Distribution Of Imperfections Research Articles

Stability of hot-finished and cold-formed steel hollow section columns: A comparative study

A comparative study into the buckling behaviour of hot-finished and cold-formed steel hollow section members subjected to axial compression is presented in this paper. The main differences between hot-finished and cold-formed hollow sections are initially discussed. An experimental programme conducted to investigate the local, global and local-global interactive buckling of hollow section columns is then described. Three S355 normalised hot-finished and three S355/S420 (dual certified) cold-formed profiles, covering circular, square and rectangular hollow sections (CHS, SHS and RHS respectively), were studied. The stress-strain characteristics of the examined materials were obtained through tensile coupon tests. 3D laser scanning was utilised to determine the distribution of geometric imperfections in selected SHS test specimens and a consistent approach to characterise different forms of geometric imperfections from the scan data is put forward. A stub column test was carried out on each cross-section to examine its local buckling behaviour, and a series of long column tests were performed on all test profiles. In total, 21 tensile coupon tests, six stub column tests and 40 long column tests were conducted in this programme. Finite element models were also developed, validated and used for parametric studies to generate supplementary numerical datasets. The obtained test and numerical data, along with the existing experimental results collected from the literature, were used to evaluate the accuracy and reliability of the Eurocode 3 (EC3) stability design provisions for hot-finished and cold-formed hollow section columns; aspects requiring improvements are highlighted to guide future studies.

Influence of random geometrical imperfection on loading capacity of scaffold based on stochastic numerical model

The existing data indicate that two-thirds of engineering accidents occur during construction among which engineering accidents caused by scaffold collapse account for a large proportion. Due to the complex mechanical behavior of connection and random nature of scaffold system caused by random geometrical imperfection, the reliability of scaffold system is lower than other kinds of building structures. However, the method considering the random geometrical imperfection is limited. To facilitate the analysis of random geometrical imperfection, the original numerical algorithm is proposed based on ANSYS Parametric Design Language. Through proposed method, two types of geometrical imperfections, i.e., the nodal location error and initial curvature can be automatically considered. The randomness in initial curvature includes random magnitude and random direction. The established numerical model is as close to reality as possible and the process of establishing stochastic numerical model can be automatically finished. The only work that needs to be done is to enter the dimensions of the scaffold. Except the propose of numerical algorithm, the objective of this study is to reveal the influence of geometrical imperfection on random distribution of loading capacity of scaffold system under different load conditions. The influence of random geometrical imperfection on probabilistic distribution of loading capacity is systematically investigated. The results indicated that there may be several buckling modes exist and the buckling mode occurred in actual condition is closely related to the random distribution of geometrical imperfection. The load factor of internal post (point 3) is 8 %–12 % larger than that of corner post. The load factor of side post is 4.7 %–7.2 % larger than that of corner post. The ultimate bending capacity Mu has little influence on the loading capacity of scaffold system when the initial bending stiffness ko is small enough.

Exploring the sintering behavior of a complex ceramic powder system using in-situ X-ray nano-tomography

As a typical example of constrained sintering, the behavior of a complex ceramic powder system with multi-heterogeneities has been investigated. This powder system comprises inherent imperfections as well as rigid inclusions that act as constraints to densification. The sintering process of the system was monitored by in-situ X-ray nano-tomography at the European Synchrotron Radiation Facility (ESRF). This technique enables three-dimensional (3D) imaging of the microstructure with a voxel size of 25 nm. The images obtained reveal the distribution of imperfections in the powder system, such as particle aggregation and pore segregation in and around them. The subsequent in-situ evaluations show the evolution of the microstructure in the presence of inclusions. The study addresses the questions pertaining to the effect of the added constraints, the consequent crack generation and their implication on the final densification of the material.

