Nonlinear FE Simulation Research Articles

An optimal penalty method for the joint stiffening in beam models of additively manufactured lattice structures

Additive manufacturing is revolutionizing structural design, with lattice structures becoming increasingly prominent due to their superior mechanical properties. However, simulating these structures quickly and accurately using the finite element method (FEM) remains challenging. Recent research has highlighted beam element simulation within FEM as a more efficient alternative to traditional solid FE simulations, achieving similar accuracy with reduced computational resources. However, a significant challenge is managing the lack of rigidity at nodes and the prevalence of low aspect ratio beams. While various methodologies have been proposed to address these issues, there is still a gap in the comprehensive evaluation of their limitations. An optimal node penalization methodology is required to expand the limited range of accurately represented lattice behavior. A preliminary study investigates lattice geometries through comparative analysis of solid and beam FE simulations. Built on this, we developed a methodology suitable to linear, dynamics and nonlinear beam FE simulations, contributing to enhanced computational speed and accuracy. Several lattice structures were printed using material jetting and quasi-static compressive tests were conducted to validate the methodology’s accuracy. The numerical results reveal a good accuracy between the proposed beam FE methodology and the experimental data, offering a better alternative to conventional FEM for energy absorption in terms of computing time.

1 experimental and numerical evaluation of residual mechanical performance of carbon/epoxy laminated coupons after integration of solid battery cells for aeronautical applications

The present study deals with a numerical and experimental evaluation of the residual mechanical performance of a quasi-isotropic carbon/epoxy laminated composite plate in which solid battery cells have been integrated. Firstly, the mechanical properties of the multifunctional Reinforced Multilayer Stack (RMS) battery cells have been determined thanks to dedicated multi-instrumented tests, while those of the AS4/8552 composite material have been extracted from the literature and validated by comparisons with tensile tests on plates without battery, considered as a reference case. Then, on the basis of the recommendations obtained from a virtual test campaign using FE simulations, a 16-ply laminated composite plate containing 6 solid battery cells was manufactured with a modified curing cycle that preserves the electrical properties of the batteries while ensuring the mechanical properties of the composite material. Various control methods, such as CT-scan and optical analysis, were used to demonstrate the promising quality of the manufactured composite coupon with embedded cells. Finally, a mechanical tensile test was carried out to experimentally determine the reduction in mechanical properties. The analysis of such a test with non-linear FE simulation has allowed a better understanding of the damage and failure process when solid battery cells are integrated into high performance laminated composite structures designed for the aeronautical industry.

A framework based on nonlinear FE simulations and artificial neural networks for estimating the thermal profile in arc welding

A framework based on nonlinear FE simulations and artificial neural networks for estimating the thermal profile in arc welding

Assessment of Effective and Minimal Slab Widths for Evaluating the Shear Capacity of RC Overhang Slabs

Abstract The effective width is a relevant parameter for the design of bridge overhang slabs under concentrated loads. Experimental tests have been used to assess expressions for its calculation. However, the load capacity increases with the width until a transition area is reached. Test specimens may have lacked enough width to reach full shear capacity, affecting thus the evaluation of the results. On the other hand, within the transition area, a threshold value has been hypothesized to match the effective width. This paper aims to provide recommendations for minimal widths that guarantee the full capacity of overhang slabs and to assess the calculation of the effective width by means of the threshold value and other formulations. The effect of the edge beam is also considered. A campaign of validated non-linear FE-simulations based on experiments on range of width-span ratios was performed. The results suggest using a width-span ratio of at least 4.0 for slabs without an edge beam and 5.3 for slabs with an edge beam for the experimental practice. The efficiency of the formulation for the effective widths is diffuse and the use of threshold value leads to unsafe predictions. Instead, linear-elastic FE-analyses are recommended for the design practice.

