Nonlinear Finite Element Simulations Research Articles

Numerical modeling and analysis of the ballistic impact response of ceramic/composite targets and the influence of cohesive material parameters

Hybrid ceramic/composite targets are acknowledged to provide effective impact protection against armor piercing projectiles, which is why the research on this topic is continuously developing further. In this work, a nonlinear dynamic finite element (FE) simulation method is developed to systematically explore the ballistic perforation behaviors of hybrid ceramic/woven-fabric reinforced polymer (WFRP) composite when impacted by a non-deformable projectile. The hybrid system is composed by an alumina ceramic plate forming the front surface and glass or carbon WFRP composite back-up plate. The simulations are carried out using ABAQUS/Explicit FE code, wherein three different constitutive material models are formulated and implemented. The Johnson–Holmquist and composite damage models are used for alumina and composite material behaviors, respectively. The brittle fracture and fragmentation of the ceramic plate and the failure criteria based on fracture of fibers or matrices of composite materials during perforation are considered. Besides, interlaminar delamination between composite plies as well as ceramic/composite interfacial decohesion are modeled using a cohesive surface method, and the behaviors of interlayer degradation and failure are described using a traction-separation law. The accuracy of the developed model is validated with available experimental and analytical results. What’s more, the perforation process against the projectile and the ballistic mechanism of each layer in the composite backplate and in the ceramic as well are profoundly explored. Meanwhile, the numerical simulations are used to evaluate the changes of energy of the projectile and ceramic/composite panels. The influence of key parameters, such as interface cohesive properties and friction, on the ballistic performance in terms of energy absorption capability is additionally addressed. For the preliminary and early design phase, the present dynamic model could provide an efficient approach for numerical predictions of ballistic impact responses of the hybrid ceramic/FRP composites.

An innovative model for predicting the displacement and rotation of column-tree moment connection under fire

In this study, we carried out nonlinear finite element simulations to predict the performance of a column-tree moment connection (CTMC) under fire and static loads. We also conducted a detailed parameter study based on five input variables, including the applied temperature, number of flange bolts, number of web bolts, length of the beam, and applied static loads. The first variable is changed among seven levels, whereas the other variables are changed among three levels. Employing the Taguchi method for variables 2–5 and their levels, 9 samples were designed for the parameter study, where each sample was exposed to 7 different temperatures yielding 63 outputs. The related variables for each output are imported for the training and testing of different surrogate models. These surrogate models include a multiple linear regression (MLR), multiple Ln equation regression (MLnER), an adaptive network-based fuzzy inference system (ANFIS), and gene expression programming (GEP). 44 samples were used for training randomly while the remaining samples were employed for testing. We show that GEP outperforms MLR, MLnER, and ANFIS. The results indicate that the rotation and deflection of the CTMC depend on the temperature. In addition, the fire resistance increases with a decrease in the beam length; thus, a shorter beam can increase the fire resistance of the building. The numbers of flanges and web bolts slightly affect the rotation and displacement of the CTMCs at temperatures of above 400°C.

Analysis of the Aerodynamics in the Heating Section of an Anode Baking Furnace Using Non-Linear Finite Element Simulations

The emissions from the industrial furnaces impact the environment. Among the various factories, those having anode baking furnaces are working on reducing the pollutant emissions. The aerodynamics in the furnace influences the emissions due to the high dependence of combustion and radiation phenomena on the mixing characteristics. Therefore, this paper aims to establish the numerical simulation results for the three-dimensional turbulent flow in a single section of an anode baking furnace with a high rate of fuel injection. The stabilized non-linear finite element approach on the Reynolds-averaged Navier-Stokes (RANS) equation is used with COMSOLMultiphysics. The turbulent viscosity ratio is highly sensitive to the mesh for the standard k-ϵ model. The requirements of the Cartesian and refined mesh near the jet development region is explained. The comparison of meshes generated by two meshing tools namely cfMesh and COMSOL Multiphysics default Mesher is carried out. The high numerical diffusion in the flow models due to the coarser mesh leads to convergence but deficit the precision in the results. This paper shows that the mesh generated by cfMesh with flow aligned refinement combined with the non-linear finite element solver in COMSOL Multiphysics proves to provide accurate results of turbulent quantities.

