Uncertainties In Geometry Research Articles

A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites

The uncertainty quantification is crucial to the high-precision prediction of composites’ effective properties. However, the unclear input uncertainties of multiscale parameters, complex uncertainty propagations of inter-scale correlations, and unaffordable computational cost of massive simulations are three primary problems at present. In this work, an innovative model with high accuracy and feasible cost for the mechanical property prediction of plain woven composites is developed encompassing minimum-size unit cells and multi-scale uncertainty quantification. For the accuracy holding, an uncertainty analysis process consists of the traceability description, inter-scale propagation and quantification is established. The uncertainties of geometry are described by uniform distributions for fiber, fiber bundle and composite scales, respectively; that of constituent properties is described by normal distributions for fiber and matrix, and its propagations to bundle and composite scales are realized by Nataf transformation methods with the consideration of parameter correlations. For the cost control, minimum-size unit cells are formulated by exhaustive analysis of structural symmetries to reduce the computational cost without accuracy compromising for the single simulation, and 1/8 and 1/16 unit cells compared with traditional full-size ones are obtained. The evolution convergence for statistical uncertainties of effective properties is finally obtained with totally reduced computational cost of 89%.

Improving electrocardiographic imaging solutions: A comprehensive study on regularization parameter selection in L-curve optimization in the Atria

BackgroundIn electrocardiographic imaging (ECGI), selecting an optimal regularization parameter (λ) is crucial for obtaining accurate inverse electrograms. The effects of signal and geometry uncertainties on the inverse problem regularization have not been thoroughly quantified, and there is no established methodology to identify when λ is sub-optimal due to these uncertainties. This study introduces a novel approach to λ selection using Tikhonov regularization and L-curve optimization, specifically addressing the impact of electrical noise in body surface potential map (BSPM) signals and geometrical inaccuracies in the cardiac mesh. MethodsNineteen atrial simulations (5 of regular rhythms and 14 of atrial fibrillation) ensuring variability in substrate complexity and activation patterns were used for computing the ECGI with added white Gaussian noise from 40 dB to -3dB. Cardiac mesh displacements (1–3 cm) were applied to simulate the uncertainty of atrial positioning and study its impact on the L-curve shape. The regularization parameter, the maximum curvature, and the most horizontal angle of the L-curve (β) were quantified. In addition, BSPM signals from real patients were used to validate our findings. ResultsThe maximum curvature of the L-curve was found to be inversely related to signal-to-noise ratio and atrial positioning errors. In contrast, the β angle is directly related to electrical noise and remains unaffected by geometrical errors. Our proposed adjustment of λ, based on the β angle, provides a more reliable ECGI solution than traditional corner-based methods. Our findings have been validated with simulations and real patient data, demonstrating practical applicability. ConclusionAdjusting λ based on the amount of noise in the data (or on the β angle) allows finding optimal ECGI solutions than a λ purely found at the corner of the L-curve. It was observed that the relevant information in ECGI activation maps is preserved even under the presence of uncertainties when the regularization parameter is correctly selected. The proposed criteria for regularization parameter selection have the potential to enhance the accuracy and reliability of ECGI solutions.

Remote sensing of high energy charged particle current (HEC) for megavoltage therapeutic electron beams

Objective. We demonstrate detection of high energy particle current (HEC) for MeV therapeutic electron beams. Detection of HEC comprises of remote sensing or acquiring information about HEC inside radiation transport medium from a distance outside of the medium. Approach. HEC is self-propelled motion of charged particles through a radiation transport medium. Remote sensing of HEC is embodied in an experimental setup, which includes homogeneous and heterogeneous phantoms irradiated with 4–15 MeV electron beams and two large area parallel-plane electrodes extraneous to the phantoms providing two-parameter detection. We also introduce a new type of scanning method (depth-scan) for probing object properties along the beamline axis. Main Results. Deterministic radiation transport simulations and measurements agree, considering differences in simulation vs experimental geometry and experimental uncertainties. Significance. This method may be suitable for range detection of charged particle beams, or for probing of radiation opaque objects in non-destructive testing.

Quantification and visualization of uncertainties in reconstructed penumbral images of implosions at Omega.