Nonlinear excitation and mesh characteristics model for spiral bevel gears

Accurate and rapid calculation of nonlinear excitation (NE) and loaded mesh characteristics (LMC) of gear pairs is a key to achieving rapid iterative optimization of gear system designs. Therefore, an analytical model (AM) was proposed for the accurate and numerically efficient calculation of NE and LMC for application to spiral bevel gears (SBG). First, a tooth contact analysis of an SBG was completed using Coons surface technology and mesh theory to determine the contact path and unloaded transmission error (UTE). Thus, an AM for the principal and relative normal curvatures of the SBG was derived using the Euler's formula. Based on the traditional calculation method for a Hertz contact ellipse, the relation between the relative curvatures was introduced to derive the formulas for the major and minor axes using the Muller's method, which could improve the programmability and avoid numerical instability of the program. Then, analytical models for the contact ellipse and pressure distribution on the contact tooth surfaces were derived using the Hertz model and geometric theory. Subsequently, based on a single tooth LMC, infinitesimal method, elasticity, and series stiffness model, a single mesh stiffness (SMS) model for SBGs was developed, which incorporates transverse tooth stiffness, transverse gear foundation stiffness, axial tooth stiffness, axial gear foundation stiffness, and Hertz nonlinear contact stiffness. Based on the SMS and UTE, compliance and load matrices were established, and the time-varying mesh stiffness, loaded transmission error, mesh force, and multi-tooth LMC models of the SBG were determined. Finally, the proposed method was validated against nonlinear FE simulations using examples. Compared to FE simulations, the proposed method requires significantly less computational effort and can be further extended to optimization or system analysis problems.

Case study of shear strengthening of RC Corbels by steel plates using fea

The study aimed to explore the possibility of strengthening RC corbels with many strengthening techniques. The research analyzed the RC corbels behavior under a wide range of variables. The theoretical study consisted of twelve models reinforced with GFRP bars with strengthening by steel plate. Finite element analysis with ANSYS APDL was used to verify five specimens. This research deals with a static nonlinear FE simulation to investigate the behavior of RC Corbels reinforced internally and externally. The verification with experimental work demonstrated a satisfactory agreement in the load-displacement relationship, ultimate load and displacement, and failure mode. The parametric study was implemented which included strengthening the four concrete corbels externally and four corbels internally by a steel plate in many configurations while the remaining three were modeled with varied compressive strength (30, 40, and 50) MPa. The external strengthening included the placing of steel plate externally around the corbel in a U-shaped form and partial strengthening by strips and bottom plate. The models with internal strengthening involved placing the steel plate internally instead of stirrups. The results discovered that the strengthening provided enrichments in the stiffness, ductility, and energy absorption by 37 %, 4 %, and 26 %. In addition, in the case of full external strengthening more than internal retrofitting, there is a maximum improvement in the cracking and ultimate load carrying capacity. The external strengthening was better than internal one due to the confinement effect of the concrete. The stress distribution and crack pattern were affected by the strengthening techniques and more cracks appeared in the corbels with external steel plates.

Ultimate Strength Assessment of Steel-Welded Hemispheres under External Hydrostatic Pressure

This paper focusses on steel-welded hemispherical shells subjected to external hydrostatic pressure. The experimental and numerical investigations were performed to study their failure behaviour. The model was fabricated from mild steel and made through press forming and welding. We therefore considered the effect of initial shape imperfection, variation of thickness and residual stress obtained from the actual structures. Four hemisphere models designed with R/t from 50 to 130 were tested until failure. Prior to the test, the actual geometric imperfection and shell thickness were carefully measured. The comparisons of available design codes (PD 5500, ABS, DNV-GL) in calculating the collapse pressure were also highlighted against the available published test data on steel-welded hemispheres. Furthermore, the nonlinear FE simulations were also conducted to substantiate the ultimate load capacity and plastic deformation of the models that were tested. Parametric dependence of the level of sphericity, varying thickness and residual welding stresses were also numerically considered in the benchmark studies. The structure behaviour from the experiments was used to verify the numerical analysis. In this work, both collapse pressure and failure mode in the numerical model were consistent with the experimental model.