Characterisation of mode-I fracture resistance of adhesive layers with imperfections

In this work, a novel procedure to evaluate the influence of imperfections at the interface (such as voids and interfacial failure) on the fracture resistance of adhesive joints in mode-I debonding is proposed, based on an image-processing analysis of the crack surface. Its application to the characterisation of fracture resistance of aluminium DCB specimens bonded with an epoxy adhesive leads to a more accurate evaluation of the ‘effective’ fracture resistance by taking into account the distribution of imperfections along the interface, therefore also confirming that the typical oscillations and drops in the load–displacement curve can be attributed to the imperfections.

Design of press-braked stainless steel C-beams subjected to global-distortional interaction buckling

A detailed finite element (FE) model studying the global-distortional (G-D) interaction of press-braked stainless steel C-beams was reported herein. According to previous bearing capacity tests, the model incorporating measured material characteristics and precise geometric imperfections was validated by comparing to the failure mode, load-vertical displacement curve and bearing capacity. Following the calibration of the model, comprehensive parametric investigations were conducted to investigate the influence of the distribution and amplitude of geometric imperfections, material strain hardening coefficient and effect of cold working. It is found that the distribution of geometric imperfections has significant and complex impacts on the failure mode and ultimate capacity, while the amplitude of imperfection could have positive or negative effects on the ultimate capacity. The accuracy of the design methods provided by EN 1993–1-4, AS/NZS 4673 and ASCE 8–22 was assessed using the test data. All codes are found to account for distortional buckling by employing the Effective Width Method (EWM) to reduce the compression plate area. The calculation results were discrete. Therefore, based on the Direct Strength Method (DSM), a novel and accurate design method was developed for the G-D interaction of stainless steel C-beams. The strong correlation between the ratio of ultimate capacity to global buckling bearing capacity and the G-D interaction slenderness was verified by 260 numerical analyses prior to proposing the new design method. The proposed design method underwent a reliability analysis using first order reliability method to meet the requirement of ASCE 8–22.

Seismic analyses of single-layer dome structures with random geometrical imperfections under stochastic ground motions

In this paper, seismic analyses of single-layer dome structures are carried out, with a particular emphasis on the incorporation of randomness in both geometrical imperfections and ground motions. First, the paper introduces models for random geometrical imperfections and stochastic ground motions, employing the Stochastic Imperfection Mode Superposition Method (SIMSM) for imperfections and utilizing the Spectral Representation Method (SRM) for ground motions. These models are designed to comprehensively account for the inherent uncertainties in real-world structural behavior. Subsequently, the Probability Density Evolution Method (PDEM) is applied to investigate the probabilistic response and seismic reliability of dome structures, which allows for a detailed examination of key performance indicators, such as displacement, plastic ratio, and strength damage, under the influence of random factors. Both deterministic and stochastic analyses are conducted to gain insights into the impact of randomness in geometrical imperfections and ground motions. The computational results unveil a crucial finding: an unfavorable distribution of imperfections can significantly compromise the dynamic performance and safety of single-layer dome structures. Furthermore, the paper delves into parametric analyses, with a specific focus on imperfection amplitude, the rise-span ratio and roof load as pivotal parameters. These analyses provide valuable insights into the sensitivity of the structural response to variations in these critical design factors.

An experimental study on shear resistance of austenitic and duplex stainless steel plate girders with perforated webs

Stainless steel is increasingly being used in the field of engineering as building construction materials, as it has an inherent ability to resist corrosion, as well as other environmental benefits. When used as plate girders, web perforations are often required to accommodate building services. In the literature, no experimental study has been reported that investigates the shear resistance of austenitic and duplex stainless steel plate girders with perforated webs. This issue is addressed herein. A detailed experimental program is described comprising eight stainless steel plate girders. The plates are austenitic grade EN 1.4301 and duplex grade EN 1.4462, and the depth of web is fixed as 500 mm and 700 mm. For comparison, specimens with perforated webs and solid webs were tested. Prior to shear tests, the distribution of initial geometrical imperfections was determined through three-dimensional (3D) scanning. Finite element (FE) models incorporating the material non-linearity and initial geometric imperfections were then developed. The results of FE models were validated against the experimental results. Using the validated FE models, a parametric study comprising 182 FE models was then undertaken, and variables which were examined included local geometrical imperfections, aspect ratio, end conditions, hole ratio and stainless steel grades. The results suggested that for those members with a hole diameter - web height ratio of 0.6, the shear resistance was reduced by 52% on average due to the web perforation. The design rules given in Eurocodes, American Specification and those design recommendations proposed by Chen et al. (2023) were evaluated.