Penumbral imaging is a technique used in plasma diagnostics in which a radiation source shines through one or more large apertures onto a detector. To interpret a penumbral image, one must reconstruct it to recover the original source. The inferred source always has some error due to noise in the image and uncertainty in the instrument geometry. Interpreting the inferred source thus requires quantification of that inference's uncertainty. Markov chain Monte Carlo algorithms have been used to quantify uncertainty for similar problems but have never been used for the inference of the shape of an image. Because of this, there are no commonly accepted ways of visualizing uncertainty in two-dimensional data. This paper demonstrates the application of the Hamiltonian Monte Carlo algorithm to the reconstruction of penumbral images of fusion implosions and presents ways to visualize the uncertainty in the reconstructed source. This methodology enables more rigorous analysis of penumbral images than has been done in the past.

Research on uncertainties in fuel centrifugal pump based on prediction and reconstruction of internal flow field

Geometric machining errors in the blade profile and variable operating conditions in the extreme operating environment are primary factors leading to the uncertainties in pump performance. This paper presents an analysis of uncertainties of fuel centrifugal pumps by modeling the geometry uncertainty in blade machining based on the Karhunen–Loève (KL) expansion and using a polynomial chaos expansion (PCE) model. First, the geometric uncertainty in the blade machining is described by the KL expansion in three sections and a stochastic simulation of the blade geometry is performed. Then, a PCE surrogate model is trained based on the least angle regression method and validated by the bootstrap method to quantify the uncertainties of performance indices. Finally, the influence mechanism and relative importance of each input uncertainty parameter are investigated using a quasi-Monte Carlo simulation method. The results show that the KL expansion of the blade profile uses the random vector perturbation superposition of three stream surface, achieving the dimensional reduction in the blade machining error. The PCE surrogate model, trained with a dataset of 3 × 106 sample points, exhibits excellent fit, and the R-squared and adjusted R-squared for head coefficient and efficiency are both above 80%. The variance of parameter control points of the reconstructed flow field is less than 0.002. The uncertainties in both operating conditions and parameters have an influence on the distribution of the global flow field, while the influence of the uncertainty in machining error on the global flow field mainly concentrates on the power-generating positions of the blade.

The impact of continental shape in 3D geomechanical models of ancient orogenic belts: An example from the Ancestral Rocky Mountain orogeny

The orientations of ancient intra-cratonic uplifts are commonly used to interpret the boundary tectonism style along concealed, modified, or destroyed continental margins. An implicit assumption is that the tectonism-linked stress field strongly correlated with uplift orientations. However, among other uncertainties, the shape of a stressed domain likely has an influence upon the interior stress field. In many cases of pre-Cenozoic orogenesis, multiple feasible restorations of a continent margin exist. To explore the influence of continent margin position and shape on a hypothetical ancient continental stress field we developed a new 3D geomechanical finite element method (FEM) to evaluate scenarios for the late Paleozoic Ancestral Rocky Mountain orogen (ARMO). Tectonic scenarios were calculated across a range of domains constrained by geologic uncertainty in the pre-ARMO geometry of the continent. Uncertainty for continent geometry prior to the ARMO is estimated from several published palinspastic restorations. The results demonstrate that 10s–100s of km of uncertainty in margin position, as is the case of the ARMO, should not prevent the linkage of stress patterns to styles of boundary tectonism. This work shows it is plausible to simplify the analysis of the ARMO stress/strain field utilizing one continental geometry.

A comprehensive study on seismic dynamic responses of stochastic structures using sparse grid-based polynomial chaos expansion

The seismic response is a critical aspect of structural engineering, as it directly influences the design and safety evaluation of such systems. Structural seismic response becomes more complicated when unavoidable uncertainties in the structure are considered. Therefore, solving and analyzing the stochastic dynamic response of structures efficiently and accurately is of great significance. Various uncertainty quantification methods such as the stochastic finite element method, Monte Carlo method, and polynomial chaos expansion method have made significant progress in this field. However, these methods do not provide a comprehensive study of the seismic response of stochastic structures and efficiency problems rapidly emerge as the number of random variables increases. This paper delivers a comprehensive study of the seismic dynamic response of space truss and reticulated shell structure considering uncertainties in material properties, geometry, and loading. To this end, the finite element model of the structure was first modeled and the deterministic solutions were obtained. Then, polynomial surrogates are modeled for the natural frequency, mode participation factor, mode superposition response, and transient response of the structure under stochastic uncertainties. The sparse grid technique is used to select sparse quadrature points, which overcomes the curse of dimensionality caused by full grid integration. The results demonstrate that the sparse grid-based polynomial chaos expansion is more efficient. Uncertainty quantification reveals the uncertainty of modal analysis, response spectrum analysis, and transient response analysis of space truss and reticulated shell under seismic excitation. In summary, this study provides valuable insights and an efficient and accurate uncertainty quantification tool for the seismic dynamic analysis of stochastic structures, ultimately contributing to safer and more robust structural designs.