Numerical Assessment of FPSO Platform Behaviour in Ship Collision

Offshore platforms may potentially collide with vessels of various types, including visiting ships such as supply ships and passing ships. The most critical and relevant conditions, including the analysis and design approaches are introduced. Different ship types having different displacements and structural designs exert different vessel impact loads on impacted structures. This paper presents the findings of collision impact analyses of the side shell panel, bow and stern structures of Floating Production Storage Offloading (FPSO) platforms in case of impact, e.g. by a supply vessel or methanol tanker. As collision impact simulations continue to be conducted conservatively, the colliding positions of the striking vessel are presumed to be bow and stern only, with side force. In order to assess hull strength in collision events, non-linear FE simulations were performed by means of the MSC / DYTRAN tool, as these collision events result in more complex reactions. The degree of hull damage suffered by an FPSO vessel in different collision scenarios and at varying impact energy levels was determined in accordance with the NORSOK N-004 standard guidelines. Post-collision analyses were conducted to establish the structural integrity of the damaged hull after being exposed to environmental conditions for one year. The reduction of hull girder strength associated with the worst damage was evaluated and accounted for in the present study, providing no further damage occurs. Furthermore, the acceptance criteria for evaluation and corresponding consequences are calculated and discussed in detail. Finally, the findings from the present paper will help clarify the impact response of offshore structures and evaluation approaches and give valuable guidance for the design and operation of FPSO platforms.

Application of Discontinuity Layout Optimization to Steel Parts and Steel Connections with a Single Bolt

Steel connections are designed with components such as bolts, plates, and welds. The proof of the plates loaded in-plane can be made by hand calculations or more realistic with a nonlinear FE-simulation. As an alternative method, a modified version of the discontinuity layout optimization (DLO) procedure is presented in this paper. The modification takes yield zone mechanisms into account. Furthermore, a compression-only contact was implemented to reproduce the bearing behaviour of bolted connections. The DLO procedure was tested on tensile specimens with and without bolts. The obtained collapse mechanisms and ultimate loads were compared to results from the Eurocode EN 1993-1-8, literature, and FE-simulations. Recommendations to the correct discretization of the tested specimens were given. Especially for the bearing behaviour, modification factors, based on a parameter study, were worked out. The DLO procedure reproduced the collapse loads and mechanisms of all considered cases correctly. The obtained bearing capacities are, in most cases, conservative compared to the Eurocode EN 1993-1-8. The presented research can be seen as the basis for future investigations on more complex problems in steel connections.

Accounting for initial plastic deformation for fatigue crack growth predictions under TMF loading condition

Crack propagation rates from isothermal and in-phase high temperature thermomechanical fatigue crack propagation tests for Inconel 792 resulted in a rather large scatter band when plotted against the linear-elastic stress intensity function ΔK. Previous observations indicated that the residual strains generated during the first few cycles in the uncracked specimen can explain, to a large extent, the differences between the tests. An effective ΔKeff was calculated for each test based on non-linear FE simulations. When the crack propagation rates for each test were plotted against the calculated ΔKeff, the curves collapsed to a smaller scatter band.

Large amplitude vibration of sandwich plates with functionally graded auxetic 3D lattice core

Full-scale modeling and nonlinear FEA are presented for large amplitude vibration of sandwich plates with functionally graded (FG) auxetic 3D lattice core. For the first time, auxetic 3D lattice metamaterials with FG configurations along the out-of-plane direction are designed, of which the fundamental vibration frequencies are analyzed and verified by experiments using 3D printed specimens. Both results suggested that the effects of FG configurations and strut incline angles are significant, and the FG-X specimen possesses the highest fundamental frequency. Subsequently, by means of full-scale nonlinear FE simulations, the large amplitude vibration characteristics are investigated for the sandwich plates, in which the novel construction of auxetic 3D lattice core with three FG configurations along the thickness direction is proposed. And the constituent material properties are taken to be temperature-dependent. Results revealed that FG configurations have distinct effect on the natural frequencies, nonlinear-to-linear frequency ratios of sandwich plates, along with EPR-amplitude curves, which will become stable when the vibration amplitude is sufficiently large.

