New or in-service truss bridges, with or without upper bracing systems, may display instability phenomena such as general lateral torsional buckling of the upper chord. The buckling of structural elements, particularly in the case of steel bridges, can be associated with the risk of collapse or temporary/permanent withdrawal from service. Buckling poses a significant danger as it often occurs at lower load values compared to those considered during the design phase. Additionally, this phenomenon can manifest suddenly, without prior warning, rendering intervention for its prevention impossible or futile. In contemporary times, most research and design calculation software offer the capability to establish preliminary values for buckling loads, even for highly intricate structures. This is typically achieved through linear eigenvalue buckling analyses, often followed by significantly more complex large displacement nonlinear analyses. However, interpreting the results for complex bridge structures can be challenging, and their accuracy is difficult to ascertain. Consequently, the objective of this paper is to introduce an original method for a more straightforward estimation of the buckling load of the upper chord in steel truss bridges. The method utilizes the theory of beams on an elastic foundation. The buckling load of the upper chord was determined using both the finite element method and the proposed methodology, yielding highly consistent results.

Weaving technology can convert two-dimensional structures such as ribbons into three-dimensional structures by specific connections. However, most of the 3D structures fabricated by conventional weaving methods using straight ribbons have some topological defects. In order to obtain smoother continuous 3D surface structures, Baek et al. proposed a novel weaving method using naturally curved (in-plane) ribbons to fabricated three-dimensional curved structures and using this method to weave new spherical weave structures that are closer to perfect spheres. We believe that this new spherical weave structure with smooth geometric properties must correspond to new mechanical properties. To this end, we investigated the buckling characteristics of different types of spherical weave structures by the combination of test and finite element method. The results of calculations and experiments show that the failure mode of the spherical weave structure under vertical loading can be divided into two stages: a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. The spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbons. The vertical buckling load of spherical weave structures using naturally curved ribbon increases with the width and thickness of the ribbon. In addition, this paper combines test, theoretical and finite element analysis to propose the buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load.

In steel structures, oblique 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 oblique panel zones. As confirmed, the buckling stresses derived from the energy method could simulate the local buckling stresses with accuracy comparable to that of finite element analysis, and an engineer-friendly design formula was proposed. Finally, we determined the correlation of the buckling stresses under biaxial stresses and presented a method for evaluating this correlation. Engineers can utilize the provided design equations to more efficiently and accurately calculate buckling loads, facilitating safer and more economical design of structures with oblique plates.

During the thinning process, in the semiconductor industry, residual stress from thin films can cause severe warpage in wafers, which can compromise their processability and packaging. This warpage can lead to bifurcation or buckling, making it important to understand this phenomenon for the manufacturing of large semiconductor wafers. We conducted a finite element analysis of the thinning process using ANSYS mechanical enterprise 2023/R2 to investigate the asymmetric curvatures resulting from bifurcation in a standard 300 mm Si (001) wafer. We induced an asymmetry in the system by applying a slight force on a point of the circumferential region perpendicularly to the substrate. We also simulated the compressive stress from the damaged layer formed during the thinning process and considered its influence on warpage and bifurcation in both linear and non-linear cases. We also included the influence of Earth's gravity induced deflection (GID) and investigated the influence of the compressive stress damaged layer on the grinding process of the whole wafer by adding a metal front layer to the ground back damaged wafer.

This paper presents an approach to the Kirchhoff-Love plate theory (KLPT) using the finite difference method (FDM). The KLPT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally in the case of KLPT, the finite difference approximations are derived based on the fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection surface. The FOPH is made for the fourth and third derivative of the deflection surface while the SOPH is made for its second and first derivative; this leads to a 13-point stencil for the governing equation. In addition, the boundary conditions and not the governing equations are applied at the plate edges. In this paper, the FOPH was made for all of the derivatives of the deflection surface; this led to a 25-point stencil for the governing equation. Furthermore, additional nodes were introduced at plate edges and at positions of discontinuity (continuous supports/hinges, incorporated beams, stiffeners, brutal change of stiffness, etc.), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at the plate edges and to satisfy the boundary and continuity conditions. First-order analysis, second-order analysis, buckling analysis, and vibration analysis of plates were conducted with this model. Moreover, plates of varying thickness and plates with stiffeners were analyzed. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. In first-order, second-order, buckling, and vibration analyses of rectangular plates, the results obtained in this paper were in good agreement with those of well-established methods, and the accuracy was increased through a grid refinement.