Dynamic and uncertainty-based assessment of the progressive collapse probability of prestressed concrete frame structures with infill walls

Since progressive collapse usually has serious consequences, the problem of progressive collapse resistance has gradually become a topical issue in recent years. However, most of the existing studies have been conducted on common reinforced concrete (RC) structures. The methodologies used in the studies are also mostly static and deterministic. There is a lack of research that considers the dynamic effects and uncertainties of pre-stressed structures with infill walls. In this paper, the assessment of progressive collapse probability considering dynamic effect and uncertainties is performed for prestressed concrete frame with infill walls (IW-PC frame) structures. The finite element software OpenSEES is chosen as the analysis platform. By introducing uncertainties in material, geometry and load, five limit states and their quantitative indicators are identified. Based on the nonlinear incremental dynamic analysis (IDA) method, the vulnerability analysis of the IW-PC frame is performed under different working conditions. The vulnerability analysis indicates that the five levels of limit states can visually evaluate the degree of structural damage. Additionally, the resistance relationships of the four structural forms are as follows: IW-PC frame > reinforced concrete frame with infill walls (IW-RC frame) > prestressed concrete frame (PC frame) > RC frame. The load carrying capacity of the frames is significantly increased by the coupling effect of the infill walls and the prestressed strands. Moreover, the prestressed strands can reduce the probability of light and moderate damage, while infill walls have an excellent preventive effect on severe damage. The reliability of the four structures is evaluated using the Zhao-Ono moment method. The results indicate that IW-PC is the safest, followed by IW-RC, PC, and RC.

Evaluation of a single-layer urban energy balance model using measured energy fluxes by scaled outdoor experiments in humid subtropical climate

Urban energy balance models can simulate the localized climate and fluxes in urban areas. They are often evaluated using real urban site observations. However, uncertainties in anthropogenic emission, geometry and materials can hinder interpretation. These uncertainties can be eliminated by scaled outdoor models. We assess the performance of a single-layer urban canopy model (SLUCM) offline in predicting surface energy balance (SEB) fluxes within a street canyon-like urban configuration using field measurements from a scaled outdoor setup in Guangzhou, China. We utilize observations of SEB fluxes and surface temperature from a homogenous scaled urban site characterized by street canyons. The scaled observations in June–December 2020 in a dense urban environment with a height-to-width ratio (H/W) of 2 are employed to assess seasonal variations in model performance. Additionally, the December data from two distinct urban scenarios (H/W = 2(2020) and 0.5(2019)) are utilized to compare model performance in deep and shallow street canyon settings. Results show that QS(R2 = ∼0.47, RMSE = ∼46.0) is the most challenging to predict, followed by QH (R2 = ∼0.92, RMSE = ∼65.5), Q*(R2 = ∼0.99, RMSE = ∼39.5), L↑(R2 = ∼0.95, RMSE = ∼33.7), and K↑(R2 = ∼0.99, RMSE = ∼6.2). SLUCM faces difficulties simulating L↑ particularly during nighttime and cloudy conditions. It also tends to underestimate daytime net radiation (Q*), especially during hot, humid months. Moreover, H/W ratio slightly affects SLUCM's performance in simulating SEB fluxes under dry cool conditions denser urban settings (H/W = 2) show better model performance in K↑, QH, and QS but worse performance in L↑ and Q*.

A Non-Intrusive Stochastic Phase-Field for Fatigue Fracture in Brittle Materials with Uncertainty in Geometry and Material Properties

A Non-Intrusive Stochastic Phase-Field for Fatigue Fracture in Brittle Materials with Uncertainty in Geometry and Material Properties

GUPNet++: Geometry Uncertainty Propagation Network for Monocular 3D Object Detection.