Multiscale damage modelling of notched and un-notched 3D woven composites with randomly distributed manufacturing defects

This work proposes a stochastic multiscale computational framework for damage modelling in 3D woven composite laminates, by considering the random distribution of manufacturing-induced imperfections. The proposed method is demonstrated to be accurate, while being simple to implement and requiring modest computational resources. In this approach, a limited number of cross-sectional views obtained from micro-computed tomography (µCT) are used to obtain the stochastic distribution of two key manufacturing-induced defects, namely waviness and voids. This distribution is fed into a multiscale progressive damage model to predict the damage response of three-dimensional (3D) orthogonal woven composites. The accuracy of the proposed model was demonstrated by performing a series of finite element simulations of the un-notched and notched tensile tests (having two different hole sizes) for resin-infused thermoplastic (Elium®) 3D woven composites. Excellent correlation was achieved between experiments and the stochastic finite element simulations. This demonstrates the effectiveness of the proposed stochastic multiscale model. The model successfully captured the stochastic nature of tensile responses (ultimate tensile strength and stiffness), damage modes (matrix damage and fibre failure), and initiation and propagation of transverse cracks in thermoplastic 3D woven composites, consistent with experimental observation. The stochastic computational framework presented in this paper can be used to guide the design and optimization of 3D textile composite structures.

Evaluation of mechanical properties of glass fiber-reinforced composites depending on length and structural anisotropy

Recently, as the size of liquid natural gas (LNG) carriers has dramatically increased, applied force in the LNG Cargo Containment System (CCS) has also increased. However, the existing E-glass fiber-reinforced composite, which plays an important role to prevent accident as secondary barrier induced LNG leakage, has remained unchanged. In case of in-situ length of the composite in membrane type of MARK-III LNG CCS, it is continuously installed as a prolonged structure by using automatic bonding machine (ABM). From this point of view, it should be considered that the length effect of the mechanical properties to represent an infinitely long distance for structural reliability. Fracture strength of a brittle material, such as glass fiber components, is generally not constant because of the variable quantity and distribution of imperfections throughout the composites. In this study, 2-parameters of Weibull distribution were derived to standardize the widely dispersed fracture strengths under the quasi-static tensile test condition. As a result of the experiments by length, the standardized failure strength associated with scale parameter (63.2% probability of failure over all the repeated tests) in the Weibull distribution increases until it reaches a specific length at 250 mm, at which point it stops rising and converges to a constant value. This tendency indicates that material properties at the specific length will be reliable for mechanical evaluation of the composites under the infinitely prolonged condition.

Probabilistic buckling of imperfect hemispherical shells containing a distribution of defects.

The buckling of spherical shells is plagued by a strong sensitivity to imperfections. Traditionally, imperfect shells tend to be characterized empirically by the knockdown factor, the ratio between the measured buckling strength and the corresponding classic prediction for a perfect shell. Recently, it has been demonstrated that the knockdown factor of a shell containing a single imperfection can be predicted when there is detailed a priori knowledge of the defect geometry. Still, addressing the analogous problem for a shell containing many defects remains an open question. Here, we use finite element simulations, which we validate against precision experiments, to investigate hemispherical shells containing a well-defined distribution of imperfections. Our goal is to characterize the resulting knockdown factor statistics. First, we study the buckling of shells containing only two defects, uncovering non-trivial regimes of interactions that echo existing findings for cylindrical shells. Then, we construct statistical ensembles of imperfect shells, whose defect amplitudes are sampled from a lognormal distribution. We find that a 3-parameter Weibull distribution is an excellent description for the measured statistics of knockdown factors, suggesting that shell buckling can be regarded as an extreme-value statistics phenomenon. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Local – distortional interaction buckling of stainless steel lipped C-section beams