Waterbomb structures are origami-inspired deformable structural components used in new types of robots. They have a unique radially deployable ability that enables robots to better adapt to their environment. In this paper, we propose a series of new waterbomb structures with square, rectangle, and parallelogram base units. Through quasi-static axial and radial compression experiments and numerical simulations, we prove that the parallelogram waterbomb structure has a twist displacement mode along the axial direction. Compared with the square waterbomb structure, the proposed optimal design of the parallelogram waterbomb structure reduces the critical axial buckling load-to-weight ratio by 55.4% and increases the radial stiffness-to-weight ratio by 67.6%. The significant increase in the radial stiffness-to-weight ratio of the waterbomb structure and decrease in the critical axial buckling load-to-weight ratio make the proposed origami pattern attractive for practical robotics applications.

The biomimetic design of engineering structures is based on biological structures with excellent mechanical properties, which are the result of billions of years of evolution. However, current biomimetic structures, such as ordered lattice materials, are still inferior to many biological materials in terms of structural complexity and mechanical properties. For example, the structure of \textit{Euplectella aspergillum}, a type of deep-sea glass sponge, is an eye-catching source of inspiration for biomimetic design; however, guided by scientific theory, how to engineer structures surpassing the mechanical properties of \textit{E. aspergillum} remains an unsolved problem. The lattice structure of the skeleton of \textit{E. aspergillum} consists of vertically, horizontally, and diagonally oriented struts, which provide superior strength and flexural resistance compared with the conventional square lattice structure. Herein, the structure of \textit{E. aspergillum} was investigated in detail, and by using the theory of elasticity, a lattice structure inspired by the bionic structure was proposed. The mechanical properties of the sponge-inspired lattice structure surpassed the sponge structure under a variety of loading conditions, and the excellent performance of this configuration was verified experimentally. The proposed lattice structure can greatly improve the mechanical properties of engineering structures, and it improves strength without much redundancy of material. This study achieved the first surpassing of the mechanical properties of an existing sponge-mimicking design. This design can be applied to lattice structures, truss systems, and metamaterial cells.

Diabetic foot is a serious complication that poses significant risks for diabetic people. The resulting reduction in protective sensitivity in the plantar region requires early detection to prevent the imminent ulceration and amputation. The primary method employed for evaluating this sensitivity loss is the 10 g f Semmes-Weinstein monofilament test, commonly used as a first-line procedure. However, the lack of calibration in existing devices often introduces decision errors due to unreliable feedback. In this paper, a new equipment designed to address these limitations and enhance the assessment of the sensitivity loss using the 10 g f monofilament is introduced. The proposed system automates metrological verification and evaluation processes, ensuring accurate and reliable results. Furthermore, it simulates the practitioner’s procedure, serving both as a valuable training tool and a means to provide force-feedback information. An analytical model of the monofilament buckling and deflection is also presented. The obtained results showed that the tested monofilaments had a very high error compared to the 10 g f declared by the manufacturers. It is aimed, by introducing this advanced equipment, to improve the precision and reliability of assessing the sensitivity loss. The integration of automated verification, simulation capabilities, and precise measurements shows great promise for diabetic patients, reducing the likelihood of adverse outcomes such as ulceration and amputation.

This paper studies the dynamic response of corner supported modular steel buildings with a core wall system, under progressive collapse scenarios, associated with corner module removals. Since using secondary systems such as concrete core in mid- to high-rise buildings is currently una-voidable, understanding their impact on load transfer between modules during collapse scenarios becomes essential. The designated buildings with four-, eight- and twelve-story were modelled using the macro-model based finite element method in Abaqus. Also, three different locations are considered for the concrete shear core within the building plan, leading to nine various case scenarios. Each vertical and horizontal inter-module connection was modelled by one axial and two shear springs with predefined nonlinear force-displacement behaviour. The local and global buckling, which plays an essential role in the building's stability, was considered to obtain accurate results. Finally, parametric studies on the building response were carried out, including the intra-module connection rigidity and inter-module connection stiffness. The results demonstrated that the core wall could maintain the robustness of modular steel building through two mechanisms dependent on its location within the plan. Also, preventing plastic hinges from forming in beams could be introduced as an anti-collapse mechanism in the corner module removal scenarios