Geometry plays a significant role in monocular 3D object detection. It can be used to estimate object depth by using the perspective projection between object's physical size and 2D projection in the image plane, which can introduce mathematical priors into deep models. However, this projection process also introduces error amplification, where the error of the estimated height is amplified and reflected into the projected depth. It leads to unreliable depth inferences and also impairs training stability. To tackle this problem, we propose a novel Geometry Uncertainty Propagation Network (GUPNet++) by modeling geometry projection in a probabilistic manner. This ensures depth predictions are well-bounded and associated with a reasonable uncertainty. The significance of introducing such geometric uncertainty is twofold: (1). It models the uncertainty propagation relationship of the geometry projection during training, improving the stability and efficiency of the end-to-end model learning. (2). It can be derived to a highly reliable confidence to indicate the quality of the 3D detection result, enabling more reliable detection inference. Experiments show that the proposed approach not only obtains (state-of-the-art) SOTA performance in image-based monocular 3D detection but also demonstrates superiority in efficacy with a simplified framework.

Quantifying Magma Overpressure Beneath a Submarine Caldera: A Mechanical Modeling Approach to Tsunamigenic Trapdoor Faulting Near Kita‐Ioto Island, Japan

AbstractSubmarine volcano monitoring is vital for assessing volcanic hazards but challenging in remote and inaccessible environments. In the vicinity of Kita‐Ioto Island, south of Japan, unusual M ∼ 5 non‐double‐couple volcanic earthquakes exhibited quasi‐regular recurrence near a submarine caldera. Following the earthquakes in 2008 and 2015, a distant ocean bottom pressure sensor recorded distinct tsunami signals. In this study, we aim to find a source model of the tsunami‐generating earthquake and quantify the pre‐seismic magma overpressure within the caldera's magma reservoir. Based on the earthquake's characteristic focal mechanism and efficient tsunami generation, we hypothesize that submarine trapdoor faulting occurred due to highly pressurized magma. To investigate this hypothesis, we establish mechanical earthquake models that link pre‐seismic magma overpressure to the size of the resulting trapdoor faulting, by considering stress interaction between a ring‐fault system and a reservoir of the caldera. The trapdoor faulting with large fault slip due to magma‐induced shear stress in the submarine caldera reproduces well the observed tsunami waveform. Due to limited data, uncertainties in the fault geometry persist, leading to variations of magma overpressure estimation: the pre‐seismic magma overpressure ranging approximately from 5 to 20 MPa, and the co‐seismic pressure drop ratio from 10% to 40%. Although better constraints on the fault geometry are required for robust magma pressure quantification, this study shows that magmatic systems beneath calderas are influenced significantly by intra‐caldera fault systems and that tsunamigenic trapdoor faulting provides rare opportunities to obtain quantitative insights into remote submarine volcanism hidden under the ocean.

A Bayesian Source Model for the 2022 Mw6.6 Luding Earthquake, Sichuan Province, China, Constrained by GPS and InSAR Observations

Until the Mw 6.6 Luding earthquake ruptured the Moxi section of the Xianshuihe fault (XSHF) on 5 September 2022, the region had not experienced an Mw >6 earthquake since instrumental records began. We used Global Positioning System (GPS) and Sentinel-1 interferometric synthetic aperture radar (InSAR) observations to image the coseismic deformation and constrain the location and geometry of the seismogenic fault using a Bayesian method We then present a distributed slip model of the 2022 Mw6.6 Luding earthquake, a left-lateral strike-slip earthquake that occurred on the Moxi section of the Xianshuihe fault in the southwest Sichuan basin, China. Two tracks (T26 and T135) of the InSAR data captured a part of the coseismic surface deformation with the line-of-sight displacements range from ∼−0.16 m to ~0.14 m in the ascending track and from ~−0.12 m to ~0.10 m in the descending track. The inverted best-fitting fault model shows a pure sinistral strike-slip motion on a west-dipping fault plane with a strike of 164.3°. We adopt a variational Bayesian approach and account for the uncertainties in the fault geometry to retrieve the distributed slip model. The inverted result shows that the maximum slip of ~1.82 m occurred at a depth of 5.3 km, with the major slip concentrated within depths ranging from 0.9–11 km. The InSAR-determined moment is 1.3 × 1019 Nm, with a shear modulus of 30 GPa, equivalent to Mw 6.7. The published coseismic slip models of the 2022 Luding earthquake show apparent differences despite the use of similar geodetic or seismic observations. These variations underscore the uncertainty associated with routinely performed source inversions and their interpretations for the underlying fault model.