Finite Element Analysis on Lining Structure of Diversion Tunnel in a Hydropower Station

Aiming at the high internal and external water pressure tunnels built in unfavorable geological bodies, this study proposes a novel type of composite support structure in which steel plates are poured inside concrete linings. Compared with traditional structures, it has the advantages of higher tensile strength, better crack resistance, and impermeability. Taking the diversion tunnel of a hydropower station as an example, based on linear and non-linear finite element simulations, mechanical properties of the steelconcrete composite lining structure for a hydraulic tunnel in soft surrounding rocks are analyzed. On this basis, the concrete crack control under this supporting condition is verified. Research results can provide a reference for the selection of reasonable steel plate thicknesses and reinforcement types in design.

2D linear finite element simulation of laser metal heating for digital twins

In the context of laser-based additive manufacturing, the thermal behavior of the substrate is relevant to define process parameters vis-à-vis piece quality. The existing literature focuses on two process variables: (a) lumped laser power and (b) process speed. However, this literature does not consider other variables, such as those related to the laser power distribution. To fill this vacuum, this manuscript includes the laser power spatial distributions (Gaussian, uniform circular and uniform rectangular) in addition to (a) and (b) above in 2D linear substrate heating simulations. The laser energy is modeled as a time dependent heat flux boundary condition on top of the domain. The total laser delivered power was identical for all spatial distributions. The results show that the laser intensity spatial distribution strongly affects the maximum temperature, and the depth and width of the heat affected zone. These 2D finite element simulations prove to be good options for digital twin based design environments, due to their simplicity and reasonable temperature error, compared to non-linear analysis (considered as ground truth for this case). Future publications address non-linear finite element simulations of the laser heating process (including convection and radiation and temperature dependent substrate properties).

Analysis and prediction of shock formation in acoustic energy transfer systems

Losses associated with nonlinear wave propagation and exhibited by acoustic wave distortion and shock formation compromise the efficiency of contactless acoustic energy transfer systems. As such, predicting the shock formation distance and its dependence on the amplitude of the excitation is essential for their efficiency, design, and operation. We present an analytical approach capable of predicting the shock formation distance of acoustic waves generated by a baffled disk with arbitrary deformation in a weakly viscous fluid medium. The lossless Westervelt equation, used to model the nonlinear wave propagation, is asymptotically expanded based on the amplitude of the excitation. Because the solutions of the first- and second-order equations decay at different rates, we implement the method of renormalization and introduce a coordinate transformation to identify and eliminate the secular terms. The approach yields two partial differential equations that can be solved to predict the formation distance either analytically or numerically much faster than time-domain numerical simulations. The analysis and results are validated with solutions obtained from a nonlinear finite element simulation and previous experimental measurements.

Experimental and numerical research on the bond‐slip behavior of square‐rebar reinforced concrete during the republic of China (1912–1949)

AbstractSquare‐rebar reinforced concrete structures during the republic of China (ROC) (1912–1949) have special material properties and structural characteristics. To perform nonlinear finite element simulations of this special type of structure more accurately, a specialized bond‐slip constitutive model is built. Eighteen central pullout specimens were designed based on the ROC concrete mix proportions and the square‐rebar. Then, the test data were fitted with the universal global optimization method and the minimum Euclidean distance point method was chosen to calculate the inflection point matrix of the bond‐slip constitutive model. Finally, the main factors influencing the bond‐slip behavior of the ROC square‐rebar reinforced concrete were analyzed. The research results show that the corrosion of the square‐rebar produces a negative effect on the whole structure and a modified bond‐slip regression curve considering the size effect is obtained. The research results can provide a scientific basis for the nonlinear calculation of ROC square‐rebar reinforced concrete structures considering the bond‐slip behaviors.

Modelling and stress analysis for double-row curvic couplings

This paper proposes a parameterized modelling method that considers the details of the machining process for double-row curvic couplings and presents a modified stress analytical method that can take the deep beam bending effect into account. The modified method provides a more accurate equivalent stress estimation than the classic Gleason method, which is demonstrated by the nonlinear finite element simulation. The contact stress and the contact status of the curvic couplings in high-speed rotation situations are analysed with the nonlinear FEA method under different loads. The results show that the strength of the weak regions of the double-row curvic couplings occur at the tooth root and the tooth to near the bolts. The bolt preload has the greatest influence on the contact stress and the contact status. The rotating speed reduces the bolt preload, causing the stress to decrease. The torque results in contact stress and contact status of different sides of the tooth being obviously different. Finally, the modified analytic method is recommended during the preliminary design, and the FEA method considering the contact effects is recommended for the detailing design.

