Nonlinear Finite Element Method Research Articles

Damage and failure of semi-rigid steel joints during progressive collapse

Ductile metal materials during a ductile failure will suffer from micro-void damage, simulation of which can contribute to the prediction of the macro fracture of steel structure. In this paper, the Gurson-Tvergaard-Needleman (GTN) constitutive model which describes the aggregate failure of metal voids is selected as the constitutive relation to investigating the damage evolution and fracture of semi-rigid joints in steel structures during a progressive collapse. During the process, specific parameters of the GTN model of steel are confirmed based on the combined results of the test and numerical simulation. The progressive collapse of two kinds of semi-rigid joints of steel pipe-to-H shaped steel were simulated by a nonlinear finite element method. A comparison between the simulation and test results verified that the GTN constitutive model can accurately simulate the fracture failure of the steel semi-rigid joints. Besides, a simplified joint failure model based on concentrated plastic hinge theory is proposed. Considering the damage and fracture of semi-rigid joints and the collision contact among different components, the progressive collapse of the semi-rigid steel frame structure is simulated by explicit dynamic analysis based on a finite particle method. Afterwards, the dynamic response of the structural progressive collapse can be predicted more accurately.

Non-linear buckling analysis of ship hull stiffened panels

Stiffened panels are crucial in maritime applications, where buckling is a primary structural failure concern. Typically, assessing the buckling capacity of these panels relies on established guidelines like DNV-RP-C201 and NS-EN 1993-1-5. Alternatively, non-linear finite element methods, guided by DNV-RP-C208, can be used. However, there’s a significant research gap in calibrating buckling capacities for large ship-hull stiffened panels. This paper bridges that gap by employing non-linear finite element analysis to evaluate the buckling capacity of ship hull stiffened panels and compare the results with DNV-RP-C201. It establishes a capacity benchmark by thoroughly comparing results for a plated panel. Subsequently, it develops a validated model using ABAQUS, introducing material and geometric nonlinearities, including a mid-stiffener span imperfection ranging from 0.06% to 1% of the stiffener span length for 99.7% calibration. The validated non-linear model then assesses the impact of holes on buckling capacity under uniaxial and gravity loads, revealing a clear correlation between reduced buckling capacity.

Preliminary Theoretical Considerations on the Stiffness Characteristics of a Tensegrity Joint for the Use in Dynamic Orthoses

Early motion therapy plays an important role for effective long-term healing of joint injuries. In many cases, conventional dynamic orthoses fail to address the intricate movement possibilities of the underlying joints, limited by their simplistic joint representations, often represented by revolute joints, enabling rotations by only one axis. In this paper, a two-dimensional compliant tensegrity joint for use in biomedical applications is investigated. It consists of two compressed members and five compliant tensioned members. Relative movement possibilities are realized by the intrinsic compliance of the structure. In the development of these systems, the first step is the determination of the static stable equilibrium. This analysis is conducted in this paper by considering the potential energy approach or by using the geometric nonlinear finite element method. The mechanical behavior of the structure is assessed with a specific emphasis on its mechanical compliance. The primary objective of this study is the investigation of the influence of structural parameters on the overall stiffness and movability of the structure. The results underscore the significant effect of member parameters on the stiffness and movability of the compliant tensegrity joint, particularly under varying load magnitudes. These findings provide insights for optimizing the joint’s performance, contributing to its potential application in advanced orthotic and exoskeleton devices.

Dynamic Mode Decomposition for soft tissue deformation modelling

This paper studies a new approach to dynamic modelling of soft tissue nonlinear deformation behavior based on dynamic model decomposition. This approach derives the deformation relationship between two continuous time points from correlated system snapshots. Subsequently, it constructs a reduced-order system by extracting most relevant information via thin-singular value decomposition to capture dynamic characteristics of the full-order deformation system. Unlike the existing methods which mainly rely on the establishment of complex constitutive equations for governing soft tissue deformation, the proposed method conducts tissue deformation directly from measured samples without involving constitutive governing equations. Simulation results show that the proposed method not only achieves real-time performance, but also sustains similar accuracy as the nonlinear finite element method.