Probabilistic capacity models and fragility estimate for NRC and UHSC panels subjected to contact blast

A Performance-based Design (PBD) framework for protective structural walls/slabs susceptible to contact blast has been developed. Performance-based capacity models are predicted for three performance levels namely, operation with minimum damage (P1), medium damage (P2) and collapse prevention (P3) allied to four damage states. The current study examines multi-level PBD instead of single-level conventional collapse-based design. All these probabilistic models are developed by combining mechanical models with dimensionless explanatory functions. Bayesian inference based on numerical data is used to evaluate the unknown model parameters. The constructed models take into account all inherent aleatoric and epistemic uncertainties of material and geometry. For Normal Reinforced Concrete (NRC) and Ultra-high Strength Concrete (UHSC) panels subjected to contact blast, finite element (FE) modelling (LS-DYNA) is used to obtain the necessary data. The validated models have a high level of agreement with chosen experimentation. In addition, local damage formulations, such as crater diameter, crater depth, spall diameter, spall depth, and perforation diameter, are also developed. The developed capacity models are used to estimate fragility, and the obtained plots demonstrate the consistency of the evaluated equations. When subjected to a contact blast, these probabilistic models can be used to construct protective structures based on the expected demand.

Life-Cycle Seismic Reliability Analysis of a Railway Cable-Stayed Bridge Considering Material Corrosion and Degradation

To study the life-cycle seismic reliability analysis (SRA) of cable-stayed bridges (CSBs) taking into account chloride-induced corrosion and degradation of components, an actual railway CSB with uncertainties in structural geometry and material corrosion coefficients was employed in this investigation, and time-dependent models of CSB components at different service times were studied. Based on the OpenSees batch program, we adapted a mass numerical computation to obtain time-dependent non-linear seismic response and probability density function (PDF) of response via the multiplier dimensional-reduction method (MDRM) and the maximum entropy method with fractional moments (FM-MEM). Next, the time-dependent failure possibility of every component and the association coefficient between the failure modes of different parts were acquired. In the end, the product of the conditional marginal (PCM) approach was employed to obtain the life-cycle failure possibility of the CSB system. The results showed that the system failure possibility of the CSB in a corrosive environment increases significantly with increasing servicing time.

Robust design of a low cost flat plate collector under uncertain design parameters

The high expenses of electrical energy needed for heating water can be significantly decreased by using flat plate collectors. Therefore, the design of flat plate collectors having optimal performance has received a lot of attention in recent research projects. However, due to the existence of uncertainties in material properties, geometry and environmental conditions, it is imperative to incorporate uncertainty analysis into the design optimization to obtain reliable results. In this work, a multi-criteria robust design based on multi-objective optimization of the flat plate collector system is developed. Firstly, a determinist optimization (non-consideration of uncertain design parameters in this optimization strategy) of flat plate collector design is conducted. The obtained results showed that the determinist optimization leads to a flat plate collector design with 30% efficiency sensitivity and 27% total cost sensitivity to design parameters uncertainty. As an alternative, the multi-criteria robust design based on multi-objective optimization is developed. For this goal, a combined multi-objective colonial competitive algorithm and polynomial chaos expansion method is developed and used. This multi-criteria robust optimization considers simultaneously four objectives functions including the flat plate collector efficiency, the flat plate collector total cost, and their sensitivities to uncertain design parameters. It is noted that the multi-criteria robust design based on multi-objective optimization offers a robust flat plate collector with performances sensitivity to design parameters uncertainty less than 4.5%. Furthermore, when compared to the literature results, the performances sensitivities of flat plate collector design, obtained by the multi-criteria robust design based on multi-objective optimization, were reduced until 64%.

Spatiotemporal variability in ocean-driven basal melting of cold-water cavity ice shelf in Terra Nova Bay, East Antarctica: roles of tide and cavity geometry

Mass loss from ice shelves occurs through ocean-driven melting regulated by dynamic and thermodynamic processes in sub-ice shelf cavities. However, the understanding of these oceanic processes is quite limited because of the scant observations under ice shelves. Here, a regional coupled sea-ice/ocean model that includes physical interactions between the ocean and the ice shelf is used as an alternative tool for exploring ocean-driven melting beneath the Nansen Ice Shelf (NIS) which is a cold-water cavity ice shelf located beside Terra Nova Bay (TNB) in East Antarctica. For the first time, this study identifies the spatiotemporal variability signatures for different modes of ocean-driven melting at the base of NIS. In February (austral summer), basal melting substantially increases where the ice shelf draft is relatively small in the vicinity of the ice shelf front, contributing 78% of the total NIS melting rate. As the dominant source of NIS mass loss, this melting is driven by tide-induced turbulent mixing along the sloping ice shelf base and summer warm surface water intruding beneath and reaching the shallow parts of the ice shelf. In contrast, the NIS has relatively high basal melting rates near the grounding line in September (austral winter) primarily because of the intrusion of high-salinity shelf water produced by polynya activity in TNB that flows into the cavity beneath NIS toward the deep grounding line. Of the total melting rate of NIS in winter, 36% comes from regions near the grounding line. In addition, the contributions of tides and realistic cavity geometry to NIS basal melting are identified by conducting sensitivity experiments. Tidal effects increase the melting of NIS throughout the year, particularly contributing as much as 30% to the areas of ice draft shallower than 200 m in summer. Sensitivity results for uncertainty in cavity geometry show that spurious vertical mixing can be locally induced and enhanced by interaction between tides and the unrealistic topography, resulting in excessive basal melting near the NIS frontal band. The sensitivity experiments have shown that tides and realistic cavity geometry bring a significant improvement in the estimation of basal melt rates through a numerical model.

