, the influence of the morphology and amplitude of measured initial geometric imperfection are studied using the finite element method. Meanwhile, the inherent reason for initial geometric imperfection affecting the buckling load is elaborated. The influence of amplitude, distribution range, and different combinations of local dent imperfections are also elucidated. In addition, the effects of inclined loading imperfection and uneven shell thickness distribution imperfection are analyzed in the form of deterministic numerical simulation. Finally, a new buckling load knockdown factor that can reasonably consider the influence of loading imperfection and shell thickness variation imperfection is proposed. This work elucidates the initial imperfection sensitivity of the thin-walled cylindrical shell structures under localized axial compression load and can provide useful guidance for the buckling design and preventing buckling failure of these structures. [ABSTRACT FROM AUTHOR]

Fault-related folds are present in most tectonic settings and may serve as structural traps for hydrocarbons. Due to their economic importance, many kinematic models present for them. Unfortunately, most of them have predominantly concentrated on the sliding mechanism parallel to the layering and often ignore the integral role of buckling in folding processes. This study is at the forefront of exploring the interplay among, sliding, buckling, and bending in the formation of the three fundamental types of fault-related folds: detachment, fault-propagation, and fault-bend folds. To this end, we developed five sets of two-dimensional (2D) finite element models, embodying both elastic and elastic- plastic behaviors. Our results indicate that sliding parallel to layering and faults, in conjunction with buckling, are the predominant mechanisms in fault-related folding. The strain ellipse patterns in our models are consistent with those observed in buckling models, thus affirming the significance of buckling in these geological structures. Furthermore, our models demonstrate that fault slip diminishes from the periphery towards the center in all three types of fault-related folds, in contrast to interlayer slip, which intensifies from the edge towards the center. In essence, a diminution in fault slip at the center is balanced by an augmentation in interlayer slip, leading to thickening and buckling. The genesis of all three fault-related fold types is attributed to the reduction in fault slip, with their distinctiveness defined by the location of this reduction: at the detachment fault tip for detachment folds, at the ramp tip for fault- propagation folds, and at the upper flat for fault-bend folds. [ABSTRACT FROM AUTHOR]

The effect of layer number, buckling sequence and drive velocity on energy dissipation per buckling event of mechanical metamaterials composed of representative volume element (RVE) is studied. Buckling behaviors of a single RVE encompassing buckling beams are investigated based on an approximate model. The metamaterials are modeled as a tandem model composed of identical N RVEs. The buckling behavior can not induce energy dissipation if N ≤ 2 for the proposed structure. As N or drive velocity increases, energy can be dissipated during elastic buckling. Besides, the dissipated energy per buckling event gradually decreases during one complete loading and unloading process. [ABSTRACT FROM AUTHOR]

Cristae are high‐curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae‐shaping proteins have been defined, analogous lipid‐based mechanisms have yet to be elucidated. Here, we combine experimental lipidome dissection with multi‐scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the inner mitochondrial membrane against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein‐mediated curvatures. This model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that cardiolipin is essential in low‐oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of cardiolipin is dependent on the surrounding lipid and protein components of the IMM. Synopsis: Dedicated proteins are known to control the architecture of the inner mitochondrial membrane; however, the role of specific lipids is less well defined. Here, a combination of methods including tomography and lipidomics is used to characterise the role of lipid composition in defining cristae architecture. As lipid ratios change, a critical breakpoint phenocopies the loss of cristae‐shaping proteins in the IMM of yeast mitochondria.Phospholipid saturation controls membrane mechanical properties and modulates ATP synthase oligomerization.The mitochondria‐specific lipid cardiolipin functionally compensates for increased phospholipid saturation and is required for cristae formation in low‐oxygen environments.A mathematical model for cristae membrane tubules predicts a snap‐through instability mediated by both protein and lipid‐encoded curvatures. [ABSTRACT FROM AUTHOR]

This research is concerned with the free vibration and buckling analysis of carbon nanotube-reinforced beams (CNT-RBs) using a novel high-order shear deformation theory (HSDT). The current HSDT is modeled by a trigonometric function without a shear correction factor, and the displacement field has only four variables. Several different carbon nanotube distributions, including two uneven CNT distributions (X-CNT and O-CNT), are considered. The mixture rule is applied to express the effective material properties of carbon nanotube-reinforced beams. The CNTR beams are rested on two springs and a shear layer (Kerr foundation). Hamilton's principle is employed to derive the governing equations, which are then solved using the Navier technique. The current theory and several parameter effects are studied and validated in comparison to benchmark studies and theories. The main purpose of this study is to enhance understanding of high-order shear theories, such as third order, sinusoidal, exponential, etc. In this context, our theory yields excellent results when compared to other theories. The difference between our theory and the exact solution is so minimal that it is superior to other theories. The second part of the study focuses on investigating the distribution of carbon nanotubes to enhance understanding. This knowledge can assist panel manufacturers in determining the appropriate distribution shape. Our results indicate that the third distribution (X-CNT) significantly influences mechanical behavior, unlike the first and second distributions (UD-CNT and O-CNT). [ABSTRACT FROM AUTHOR]