The modified force density method for form-finding of cable net structure

Form-finding is crucial for the design of typical cable net structures. Based on the original basic force density method, a modified force density method utilizing the concept of relation matrix is proposed in this paper. The modified method realizes the establishment of a clear correspondence between members and nodes of cable net structures. On the basis of the relation matrix, the find function is introduced, and the calculation formula of the modified branch-node matrix is derived. Meanwhile, the corresponding analysis steps and calculation process are given. The modified method is verified by the analysis of representative structural forms. The results show that for the saddle-shaped orthogonal cable net structure, the outcomes obtained from the modified force density method highly agree with the theoretical values, providing preliminary verification of the method's effectiveness. For single-layer spoke cable net structures, the relative error between the results calculated by the modified force density method and the numerical solution is approximately 5 %. The results of both methods are relatively consistent, and the relative error varies in relation to the ratio of inner ring cable force density to radial cable force density. For circular single-layer crossed cable net structure without inner ring, the results of the modified force density method are very close to the numerical solution. The maximum relative error between the two is 6.95 %, and the accuracy is higher than that of the nonlinear finite element method. The outcome of this research demonstrates the accuracy of the modified force density method and its effective application in the form-finding of actual cable net structures.

Structural analysis and optimization of steel truss bridge based on finite element method

In view of the defects of the current mainstream structural safety analysis method of Truss bridge, the safety analysis method at the component level should be further developed. Therefore, it is necessary to carry out the overall safety analysis and structural optimization at the structural level. Based on the concrete data of the actual steel truss beam bridge, this paper uses ABAQUS and MIDAS finite element software to model the truss structure. First of all, the static analysis is carried out, and then the structural analysis and optimization of the steel truss beam bridge is carried out with the elastic modulus reduction method. Based on the linear elastic finite element method, the bearing state of each component is solved, and the ultimate bearing capacity of the whole structure is calculated iteratively. Thus, the limitation of incremental nonlinear finite element method is overcome, and higher calculation accuracy and efficiency are realized.

Methodology for shape prediction and conversion of a conventional aerofoil to an inflatable baffled aerofoil

AbstractInflatable wings for UAVs are useful where storage space is a severe constraint. Literature in the field of inflatable wings often assumes an inflated aerofoil shape for various analyses. However, the flexible inflatable aerofoil fabric might deform to another equilibrium shape upon inflation. Hence accurate shape prediction of the inflated aerofoil is vital. Further, no standardised nomenclature or a process to convert a smooth aerofoil into its corresponding inflatable aerofoil counterpart is available. This paper analytically predicts the equilibrium shape of any inflatable aerofoil and validates the analytical prediction using non-linear finite element methods. Further, a scheme for the generation of two types of inflatable aerofoils is presented. Parameters such as the number and position of compartments and aerofoil length ratio (ALR) are identified as necessary to define the aerofoil’s shape fully. A process to minimise the deviation of the inflatable aerofoil from its original smooth aerofoil using particle swarm optimisation (PSO) is discussed. Research presented in this paper can help in performing various analyses on the actual equilibrium shape of the aerofoil.

Examination of Thinning Inspection Method for Ferromagnetic Steel Tubes Using Velocity Effect of Static Magnetic Field

The high-speed movement of an electromagnetic sensor comprising static excitation and detection coils in a steel tube generates an eddy current in the tube. The presence of a defect in the steel tube may be detected via changes in the eddy current. In general, the ferromagnetic heat transfer tubes in oil and chemical plants are inspected for defects by moving an internally inserted electromagnetic sensor at a high speed of 1 m/s. Although previous studies have focused on the detection of localized thinning in the steel tube, there are no reports on a wide range of thinning in the steel tube. Therefore, this study investigated a thickness measurement method for a wide range of thinning in the steel tube using only static magnetic field. Consequently, the possibility of measuring the thickness in the steel tube based on the flux density inside the detection coil of the proposed static magnetic inspection sensor moving at 1 m/s was demonstrated. The flux density in the steel tube was evaluated by the three-dimensional nonlinear finite element method considering the velocity effect.

Empirical formula to assess ultimate strength of side shell on passenger ship under combined axial and shear load based on experimental and numerical analysis

This study proposes an empirical formulation to assess the ultimate strength of side shells on passenger ships subjected to combined effects of axial compression and shear loads. The deteriorating effects of large openings and strengthening effects of stiffener reinforcements were considered in the proposed formulation for a wider range of applications. To verify accuracy of the empirical formula, an experimental test was first conducted to inspect the collapse behaviour and influential parameters of the side shell. More than 5000 side-shell scenarios were subsequently adopted as the input dataset based on the experimentally validated nonlinear finite element method. A simplified polynomial shape was proposed for the empirical formula by comparing various generation sets of the four-parameter-based formulations. A reliable solution to the proposed empirical formula was obtained with respect to a high determination coefficient compared to the numerical results. The developed empirical formula can be considered as applicable and beneficial for practical structural design work of side shells with large openings in modern passenger ships.