Based on a bearing capacity test of 10 specimens composed of 20 stainless steel lipped C-section components, a refined finite element model was established and verified to investigate the failure mode and bearing capacity. 267 numerous parametric analyses were carried out to investigate the effects of the distribution and amplitude of initial geometric imperfections, strength improvement of corner and buckling slenderness ratio on the buckling modes and bearing capacity of stainless steel beams. The effects of both distribution and amplitude of initial geometric imperfections on the bearing capacity were significant. However, the effect of amplitude of initial geometric imperfections on the buckling modes was small. When the ratio of cross-sectional area of corner to the whole cross-sectional area was smaller than 5%, the increase of strength improvement of corner to the bearing capacity was within 5%. When the ratio was larger than 5%, the increase was more significant. The existing methods for calculating the bearing capacity of local – distortional interaction buckling of carbon steel and high-strength steel lipped C-section beams underestimate that of stainless steel lipped C-section beams. Therefore, two design methods for local – distortional interaction buckling of stainless steel lipped C-section beams based on Direct Strength Method were proposed for the first time. A reliability analysis of the proposed methods was conducted to verify the reliability for engineering application.

Stochastic Buckling of Geometrically Imperfect Beams on Elastic Foundation

Abstract Geometrical imperfections are ubiquitous in load-bearing structures, including beams, columns, and shells. Fabrication processes of structural members most often create geometrical imperfections of random size and shape, which lead to non-deterministic load-carrying capacity. This study investigates the statistics of the buckling load of a beam with a random initial imperfection profile that rests on a nonlinear elastic foundation. The geometrical imperfection is represented by a zero-mean Gaussian random field, generated using the Karhunen–Loève expansion. The spatial distribution of the random imperfection is characterized by the probability distribution of the local imperfection magnitude and a spatial autocorrelation function. A finite-difference scheme is used to solve the governing equilibrium equation for a given initial imperfection profile, from which the buckling load is determined. Through a set of Monte Carlo simulations, the mean and variance of the buckling load are determined. The simulations reveal the influence of different length scales on the statistics of the buckling load, including the beam length and the autocorrelation length of the geometrical imperfection. The size effects predicted with the simplified model have implications for reliability-based structural design.

Influence of Initial Imperfections on PMMA Spherical Shell

This paper focused on the influence of initial imperfection on the critical load of PMMA pressure spherical shell by introducing buckling modes as the initial defect. Four types of pressure spherical shells including complete spherical shell, spherical shell with single penetration, spherical shell with double penetrations, and hyperspherical shell were studied. The distribution of initial imperfections was given through the modal configuration of linear eigenvalue analysis, and then the buckling critical load of the spherical shell was analyzed by using the consistent modal defect method and N-order modal defect method. Results confirmed that: Initial imperfections have a great different influence on pressure spherical shells with varying penetration. It has the greatest influence on the critical load of a spherical shell with double penetration at a 5 mm defect. With the increase of defect amplitude, the critical load of the spherical shell decreases. The analysis results also show that the first-order mode is usually not the worst geometric defect configuration of PMMA pressure spherical shell. And the worst mode may appear in higher-order mode due to the influence of penetration, initial defect amplitude, and different thickness-diameter ratio.