Width and Edge Beam Effects on the Ultimate Behaviour of RC Bridge Overhangs

Abstract The bearing capacity of RC overhangs under concentrated loads can be dependent on the width of the slab. The goal of this paper is to investigate the effect of different widths using tests from the literature and non-linear FE-simulations as a reference. Shear force redistributions along the loading process and the shear concrete capacity are analysed. The shear effective width and the influence of an edge beam are also addressed. The results show that the bearing capacity of RC overhangs increase with the width until a transition area is reached and the increase flattens. An increased shear distribution sideways and posterior redistributions under the loading process are enabled. The shear capacity of concrete increases with the width and for loads close to the root an arch effect is observed. The edge beam contributes to a further increase of the ultimate capacity for wide enough overhangs. The effect of the width and the edge beam is not only quantitative but also qualitative since the failure mode and the critical section are influenced. Existing formulation for shear effective widths should be revisited. Experimental tests used for this purpose should consider wide enough specimens to capture the real behaviour of a bridge overhang slab.

On the seismic response of a propped r.c. diaphragm wall in a saturated clay

A series of nonlinear dynamic FE simulations have been performed to investigate the seismic performance of a flexible propped retaining wall in a saturated clay. The simulations have been carried out considering different acceleration time histories at the bedrock and two different inelastic soil models: the classical elastoplastic Modified Cam Clay model and the advanced hypoplastic model for clays proposed by Masin (Int J Numer Anal Methods Geomech 29:311–336, 2005) equipped with the intergranular strains extension. The results of the simulations highlight the major role played by the choice of the constitutive model for the soil on the predicted seismic response, in terms of predicted wall displacements and structural loads. In particular, the results show that a key role is played by the model ability to correctly reproduce soil dilatancy as a function of the current stress state and loading history. This has a major impact on the inelastic volumetric deformations accumulated during the undrained seismic shearing and on the development of excess pore water pressures around the excavations.

Evaluation of Plastic “Eta” Factor for Welds of SS316L(N) with High Strength Mismatch Ratio

Fracture testing standards of ASTM and ISO recommend expressions for plastic η factor of various fracture test specimen geometries to evaluate the fracture behavior of materials. These are intended for homogenous specimens, but according to ISO 15653, it can be extended for weldments up to a strength mismatch ratio (M) of 1.25. In practice, M > 1.25 is encountered in many applications. In the present study, η factor has been evaluated for welded compact tension specimens using a limit load-based approach. The η factors obtained using this approach for homogenous specimens with elastic–perfectly plastic material model are found to be within ± 4% of those from the ASTM E 1820-17a, thereby validating the procedure. For welds, the limit load is obtained from nonlinear (elastic–plastic) FE simulations. η factors for specimens with various crack lengths (a), weld width (h) and strength mismatch have been evaluated and found to be significantly influenced by these parameters. For M > 1.25, the estimated η values were found to be ~ 16% lower compared to that from the ASTM E 1820-17a. Thus, the use of the η values from the proposed method provides a conservative estimate of J–R curve for the welds. Further, it has been observed that depending on the slope of the blunting line, the JIc value may vary significantly with the estimated η values.

Study on the Influence of Stiffener’s Arrangement on the Impact Safety of Layer Door

In this paper, the nonlinear FE simulation software LS-DYNA was used to simulate the impact on six kinds of layer doors. The results show that vertical stiffener can absorb partial impact kinetic energy, optimize the stress distribution, and significantly improve the safety performance of layer door. Conversely, the transverse stiffener reduce the impact safety of layer door. At the same time, the impacting test on layer door is carried out, and the experimental result was consistent with the simulation analysis, which verified the correctness of finite element analysis. The conclusions of simulation analysis and experiment will be helpful to the optimization design of stiffener’s arrangement.

MARSTRUCT benchmark study on nonlinear FE simulation of an experiment of an indenter impact with a ship side-shell structure

This paper presents a benchmark study on collision simulations that was initiated by the MARSTRUCT Virtual Institute. The objective was to compare assumptions, finite element models, modelling techniques and experiences between established researchers within the field. Fifteen research groups world-wide participated in the study. An experiment involving a rigid indenter penetrating a ship-like side structure was used as the case study. A description of how the experiment was performed, the geometry model of it, and material properties were distributed to the participants prior to their simulations. The paper presents the results obtained from the fifteen FE simulations and the experiment. It presents a comparison of, among other factors, the reaction force versus the indenter displacement, internal energy absorbed by the structure versus the indenter displacement, and analyses of the participants' ability to predict failure modes and events that were observed in the experiment. The outcome of the study is a discussion and recommendations regarding mesh size, failure criteria and damage models, interpretation of material data and how they are used in a constitutive material model, and finally, uncertainties in general.