MSD applied to the construction of the British Library basement: a multi-stage excavation in London Clay

This note presents the application of the mobilisable strength design (MSD) method to the monitoring results of the multi-propped excavation in the south area of the British Library Euston, constructed in a highly overconsolidated stiff clay deposit. The MSD method is an energy-based approach (a nonlinear finite-element method for a single-degree-of-freedom soil-wall system) introduced to develop a simplified design methodology that satisfies both ultimate and serviceability limit states. Wall displacement predictions based on the MSD method are compared with considerable field monitoring data. The sensitivity of the method to reasonable variations in input parameters is considered. A spreadsheet and python code demonstrating the MSD analysis from this paper are provided in the online supplement alongside details of the mathematical formulation.

NUMERICAL MODELLING OF REINFORCED CONCRETE FRAMES RETROFITTED WITH BUCKLING RESTRAINED BRACE INCORPORATING STEEL AND SUPERELASTIC SHAPE-MEMORY ALLOY CORES

The numerical response of one-storey reinforced concrete frames designed following design standards before the enactment of modern seismic provisions was investigated in this study using the nonlinear finite element method. An unbraced frame and two frames retrofitted with a buckling restrained brace (BRB) incorporating either a stainless steel or chrome molybdenum core bar were modelled. The nonlinear static reverse cyclic loading performance of the frames was assessed. Modifications to the BRB are proposed to mitigate deficiencies identified with the original BRB and steel core bars. The modified BRB incorporating a superelastic shape-memory alloy (SE-SMA) core bar was further modelled. The results illustrate the benefits of implementing SE-SMA as a retrofit strategy to control permanent displacements. The modified BRB with a SE-SMA core exhibited improved lateral strength and displacement capacities relative to the frames retrofitted with steel cores and the control bare frame.

Comparative study of shell element formulations as NLFE parameters to forecast structural crashworthiness

Abstract This work made a comparison of the effects of selected element formulations (EFs) through nonlinear finite element analysis (NLFEA) and physical configurations in scenario design, particularly target locations. The combined results help in quantifying structural performance, focusing on crashworthiness criteria. The analysis involves nonlinear dynamic finite element methods, using an explicit approach applied to an idealized system. This system models ship-to-ship collisions, specifically the interaction between Ro and Ro and cargo reefer vessels, with one striking the other. Summarizing initial NLFEA results reveals that the chosen EF significantly influences the crashworthiness criteria. Notably, differences in formulations lead to different calculation times. The Belytschko–Tsay (BT) EF is the quickest, followed by the Belytschko–Leviathan (BL), with around a 36% difference. Conversely, formulations such as the Hughes–Liu involve much longer processing times, more than twice that of BT. To address the potential impact of shear locking and hourglassing on calculation accuracy during impact, the fully integrated (FI) version of the EF is used. It mitigates these undesired events. For formulations with the same approach, the FI BT formulation suppresses hourglassing effectively, unlike others that show orthogonal hourglassing increments. To ensure reliability, rules were set to assess hourglassing. The criterion is that the ratio of hourglass energy to internal energy should be ≤10%. All formulations meet this criterion and are suitable as geometric models in NLFEA. Regarding reliability and processing time, analyzing the computation time offers insights. Based on calculations, BL is the fastest, followed by Belytschko–Wong–Chiang, while the FI BT formulation takes more time for the same collision case.

Propagation and arrest of collapse failures in a buried offshore pipeline crossing reverse fault areas