Artificial intelligence is increasingly used in various branches of engineering. In this article, artificial neural networks are used to predict the crush resistance of corrugated packaging. Among the analysed packages were boxes with ventilation openings, packages with perforations, and typical flap boxes, which makes the proposed estimation method very universal. Typical shallow feedforward networks were used, which are perfect for regression problems, mainly when the set of input and output parameters is small, so no complicated architecture or advanced learning techniques are required. The input parameters of the neural networks are selected so as to take into account not only the material used for the production of the packaging, but also the dimensions of the box and the impact of ventilation holes and perforations on the load capacity of individual walls of the packaging. In order to maximize the effectiveness of neural network training process, the group of input parameters was changed so as to eliminate those to which the sensitivity of the model was the lowest. This allowed the selection of the optimal configuration of training pairs for which the estimation error was on the acceptable level. Finally, models of neural networks were selected, for which the training and testing error did not exceed 10%. The demonstrated effectiveness allows to conclude that the proposed set of universal input parameters is suitable for efficient training of a single neural network model capable of predicting the compressive strength of various types of corrugated packaging.

Weaving is an ancient and effective structural forming technique characterized by the ability to convert two-dimensional ribbons to three-dimensional structures. However, most 3D structures woven from straight ribbons have topological defects. Baek et al. proposed a method to weave smoother continuous 3D surface structures using naturally curved (in-plane) ribbons, obtained a new surface structure with relatively continuous variation of Gaussian curvature, and analyzed its geometric properties. We believe that this new 3D surface structure with smooth geometric properties must correspond to new mechanical properties. To this end, we investigated a 3D surface structure using naturally curved (in-plane) ribbon weaving, and the results of calculations and experiments show that such structures have better buckling stability than those woven with straight ribbons. It is observed that the number of ribbons influences the buckling behavior of different types of woven structures.

This paper presents an approach to the two-dimensional analysis of elastic isotropic deep beams using the finite difference method (FDM). Deep beams are subjected to in-plane loading and present a shear span to height ratio of less than 2.50; consequently, Euler-Bernoulli beam theory and Timoshenko beam theory do not apply. Deep beams analysis is generally conducted using numerical methods such as the finite element method and to a lesser extent the FDM; the strut-and-tie model and the stress field method are also widely utilized. Analytical approaches usually make use of the Airy stress function, where stresses are formulated in terms of the stress function; however, the exact solution of this function satisfying all of the boundary conditions can hardly be found, even for simple cases. In this paper, deep beams were analyzed using the FDM. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected nodes of the structure. Therefore, the deep beam was discretized with a two-dimensional grid, and additional nodes were introduced at the boundaries and at positions of discontinuity (openings, brutal change of material properties, non-uniform grid spacing), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary and continuity conditions. An Airy stress function approach and a displacement potential function approach were considered in this study whereby strong formulations of equations (equilibrium, kinematic, and constitutive) were set. Stress and stability analyses were carried out with this model; furthermore, deep beams of varying stiffness, layered beams, and beams having openings were analyzed. For slender beams, the results obtained with the Airy stress function approach showed good agreement with those of the Euler-Bernoulli beam theory, and for deep beams, the shapes of stress distributions were in good agreement with a proper understanding of the behavior of structures. On the other hand, the displacement potential function approach delivered unsatisfactory results, probably due to the use of an inefficient equation solver; a more powerful tool will be needed in future research for this purpose.

Hard tissue apposition along the root canal walls is a slow, normally occurring physiological aging process. In response to tooth wear, local deposition of hard tissue may also occur in the pulp at a slow pace. Sometimes, the rate of hard tissue deposition acceleration may seem to be uncontrolled after dental trauma, autotransplantation, and orthodontic therapy, leading to rapid partial or total obliteration of the root canal space. This situation is called calcific metamorphosis (CM) or pulp canal obliteration (PCO). Although the incidence of pulpal necrosis in these teeth is believed to be infrequent, conventional endodontic therapy in severely calcified canals poses extreme difficulties and a higher risk for procedural accidents. This article aims to review the available approaches for the predictable negotiation of calcified canals and to introduce the buckling resistance activation test (BRAT) technique.