Impact behavior of beam-column joint with geometric imperfections at weld root

This study numerically investigates dynamic response of welded beam-column joint with different weld imperfections at weld root. The imperfections at weld root, such as incomplete root penetration, shrinkage groove and root concavity, are considered in this study. The size and shape of these imperfections are determined in accordance with ISO 5817 code. Numerical model of welded beam-column joint with imperfections is developed and calibrated by the test results of welded beam-column joint without imperfection under impact load as well as the numerical results of butt-welded joint with grinding profile under static load. The factors of the imperfections, such as the distribution and length of imperfections and the weld quality levels are considered to investigate their effects on the damage mode, dynamic response, and energy dissipation of welded joints subjected to impact loads, as well as the post impact behavior of the joint. Parametric study is carried out to investigate the effect of impact velocity and impact mass on welded joint with different root imperfections. The effect of different weld imperfections on the energy dissipation of joint is also investigated. The most vulnerable form of root imperfection is identified by comparing the joints with different imperfections in terms of damage mode, dynamic response and energy dissipation.

Numerical simulation and constructal design applied to biaxial elastic buckling of plates of composite material used in naval structures

Thin plates when subjected to compressive loads can present a structural instability phenomenon known as buckling, causing displacements out of the plane of the plate. In addition, it is known that the use of composite materials in naval engineering can bring many benefits in the medium and long term, like the major corrosion resistance, when compared with steel structures. Moreover, for specific applications perforated plates are necessary, like passage of cables and pipes, inspection windows, among others. Therefore, to find the optimal geometry of a composite plate with a centered elliptical hole the Constructal Design (CD) was applied in association with the Exhaustive Search (ES) technique and Finite Element Method (FEM). The CD allows the evaluation of the geometry that provides the optimal distribution of imperfections, leading to the maximum value of the performance parameter used for the analysis of solids mechanics problems. Applying different laminations, it was observed an increase in the critical buckling load for a composite plate without perforations of up to 10.47%. In its turn, despite suffering a reduction in the critical load value if compared to the plate without holes, an improvement of 16.89% was observed when optimal and worst geometries for the perforated plates are compared.

Experimental response of hot-rolled stainless steel angle columns

This paper reports on experiments addressing the buckling and collapse behaviour of pin-ended hot-rolled stainless steel equal-leg angle columns under pure axial compression, aiming to provide reliable experimental data needed to develop explicit design guidelines for hot-rolled stainless steel angle columns currently absent in European standard. The systematic experimental programme included two test groups of specimens with nominal dimensions of 60 ×60× 6 mm and 100 ×100× 10 mm produced from austenitic grade EN 1.4301, and involved tensile material tests, geometric imperfection measurements, residual stress measurements, 6 stub column tests and 20 global compression tests. A wide range of column slenderness ratios was carefully selected to account for both elastic and inelastic failure characteristics including flexural and flexural–torsional modes and the influence of the legs’ width-to-thickness ratios. The test setup and procedure together with the key experimental results and characterised failure modes, were fully reported and discussed. The test results were compared with those predicted using the design methods for compressed stainless steel angle columns provided in European and North American standards. It was observed that the specifications offer conservative strength predictions of the tested columns, primarily due to the lower distribution of initial geometric imperfections of tested columns in comparison with the permissible fabrication tolerances that are usually used as the basis of stability checks in codified design.

Leaders and obstacles raise cultural boundaries

We employ an agent-based model for cultural dynamics to investigate the effects of spatial heterogeneities on the collective behavior of a social system. We introduce heterogeneity as a random distribution of defects or imperfections in a two-dimensional lattice. Two types of defects are considered separately: obstacles that represent geographic features, and opinion leaders, described as agents exerting unidirectional influence on other agents. In both cases, we characterize two collective phases on the space of parameters of the system, given by the density of defects and a quantity expressing the number of available states: one ordered phase, consisting of a large homogeneous group; and a disordered phase, where many small cultural groups coexist. In the case of leaders, the homogeneous state corresponds to their state. We find that a high enough density of obstacles contributes to cultural diversity in the system. On the other hand, we find a nontrivial effect when opinion leaders are distributed in the system: if their density is greater than some threshold value, leaders are no longer efficient in imposing their state to the population, but they actually promote multiculturality. In this situation, we uncover that leaders, as well as obstacles, serve as locations for the formation of boundaries and segregation between different cultural groups. Moreover, a lower density of leaders than obstacles is needed to induce multiculturality in the system.