Experimental & numerical investigation of mechanical properties in steel fiber-reinforced UHPC

This paper presents experimental and numerical investigations on mechanical properties of ultra-high-performance fiber-reinforced concrete (UHPFRC) with four types of steel fibers; micro steel (MS), crimped (C), round crimped (RC) and hooked-end (H), in two fiber contents of 1% and 2% (by volume) and two lengths of 13 and 30 mm. Compression, direct tension, and four-point bending tests were carried out on four types of specimens (prism, cube, dog-bone and cylinder), to study tensile and flexural strength, fracture energy and modulus of elasticity. Results were compared with UHPC specimens without fibers, as well as with available equations for the modulus of elasticity. Specimens with MS fibers had the best performance for all mechanical properties. Among macro fibers, RC had better overall performance than H and C fibers. Increased fibers improved all mechanical properties of UHPFRC, except for modulus of elasticity, which saw a negligible effect (mostly less than 10%). Moreover, nonlinear finite element simulations successfully captured flexural response of UHPFRC prisms. Finally, nonlinear regression models provided reasonably well predictions of flexural load-deflection behavior of tested specimens (coefficient of correlation, R2 over 0.90).

Perturbation theory for Kerr nonlinear leaky cavities.

In emerging open photonic resonators that support quasinormal eigenmodes, fundamental physical quantities and methods have to be carefully redefined. Here, we develop a perturbation theory framework for nonlinear material perturbations in leaky optical cavities. The ambiguity in specifying the stored energy due to the exponential growth of the quasinormal mode field profile is lifted by implicitly specifying it via the accompanying resistive loss. The capabilities of the framework are demonstrated by considering a third-order nonlinear ring resonator and verified by comparing against full-wave nonlinear finite element simulations. The developed theory allows for efficiently modeling nonlinear phenomena in contemporary photonic resonators with radiation and resistive loss.

Systematic two-scale image analysis of extreme deformations in soft architectured sheets

The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations. The present work demonstrates that state-of-the art image processing methods combined with numerical and analytical models provide a comprehensive quantitative description of these solids and their global behaviour, including the influence of the boundary conditions, of the manufacturing process, and of geometric and constitutive non-linearities. To this end, an adapted multi-scale digital image correlation analysis is used to track both elongations and rotations of particular features of the unit cell at the local and global (homogenized) scale of the material. This permits to observe with unprecedented clarity the strain fields for various unit cells in the structure and to detect global deformation patterns and heterogeneities of the homogenized strain distribution. This method is here demonstrated on elastic sheets undergoing extreme longitudinal and shear deformations. These experimental results are compared to non-linear finite element simulations, which are also used to evaluate the effects of manufacturing imperfections on the response. A skeletal representation of the architectured solid is then extracted from the experiments and used to create a purely-kinematic truss-hinge model that can accurately capture its behaviour. The analysis proposed in this work can be extended to guide the design of two-dimensional architectured solids featuring other regular, quasi-regular or graded patterns, and subjected to other types of loads.

A Hybrid Approach for Fusing Physics and Data for Failure Prediction

This work describes the architecture for developing physics of failure models, derived as a function of machine sensor data, and integrating with data pertaining to other relevant factors like geography, manufacturing, environment, customer and inspection information, that are not easily modeled using physics principles. The mechanics of the system is characterized using surrogate models for stress and metal temperature based on results from multiple non-linear finite element simulations. A cumulative damage index measure has been formulated that quantifies the health of the component. To address deficiencies in the simulation results, a model tuning framework is designed to improve the accuracy of the model. Despite the model tuning, un-modelled sources of variation can lead to insufficient model accuracy. It is required to incorporate these un-modelled effects so as to improve the model performance. A novel machine learning based model fusion approach has been presented that can combine physics model predictions with other data sources that are difficult to incorporate in a physics framework. This approach has been applied to a gas turbine hot section turbine blade failure prediction example.