Many combinatorial optimization problems are hard to solve within the polynomial computational time or NP-hard problems. Therefore, developing new optimization techniques or improving existing ones still grab attention. This paper presents an improved variant of the Ant Colony Optimization meta-heuristic called Enhanced Hyper Cube Framework ACO (EHCFACO). This variant has an enhanced exploitation feature that works through two added local search movements of insertion and bit flip. In order to examine the performance of the improved meta-heuristic, a well-known structural optimization problem of laminate Stacking Sequence Design (SSD) for maximizing critical buckling load has been used. Furthermore, five different ACO variants were concisely presented and implemented to solve the same optimization problem. The performance assessment results reveal that EHCFACO outperforms the other ACO variants and produces a cost-effective solution with considerable quality.

This paper studies the combined effect of corrosion and fatigue on the growth of cracks in aircraft and on the effect of skin corrosion and stress corrosion cracking on the load bearing capacity of rib stiffened aircraft wings. In this context it is shown that the growth of cracks from surface pitting, and also from intergranular cracking at a fastener hole, can be accurately computed using the Hartman-Schijve variant of the NASGRO crack growth equation. The examples studied support the lead crack approach, that has been independently developed by the USAF and the Australian Defence Science Technology Group, in which the growth of lead cracks is often exponential. In the case of skin corrosion it is shown that to be consistent with the US Joint Service Structural Guidelines (JSSG2006) assessment of its effect on the load bearing capacity of the wing should involve an assessment of whether at 115% DLL the remaining material exceeds the yield stress of the material.

Background: Previous investigations have found a correlation between abnormal curvatures and a variety of patient complaints such as cervical pain and disability. However, no study has shown that loss of the cervical curve is a direct result of exposure to a motor vehicle collision (MVC). This investigation presents a retrospective consecutive case series of patients with both a pre-injury cervical lateral radiograph (CLR) and a post-injury CLR after exposure to a MVC. Computer analysis of digitized vertebral body corners on CLRs was performed to investigate the possible alterations in the geometric alignment of the sagittal cervical curve. Methods: Three spine clinic records were reviewed, over a 2-year period, looking for patients where both an initial lateral cervical x-ray and an examination were performed prior to the patient being exposed to a MVC; afterwards an additional exam and radiographic analysis were required. A total of 41 patients met the inclusion criteria. Examination records of pain intensity on numerical pain rating scores (NPRS) and neck disability index (NDI), if available, were analyzed. The CLRs were digitized and modeled in the sagittal plane using curve fitting and the least squares error approach. Radiographic variables included total cervical curve (ARA C2-C7), Chamberlain’s line to horizontal (skull flexion), horizontal translation of C2 relative to C7, segmental translations (retrolisthesis and anterolisthesis), and circular modelling radii. Results: There were 15 males and 26 females with an age range of 8-65 years. Most participants were drivers (28) involved in rear end impacts (30). The pre-injury NPRS was 2.7 while the post injury was 5.0; p < 0.001. The NDI was available on 24 /41 (58.5%) patients and was found to increase following exposure to the MVC: 15.7% to 32.8%, p < 0.001. An altered cervical curvature was identified following exposure to MVC, characterized by an increase in radius of curvature and an approximate 8° reduction of lordosis from C2-C7; p < 0.001. The mid cervical spine (C3-C5) showed the greatest curve reduction with localized mild kyphosis at these levels on average. Several participants developed segmental translations that approached the instability value of translation > 3.5mm. Conclusions: Abnormalities of cervical lordosis occurred following exposure to a MVC. The average loss of cervical curvature was 8° from C2-C7, with mild flexion of the mid cervical segments. Snap through type or dynamic buckling during the MVC may explain our findings. The primary contribution of this study to the motor vehicle collision literature is that altered cervical lordosis may result from MVC exposures and the consequences of an altered cervical alignment, in turn, may lead to future pain, disability and decreased health-related quality of life.

This study investigates the elastic buckling behaviour of skew Functionally Graded Material (FGM) thin plates featuring a circular opening. FGM materials, 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 modelling 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 the increment of 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%. This research contributes to the advancement of understanding FGM thin plates’ behaviour 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.