In situ X-ray micro-computed tomography study of the damage evolution of prefabricated through-holes in SLM-Printed AlSi10Mg alloy under tension

Drilling holes used to mechanically connect complex structures would affect the residual stress of metal alloys, resulting in delamination of selective laser melting (SLM)printed bulk samples. These limitations could be overcome by the pre-fabrication of through-holes during SLM processing using computer-aided design (CAD) models with holes. However, thus far, there has been rarely study discussing the impact of pre-fabricated through-holes on damage evolution and failure mechanisms of SLM-manufactured structures under quasi-static tension. In this study, damage evolution in SLM-printed AlSi10Mg alloys with two prefabricated through-holes was investigated. In situ X-ray tomography tensile tests were performed to evaluate the morphology, location, and distribution of geometric imperfections and to clarify their role in the mechanical response of samples under quasi-static tension. To numerically reproduce the experiments at the meso-scale, an image-based finite element model (FEM) was constructed from 3D images and the results were compared to those obtained by ideal CAD model simulation. In addition, damage evolution of geometric defects was extracted from the FEM and experimental results. The geometric defects increased the in-plane shear stress remarkably and resulted in the crack propagation in AlSi10Mg alloys. It was shown that the mechanical response of AlSi10Mg bulk samples was linked to the initial morphological features of through-holes. This comprehensive combined geometric morphology of defects and the mechanical response will serve to complete the dimensional compensation design and replacement of secondary drilling holes in additive manufacturing technology in future studies.

Experimental behaviour of stainless steel plate girders under combined bending and shear

The behaviour of stainless steel plate girders subjected to combined bending and shear was experimentally studied in this paper. Both tensile and compressive material properties of the two adopted stainless steel alloys, including austenitic grade EN 1.4301 and duplex grade EN 1.4462, were determined by standard coupon tests. The three-dimensional (3D) optical scanning technology was introduced to acquire an accurate distribution of initial geometric imperfections for each plate girder specimen. A total of six plate girders were fabricated by hot-rolled stainless steel plates, and were tested to failure under combined bending and shear. In-depth analyses of the critical buckling characteristics, the ultimate resistances and the collapse behaviour of the tested specimens were all presented. The obtained ultimate resistances were further employed to assess the existing moment and shear (M-V) interaction design methods in EN 1993-1-5, GB 50017-2017, ANSI/AISC 360-16 and SEI/ASCE 8-02, and the design proposal presented by Jáger et al. It has been found that most of the existing codified M-V interaction formulae can be applicable for both carbon steel and stainless steel plate girders, yet they lead to relatively conservative predictions for stainless steel plate girders, except that the design method in ANSI/AISC 360-16 provides apparently unsafe strength predictions.

Mesoscale damage analysis of needle-punched carbon/carbon composite considering randomness of inherent defects

Needle-punched carbon/carbon composites (NP C/Cs) are widely used in aerospace applications thanks to their good high-temperature mechanical properties with relatively low cost. To improve their out-plane stiffness and strength, short-cut fibres are introduced into interlayers between plies using a needle-punching technology. This could result in some defects that decrease their in-plane stiffness and strength. Circle-arc beam elements and extended spring elements are proposed in this research to model mechanical performances of punched fibre bundles, isotropic pyrocarbon matrix and short-cut carbon fibre felts in NP C/Cs, respectively. Aided by this beam-spring finite element model, the impacts from features of mesoscopic defects, e.g. irregularity of distribution of local imperfection in planar fiber bundle caused by punching process, to mechanical properties of NP C/Cs are focused in this study. The ranges of bending modulus and bending strength for a NP C/C are estimated considering the randomness of these defects.