Full-scale fire test on a high-rise RC wall

This paper describes a full-scale test carried out on a high-rise reinforced concrete wall subjected to fire loading conditions in the special Vulcain furnace (very large and modular gas furnace) at CSTB, France. The test sample was designed to represent a slender wall with a very large height/thickness ratio. The experimental results showed a large deflection of the high wall in fire conditions (almost equal to the wall height/24) even for a fire exposure time of 90 min. Such a deflection was significantly higher than the maximum value recommended by design codes (about the wall height/30 for 120 min of fire exposure). Furthermore, other test results (full-field displacements in the 3 directions, residual deformed shape after the heating and cooling phases) may also provide additional useful experimental data for validating available or future models (which are usually based on some specific assumptions). In addition, the measurements of thermal-induced deformed shape of the wall are compared to those predicted by an analytical solution derived from a simplified one-dimensional (1D) beam model, as well as to those obtained from non-linear finite-element simulations (with 2D plate elements), in order to assess the practical applicability of these simulations. These comparisons show a reasonably good agreement between the experimental results and the predictions of these models, thereby providing a first validation of the latter.

Numerical modeling of axially compressed circular concrete columns

Concrete compressive strength and ductility are strongly affected by the level of confinement and significantly improve with its magnitude. In concrete columns such enhancement can be achieved by properly designed transverse reinforcement. The behavior under axial loading can be accurately described by numerous models from the literature or more conservatively using the design codes; however, their applicability is rather limited to the most common reinforcement layouts and very often to monotonous axial compression.This deficiency can be eliminated by incorporating nonlinear finite element simulations, which allow for arbitrary loading configuration and topology, into the design process. In this paper an advanced constitutive model Concrete Damage-Plastic Model (CDPM 2) by Grassl and coworkers is thoroughly compared against the experimental data from the literature on confined concrete. Subsequently, based on numerical simulations of axially compressed circular columns with various alternatives of reinforcement it is shown that the results are inconsistent with the generally accepted assumptions incorporated into the design codes in the case of spiral reinforcement but perfectly match when the circular hoops are used.

Thermal analysis of the RFX-mod2 operating conditions for the design of the temperature measurement system

High heat fluxes are exchanged in fusion machines (up to 50 MW m−2), thus producing elevated temperature and requiring thermal monitoring and control. The design of a temperature measurement system for the RFX experiment is developed through three-dimensional nonlinear transient finite element simulations of the torus assembly under upgrade from “mod” to “mod2” with enhanced magnetic front-end, vacuum confinement barrier, and first wall. Analyses show how heat fluxes applied at the plasma-facing materials are transmitted, attenuated and delayed, through the machine parts. Results identify the passive stabilising shell as the instrumentable component closest to the plasma boundary able to follow the thermal behaviour by the detection of temperature variations at least of 10 °C during plasma pulses with a response time of about 200 s. Allowable temperature limits of materials are verified simulating a full experimental day with 24 plasma pulses, in particular at the shell supporting rings made of polyamide-imide and at the vessel spacers made of polyether-ether ketone-coated stainless steel. Simulations of the pulse discharge cleaning demonstrated the capability of the system to provide the required power for first wall conditioning (25 kW) and the need to realise a duty cycle (1-h on/3-h off) limiting the average heat flux and the maximum temperature (55 °C) at the vacuum vessel sealing elements in order to minimise differential thermal deformations. Proposed layouts of temperature sensors are able to detect the maximum temperatures expected during operation.

Optimization of mooring systems in the context of an integrated design methodology

This work describes an enhanced mooring optimization procedure, oriented towards recent floating production systems (FPS) for oil & gas exploitation in ultra-deep-water scenarios, which may present a large number of risers in an asymmetric layout. Acknowledging that the risers are the key component of an FPS, the optimization procedure is associated to an integrated mooring-riser design methodology; thus, instead of simply minimizing the platform offsets and/or the costs of the mooring system itself, one of the main objectives is to obtain a mooring configuration that ensures the integrity of the risers. Other highlights of the optimization procedure include the following aspects: Enhancements in the modeling of the optimization problem (including the definition of design variables, objective function and constraints that are relevant for such actual applications); The use of the PSO optimization algorithm associated to the ε-constrained method to efficiently handle the constraints; Enhancements in the evaluation of candidate solutions, by full nonlinear time-domain dynamic Finite Element simulations with coupled models; and the implementation in a parallel computing environment to deal with the high associated computational costs. A case study considering an FPS representative of actual applications in deepwater scenarios is presented to illustrate the practical application of the optimization tool.