Improved interval finite element for analysis of planar frames

The Interval Finite Element Method (IFEM) can be used for the analysis of structures with uncertainties in load, geometry, and material. However, a naïve application of IFEM leads to meaningless overestimated enclosures due to interval dependency. In this work, a new finite element solution for planar frames under interval uncertainties is introduced. In particular, for a beam element, we present a new decomposition of the stiffness matrix that yields a significant reduction of overestimation. The IFEM equations are solved utilizing a new variant of the iterative enclosure method. Further, both primary and derived variables are simultaneously solved attaining the same accuracy. As a result, the proposed formulation gives the tightest guaranteed enclosure of the exact solution in comparison with other known interval methods, as illustrated in several numerical examples.

Effect of uncertain clinical conditions on the early healing and stability of distal radius fractures

Background and objectivesThe healing outcomes of distal radius fracture (DRF) treated with the volar locking plate (VLP) depend on surgical strategies and postoperative rehabilitation. However, the accurate prediction of healing outcomes is challenging due to a range of certainties related to the clinical conditions of DRF patients, including fracture geometry, fixation configuration, and physiological loading. The purpose of this study is to investigate the influence of uncertainty and variability in fracture/fixation parameters on the mechano-biology and biomechanical stability of DRF, using a probabilistic numerical approach based on the results from a series of experimental tests performed in this study. MethodsSix composite radius sawboneses fitted with titanium VLP (VLP 2.0, Austofix) were loaded to failure at a rate of 2 N/s. The testing results of the elastic and plastic behaviour of the VLP were used as inputs for a probabilistic-based computational model of DRF, which simulated mechano-regulated tissue differentiation and fixation elastic capacity at the fracture site. Finally, the probability of success in early indirect healing and fracture stabilisation was predicted. ResultsThe titanium VLP is a strong and ductile fixation whose flexibility and elastic capacity are governed by flexion working length and bone-to-plate distance, respectively. A fixation with optimised designs and configurations is critical to mechanically stabilising the early fracture site. Importantly, the uncertainty and variability in fracture/fixation parameters could compromise early DRF healing. The physiological loading uncertainty is the most adverse factor, followed by the negative impact of uncertainty in fracture geometry. ConclusionsThe VRP 2.0 fixation made of grade II titanium is a desirable fixation that is strong enough to resist irreparable deformation during early recovery and is also ductile to deform plastically without implant failure at late rehabilitation.

Non-Linear Behavior and Design of Steel Structures: Review and Outlook

The high strength and stiffness-to-weight ratios of structural steel often result in relatively slender members and systems, which are governed to a great extent by stability limit states. However, predicting the stability of slender structures is difficult due to various inherent uncertainties in material and geometry. Generally, structural and member stabilities are nonlinear problems that cannot be directly evaluated based on the section strength using conventional analysis method. Nonlinear behaviors are basically categorized as materially and geometrically nonlinear, which can be observed at the cross-sectional, member, and frame levels. To provide a comprehensive understanding of the current state-of-the-art non-linear behavior and design of steel structures and to identify key areas for future research and development, this paper presents a review on the materially and geometrically nonlinear effects of steel structures. A discussion of the effects of material yielding accentuated by the presence of residual stresses, initial imperfections, and end conditions will be conducted. The stiffness reduction due to second-order effects and material yielding will be illustrated. Moreover, current and emerging design approaches that consider nonlinear responses will also be reviewed and evaluated. Lastly, with the development of modern flexible and complex steel structures, which sometimes violate fundamental assumptions of the current stability design method, the application of advanced analysis and design methods will be explored.