A new utilization of entropy in the context of buckling is presented. The novel concept connecting strain energy and entropy for a pin-ended strut is derived. This concept rationalizes the ranking of buckling modes based on 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 modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of buckling modes that coincide with the measurement of 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 given energy roughly decreases with the inverse square of the mode index. For practical engineering, the 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.

Steel fibres provides ductility to concrete structures. This in turn gives possibility to replace or reduce conventional reinforcement in structural elements. In this study the focus is on structural walls and the fibres as potential replacement for horizontal reinforcement in areas where vertical re-bars are needed. An experimental study was conducted, in which prismatic specimens with longitudinal re-bars were subjected to centric loading. Ten samples with 12 specimens in each were tested. The parameters considered were: fibre content, concrete cover for the longitudinal bars, and presence of stirrups. Self-compacting concrete with 30 and 60 kg/m3 steel fibres was used. The influence of fibres on maximum load, stiffness, and ductility of the specimens is evaluated. The results show that fibres eliminated brittle collapse and spalling of concrete at failure. Samples with fibres tend to have reduced maximum force and stiffness but increased ductility. The specimens with fibre content of 60 kg/m3 showed more ductile behaviour than the ones with minimum amount of conventional stirrups. The study suggests that combination of steel fibres and conventional re-bars can lead to less qualitative compactness of the self-compacting concrete, which in turn may reduce load bearing capacity and stiffness of the structure.

Gol'denveizer's problem of a torus has been analyzed by Audoly and Pomeau (2002) and Sun (2021). However, all of the investigations of Gol'denveizer's problem of an elastic torus have been linear. In this paper, the finite element method is used to more accurately address this problem. Furthermore, Sun (2021) cannot be solved by nonlinear analysis. We research the nonlinear mechanical properties of Gol'denveizer's problem of circular and elliptic tori, and relevant nephograms are given. We study the buckling of Gol'denveizer's problem of an elastic torus, and propose failure patterns and force-displacement curves of tori in the nonlinear range. Investigations reveal that circular tori have more rich buckling phenomena as the parameter a increases. Gol'denveizer's problem of the buckling of an elliptic torus is analyzed, and we find a new buckling phenomenon called a "skirt." As a/b increases, the collapse load of an elliptic torus of the Gol'denveizer problem is enhanced gradually.

Variable cross-section arch is widely used in practical engineering because of its beautiful arc and excellent mechanical properties. However, there is still no systematic and comprehensive study on the out-plane buckling of variable cross-section arch. In view of this, this paper is concentrated on an elastic analytical research of out-plane buckling of arches with variable cross-section under a uniformly distributed radial local load. The pre-buckling and out-plane buckling behaviour of a variable cross-sectional arch under an external load is quite different from that of an arch with uniform cross-section. The Castigliano's second theorem is used to establish pre-buckling force method equilibrium equations for variable cross-sectional arches under a uniformly distributed radial local load, and corresponding analytical solutions of normal stress, axial compression and the bending moment are obtained. Based on the energy method and the Ritz method, analytical solutions of the critical load for the elastic out-plane buckling of arches with variable cross-section are derived. Comparisons with ANSYS results indicated that the analytical solutions are able to accurately predict the pre-buckling internal forces and critical out-plane buckling load of variable cross-section arches subjected to a uniformly distributed radial local load. It is found that the internal forces and the out-plane buckling load of an arch are significantly affected by the variation of cross-sectional height. With the ratio of cross-sectional height of the top to the end increase, the bending moment decreases and the axial force and critical out-plane buckling load increase. Analytical solutions of pre-buckling internal force and critical out-plane buckling load problems for arches with variable cross-section have a wider significance, since they can provide an effective explicit analytic method for the optimal design of arch structure.

Buckling defect will appear on the outer surface of the deformed ring during constrained ring rolling (CRR) of aluminum alloy thin wall conical ring with inner high ribs (AATWCRIHR), if the geometrical dimension of the ribs doesn't 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 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 design variables and defining the area of buckling profile as 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. Also the optimal parameter combination to minimize the area of buckling profile is obtained and verified using FE simulation. Results show that the AATWCRIHR after optimization doesn’t generate the buckling defect during constrained ring rolling, and it is proved 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.