Offshore pipelines crossing fault rupture areas suffer the risk of local buckling, which can in turn initiate propagating buckles. This study presents the results of evaluating several series of local collapses, subsequent propagating buckles, temporary buckling arrests, and crossover simulations of a deformed (due to reverse fault displacements) offshore pipeline under external overpressure. A numerical model of a buried pipeline with a single (twin) integral arrestor(s) was developed using a nonlinear vector form intrinsic finite element method. The residual external pressure capacity of a deformed pipeline after reverse fault displacements was assessed. Single integral arrestors at different installation sites and twin integral arrestors of different lengths were tested. Effects of fault dip angles on the propagation and arrest of collapse failures were investigated. The longitudinal and bending deformations caused by reverse fault displacements result in a significant decrease in the external pressure resistance of offshore pipelines. Four weak areas appeared around the bending regions, the size relationship of their collapse pressures determined the sequence of multiple local collapses and directions of the subsequent propagating buckles. Integral arrestors are effective designs with significant arresting efficiency in such scenarios. The flexure curve of the pipeline changed significantly only when an arrestor was installed in the left- or right-bending region. A large fault dip angle leads to both higher first collapse pressures and crossover pressures due to smaller bending deformations. A flipping crossover occurs when a downstream reverse ovality develops, which rotates the collapse direction by 90°. The material efficiency of integral arrestors will decrease with the occurrence of flipping crossovers.

Cyclic performance welded steel reduced beam section moment connections using longitudinal slots in flanges

A new type of steel reduced beam section connection using longitudinal slots in the beam flanges is introduced. The effect of different parameters has been studied by the non-linear three-dimensional finite element method. Parameters have been the distance between the slot and column face, the length and width of the slot, the distance between the slot and the edge of the beam flange, the number of slots, the distance between slots, and the dimensions of the beam. The displacement controlled cyclic loading protocol recommended by SAC has been imposed. The von Mises yield criterion has been used. Obtained results show that creating the slots in the beam flange improves considerably the performance of the connection. The bending moment at the column face and plastic strains in the weld decrease by 32% and 94%, respectively, by increasing the slot length by 264%. The bending moment and dissipated energy reduce by 59% and 66%, respectively, when the slot width is increased by 430%. By increasing the length and width of the slot from a specific value and by moving the slot towards the beam web, the behaviour of the connection becomes unsatisfactory. The effect of the beam height is more than that of other dimensions of the beam. Based on the results obtained, recommendations for the design implications related to the geometric dimensions of the slots have been formulated.

Simulation of three-dimensional temperature field in high-frequency welding based on nonlinear finite element method

Abstract In modern industrial production, many advanced manufacturing technologies are constantly developing with the progress of social sciences. Welding, as an indispensable manufacturing technology in industrial production, has received close attention from various industries. High frequency welding technology is needed in fields such as mechanical manufacturing, machine making in the food industry, and intelligent robot model making. High frequency welding is an important technical means in the production process of welded pipes, and the level of welding temperature has a significant impact on the quality of welded pipe welds. This article studied the shortcomings of traditional high-frequency welding, analyzed the application method of nonlinear finite element method in high-frequency welding, and analyzed the dynamic process of welding and its influencing factors. The finite element method formula is used to stabilize the value of three-dimensional (3D) temperature field. This work studied the temperature distribution of welded pipe welding, welded pipe materials, inside and outside of welded pipe, and temperature changes under different voltages. The experimental results showed that the error value between the simulation results of the 3D temperature field of high-frequency welding and the measured experimental results was about 4.3542°C, which was basically similar, indicating the effectiveness of the 3D temperature field simulation experiment. With the development of science and technology, high-frequency welding technology would continue to improve, and the quality of welded pipe welds would become better and better with the progress of technology. The improvement in quality promotes the development and progress of industry, and maintains the quality of machine manufacturing. The simulation experiment method of 3D temperature field has shortened the experimental time and reduced the experimental cost, providing a new reference for other temperature related experiments.

Ultimate strength assessment of rectangular plates subjected to in-plane compression using a statistical model of welding initial deflection

Stiffened panels in steel ships and offshore structures are usually fabricated by fillet welding to attach stiffeners to a plating. Thermal contraction due to the welding causes angular distortion of the plate along the stiffeners, and the plate initially deflects. This welding initial deflection significantly affects the ultimate strength and collapse behavior of the stiffened panels, and it is one of the important uncertainty factors in ultimate strength assessment. This study proposes a methodology to quantify the uncertainty of the ultimate strength of rectangular plates due to the welding initial deflection. This paper has twofold. One is the development of a statistical model of the initial deflection shape based on measured data in past studies. Bayesian statistics is adopted since it can consider uncertainty accompanied by the insufficient number of measured data. A regression model of the initial deflection is selected as the best model from several candidate models based on an information criterion. The other is the assessment of probability distributions of the ultimate strength of simply supported rectangular plates. The probabilistic distributions of the ultimate strength are calculated by Monte Carlo simulation using a nonlinear finite element method. Initial deflection samples are generated from the developed statistical model and applied to finite element models of the rectangular plates. The analysis result indicates that the probability distribution of the ultimate strength depends on the collapse mode which is changed by the initial deflection shape. As a usage example of the proposed methodology, existing formulas of the ultimate strength are evaluated and adjusted to give safe side estimations for design.