Numerical analysis of liquefaction-induced differential settlement of shallow foundations on an island slope

Seismic differential settlement of shallow foundations on an island slope with a liquefiable sand stratum can significantly reduce the foundation's bearing capacity. Now, most studies focused on the settlement of foundation, while few efforts have provided a description of the differential settlement of foundation. In this study, we therefore adopted an approach using three-dimensional (3D) nonlinear finite element (FE) simulation. A special case that the water table located at the interface between the liquefiable sand layer and the clay layer was employed in this model. A series of parametric studies involving soil properties, surcharge load, foundation location, and the typical shaking characteristics of earthquake events were conducted to identify their impact on liquefaction-induced differential settlement. Generally, a more permeable sand stratum and a larger cohesion of the upper clay stratum were found effective at decreasing differential settlement. A foundation's length/width ratio also played an important role in reducing differential settlement and, when the distance of the foundation from the crest of an island slope reached a critical value, the differential settlement tends towards a steady value. Heavily-loaded shallow foundations resulted in more differential settlement, leading to a reduction in their seismic bearing capacity. The peak ground acceleration and Arias intensity of an earthquake had a significant effect as well. In addition, some preliminary design considerations for shallow foundation under the earthquakes were proposed. Overall, the numerical results offer some valuable references to improve the design and construction of foundations on an island slope under the seismic loadings.

Scaling Analysis of the Thermal Stress Field Produced by a Moving Point Heat Source in a Thin Plate

AbstractThis study presents a scaling analysis of thermally induced stresses and strains produced during welding and additive manufacturing of thin structures such as plates or walls. The order of magnitude scaling (OMS) technique was used to develop an appropriate dimensionless formulation, to obtain asymptotic expressions, and to determine the limits of validity. Nonlinear finite element simulations of welding procedures were performed to validate the asymptotic model; plasticity and temperature dependent materials properties for structural steel, stainless steel, and aluminum were considered. Thermal stresses cause plasticity when the temperature reaches a critical temperature termed the first yield temperature. The model developed is valid when the first yield isotherm is elongated, which is the case for most welding and metal additive manufacturing applications. A rigorous novel expression for the criterion of applicability is presented and utilized for prediction of the width of the plastic zone surrounding a weld or additive manufacturing bead. Extrapolations beyond the region of applicability show a consistent trend, which is captured in the form of a general dimensionless empirical expression. This work establishes the foundation for the estimation of forces and distortions induced by welding or additive manufacturing processes, and also the incorporation of effects of departure from idealizations.

Experimental and numerical assessment of welded steel beam-column connections under impact loading

This paper describes experimental and numerical investigations into the behavior of fully welded steel beam-to-column connections subjected to static and dynamic impact loads. The experimental assessment includes static and dynamic tests on four large-scale specimens, depicting two connection configurations incorporating different weld access-hole details. After providing a detailed account of the specimen details and testing arrangements, the main results and observations are presented and discussed. Particular emphasis is placed on assessing the static and dynamic forces, displacement response, and energy dissipation. Additionally, in order to provide further insights into the performance, detailed nonlinear dynamic finite element simulations are carried out and compared against the experimental results. The validated finite element models are employed in order to examine the effects of the local weld detail on the behavior of the connection, in terms of sectional internal forces and energy absorption under impact loading conditions. The numerical model is also adopted within a parametric assessment to develop a simplified relationship between the plastic rotation of the connection and the input impact energy, for use in practical application.

Metamodel-Based Prediction of Structural Damages due to Tunneling-Induced Settlements

Tunneling-induced settlements in soft soil are inevitable and often suspected to impair buildings along the alignment. Public focus is thus targeted toward the consequences rather than the benefits of tunneling projects. To reduce the risk of damage, costly compensation is frequently applied in practice when crossing below critical structures, and critical scenarios are usually assessed via deterministic analyses of analytic models. These models are well known and overestimate potential damage since they conceive of buildings as idealized, simple Timoshenko beams without considering soil–structure interaction. The present study introduces an approach to providing an efficient prediction of realistically idealized structures prone to settlement-induced damages based on random input. This approach uses a nonlinear finite-element simulation of façades to render damage assessment. Global sensitivity analysis that uses both elementary effects and Sobol indices identifies random but irrelevant input that is consequently fixed to mean values. Response surfaces yield surrogate models for subsequent damage prediction via polynomial regression. As input, these surfaces employ ordinary distribution functions and extreme value distributions to ensure predictability at the tails. The inherent error of any prediction with response surfaces is first reduced by cross-validation and then comparatively rated with alternative forecasts through artificial neural networks. Finally, the mean probabilities of occurrence and standard deviations are determined considering the imperfection of the surrogate models for the classified damage events.