Progressive failure analysis of thin-walled Fibre Metal Laminate columns subjected to axial compression

The subject of the paper is the progressive failure analysis (PFA) of thin-walled Z-shape cross section members subjected to axial compression. This study concerns angle-ply multi-layered Fibre Metal Laminates (FMLs) which consist of alternating thin layers of aluminium and glass fibre-reinforced unidirectional prepreg. Laboratory damage tests were performed by the static testing unit that provided displacement control loading. Experimental results were compared with FEA wherein based on the profile's nonlinear stability investigations the failure analysis was performed. Nonlinear FE simulation combined with available progressive failure mechanics allowed to predict the initiation and propagation of the multi-failure modes within composite material. Hashin failure criterion was used to monitor the initiation of damage, whereas material degradation method (MPDG) was applied in FRP layer to define the damage evolution law. Damage variables were specified according to FEM modelling procedures in order to control material stiffness reduction after damage initiation. For aluminium layers the J2 plasticity model was employed. Progressive failure assessment by FEM allowed to estimate the post-buckling equilibrium paths and damage modes with particular regions of laminate's fracture that were found to be in a good agreement with experimental evidences.

Modeling and computing parameters of three-dimensional Voronoi models in nonlinear finite element simulation of closed-cell metallic foams

ABSTRACTModeling and computing parameters in nonlinear finite element simulations significantly affect simulation accuracy and efficiency even when it is carried out using commercial software, such as ABAQUS, ANSYS, etc. Yet comprehensive effects of these parameters on simulation results have seldom been reported. In this article, we explore the effects of several important parameters, such as mass scaling type and value, element type and size, and loading velocity, on the accuracy and efficiency of nonlinear finite element simulation of metallic foams based on three-dimensional Voronoi mesostructures. Analysis indicated that these parameters did affect simulation accuracy and efficiency, and three optimized nondimensional parameters were recommended. Based on the verified model and optimized parameters, effects of cell-wall thickness distribution on the uniaxial properties of metallic foams were also investigated. Simulation results showed that the different distribution of cell-wall thickness in modeling may induce varied elastic moduli and yield stress of metal foams. Our analysis showed that modeling and computing parameters must be paid attention to in the nonlinear FE simulation, and that the recommended parameters constitute a good reference for numerical simulation of metallic foams in predicting mechanical behaviors.

Nonlinear FE Simulation on Damage and Fracture of Polymers

Nonlinear FE Simulation on Damage and Fracture of Polymers

Nonlinear FE simulations of structural behavior parameters of reinforced concrete beam with epoxy-bonded FRP

AbstractIn the present study, investigations on fiber-reinforced plastic (FRP) plated-reinforced concrete (RC) beam are carried out. Numerical investigations are performed by using a nonlinear finite element analysis by incorporating cracking and crushing of concrete. The numerical models developed in the present study are validated with the results obtained from the experiment under monotonic load using the servo-hydraulic actuator in displacement control mode. Further, the validated numerical models are used to evaluate the influence of different parameters. It is found from the investigations that increase in the elastic modulus of adhesive layer and CFRP laminate increases the interfacial stresses whereas increase in laminate modulus decreases the displacement and reinforcement strain of the beam. It is also observed that increase in the adhesive layer can largely reduce the interfacial stresses, whereas increase in laminate thickness increases it. However, increase in laminate thickness decreases the displacement and reinforcement strain of the beam significantly. It is mention worthy that increase in laminate length reduces the interfacial stresses, whereas CFRP width change does not affect the interfacial stresses. The study will be useful for the design and practicing engineers for arriving at the FRP-based strengthening schemes for RC structures judiciously.