Energy dissipation mechanism and ballistic characteristic optimization in foam sandwich panels against spherical projectile impact

This study systematically examines the energy dissipation mechanisms and ballistic characteristics of foam sandwich panels (FSP) under high-velocity impact using the explicit non-linear finite element method. Based on the geometric topology of the FSP system, three FSP configurations with the same areal density are derived, namely multi-layer, gradient core and asymmetric face sheet, and three key structural parameters are identified: core thickness (tc), face sheet thickness (tf) and overlap face/core number (no). The ballistic performance of the FSP system is comprehensively evaluated in terms of the ballistic limit velocity (BLV), deformation modes, energy dissipation mechanism, and specific penetration energy (SPE). The results show that the FSP system exhibits a significant configuration dependence, whose ballistic performance ranking is: asymmetric face sheet > gradient core > multi-layer. The mass distribution of the top and bottom face sheets plays a critical role in the ballistic resistance of the FSP system. Both BLV and SPE increase with tf, while the raising tc or no leads to an increase in BLV but a decrease in SPE. Further, a face-core synchronous enhancement mechanism is discovered by the energy dissipation analysis, based on which the ballistic optimization procedure is also conducted and a design chart is established. This study shed light on the anti-penetration mechanism of the FSP system and might provide a theoretical basis for its engineering application.

Multiscale finite element method combined with local preconditioning for solving Euler equations

In this work we present a nonlinear multiscale finite element method combined with local preconditioning for solving compressible Euler equations in conservative variables. The formulations are based on the strategy of separating scales, in which it is the core of the variational multiscale (finite element) methodology. The subgrid scale space is defined using bubble functions that vanish on the boundary of the elements, allowing to use a local Schur complement to define the resolved scale problem. The resulting numerical procedure allows the fine scales to depend on time. The formulation proposed added artificial viscosity isotropically in all scales of the discretization. Due to the fact that, density-based schemes suffer with undesirable effects of low speed flow including low convergence rate and loss of accuracy, local preconditioning is applied to the set of equations in the continuous case. We evaluate the multiscale formulation with local preconditioning in the low Mach number comparing with the non-preconditioned case. The experiments show that density-based schemes combined with local preconditioning yields good results.

Low cycle fatigue lifetime prediction of superplastic shape memory alloy structures: Application to endodontic instruments

In this paper we propose a methodology for a fast numerical determination of low cycle fatigue lifetime of superelastic shape memory alloy structures. This method is based on the observation that generally, in low cycle fatigue, shape memory alloy (SMA) structures are subject to loadings that lead to a confined non-linear behaviour at stress concentration points, such as notches. Numerical fatigue lifetime prediction requires the computation of the mechanical state at critical points. However, classical computational methods, like the non-linear finite element method, lead to a prohibitive computation time in a non-linear cyclic framework. To overcome this issue, we propose to use fast prediction methods, based on localization laws. Following the determination of the stabilized behaviour, an energetic fatigue criterion is applied. The numerical fatigue life prediction model is validated experimentally on SMA endodontic instruments.

Finite element analysis and experimental validation of the failure characteristic of pressurized cylinder

PurposeThe high-pressure accumulator has been widely used in the hydraulic system. Failure pressure prediction is crucial for the safe design and integrity assessment of the accumulators. The purpose of this study is to accurately predict the burst pressure and location for the accumulator shells due to internal pressure.Design/methodology/approachThis study concentrates the non-linear finite element simulation procedure, which allows determination of the burst pressure and crack location using extensive plastic straining criterion. Meanwhile, the full-scale hydraulic burst test and the analytical solution are conducted for comparative analysis.FindingsA good agreement between predicted and measured the burst pressure that was obtained, and the predicted failure point coincided very well with the fracture location of the actual shell very well. Meanwhile, the burst pressure of the shells increases with wall thickness, independent of the length. It can be said that the non-linear finite element method can be employed to predict the failure behavior of a cylindrical shell with sufficient accuracy.Originality/valueThis paper can provide a designer with additional insight into how the pressurized hollow cylinder might fail, and the failure pressure has been predicted accurately with a minimum error below 1%, comparing the numerical results with experimental data.