Number Of Finite Element Simulations Research Articles

Computationally-efficient optimization of the remanence angles of permanent magnet circuits for magnetic refrigeration

Permanent magnets are used in many engineering fields, but their high cost and restricted availability demand optimization techniques to generate high magnetic fields over large areas with minimal material. This paper advances an optimization technique for magnetic circuits composed of NdFeB and iron wedges. The remanence angles of each magnetized block are optimized to generate a desired magnetic waveform in the air gap, a critical parameter of the magnetocaloric cooling response in magnetic refrigerators. An advantage of the proposed method is that the number of finite element simulations is twice the number of magnetized blocks, often capped due to cost reasons. Therefore, the method can fully optimize a given geometry in a few minutes. Two-dimensional and three-dimensional models are developed and compared, and the full three-dimensional model is used to design the magnetic circuit for an actual magnetic refrigerator, capable of achieving 1.1T in the high field region. An encouraging agreement is observed between the modeling results and the local experimental magnetic field measured within the air gap. The most significant deviations between simulated and measured values, never higher than 40%, are observed in the region where the magnetic field gradient is the steepest and are likely caused by manufacturing imperfections that are hard to control, such as magnetization magnitude and direction deviations and localized self-demagnetization. Deviations between experimental data and numerical results smaller than 20% are observed in the high field region.

P19. Effect of stature and lordosis on vertical falls in the female lumbar spine

P19. Effect of stature and lordosis on vertical falls in the female lumbar spine

A Versatile Punch Stroke Correction Model for Trial V-Bending of Sheet Metals Based on Data-Driven Method.

During air bending of sheet metals, the correction of punch stroke for springback control is always implemented through repeated trial bending until achieving the forming accuracy of bending parts. In this study, a modelling method for correction of punch stroke is presented for guiding trial bending based on a data-driven technique. Firstly, the big data for the model are mainly generated from a large number of finite element simulations, considering many variables, e.g., material parameters, dimensions of V-dies and blanks, and processing parameters. Based on the big data, two punch stroke correction models are developed via neural network and dimensional analysis, respectively. The analytic comparison shows that the neural network model is more suitable for guiding trial bending of sheet metals than the dimensional analysis model, which has mechanical significance. The actual trial bending tests prove that the neural-network-based punch stroke correction model presents great versatility and accuracy in the guidance of trial bending, leading to a reduction in the number of trial bends and an improvement in the production efficiency of air bending.

The response surface method-genetic algorithm for identification of the lumbar intervertebral disc material parameters

Long-term compressive load on the lumbar intervertebral disc (IVD) might lead to lumbar IVD herniation. Exploring the material parameters of normal and degenerative enucleated IVDs is the basis for studying their mechanical behavior. According to the inverse analysis principle of the parameter estimation, an optimization method was proposed to identify the parameters of the porous material of the lumbar IVD based on finite element inverse analysis. The poroelastic finite element models were established in line with the compression creep experiment. The material parameters were combined by Box–Behnken design (BBD), and the response surface (RS) models were constructed using a quadratic polynomial with cross terms and optimized by genetic algorithm (GA). The results showed that the simulation result of the best material parameter combination had a good agreement with the experiment. Compared with the normal lumbar IVD, the elastic modulus and permeability decreased, and Poisson's ratio increased for the enucleated disk, resulting in a significant difference in mechanical properties. The algorithm used in this study can reduce the parameter identification error compared with only the RS method, and decrease the number of finite element simulations compared with only the GA.

Improvement of indentation technique for measuring general biaxial residual stresses in austenitic steels

Investigations on engineering structures show that residual stresses in combination with external loads can cause failure in loads that are less than the design threshold. Due to the applicability of austenitic steel in important industries (such as oil pipelines), accurate measurement of residual stress in this material is very important. Indentation is a new method for estimating residual stress. In this paper, by performing a large number of finite element simulations, the accuracy of residual stress measurements in austenitic stainless steels using indentation was studied by performing a large number of finite element simulations. Three different models (Suresh's, Wang's and Lee and Kwon's model) were investigated and it was found that the Lee and Kwon's model has a more accurate prediction of residual stress values in austenitic steels.Based on these numerical simulations and by studying how the residual stress measurement error of Lee and Kwon's model changes according the stress ratio, a method is suggested to correct this error and calculate the real amount of non-equibiaxial residual stresses in austenitic steels. The procedure is significantly reducing the error of residual stress measurement (from about 50% to less than 10%) and has been verified by conducting experimental test on a sample made from austenitic steel.

An Inverse Approach Towards Determination of Friction in Friction Stir Spot Welding

Friction stir spot welding (FSSW) is a solid-state joining process in which a rotating tool is pressed against two materials to be joined for creating a spot weld. The rotating tool comprises a pin with a shoulder. The pin gets inserted inside the material, whereas the shoulder rubs on the surfaces of the two materials. The process encounters friction at the pin-workpiece and shoulder-workpiece interfaces. In order to carry out a realistic simulation of the process, the knowledge of friction is a must. In most of the published work, scant attention has been devoted to the quantitative determination of friction force. This article proposes an inverse approach to the determination of friction force in FSSW. It is assumed that the frictional behaviour at the pin-workpieces interface is sticking in nature and at times, there is a possibility that frictional shear stress is more than the shear strength of the materials due to welding of asperities. This aspect is analysed by carrying out a number of finite element simulations using DEFORM-3D on a shoulder-less pin and validating it through in-house experiments. Later on, a hybrid friction model (combination of Coulomb’s and constant shear models) is used on the shoulder-workpieces interface. The friction parameters are adjusted through an optimization approach by minimizing the error between experiments and simulation. In a typical case, the friction factor (m) on the pin-workpiece interface was found to be 1.05. Friction at the shoulder-work interface was best represented by a hybrid model, with m = 0.77 for the high-pressure region and µ = 0.29 for the low-pressure region, where µ is the Coulomb’s coefficient of friction. Computations with estimated friction predicted temperatures with a reasonable accuracy. It also predicted fairly accurate torque for a tool of different size.

The HDMR-hybird Network Method of Model Approximation for the Stochastic Analysis of Semi-rigid Joint

The huge economic costs with the experimental analysis and computationally expensive with the simulation are the difficulties for the stochastic analysis of engineering structures. The structural data of stochastic analysis is based on the probability of statistical results. Therefore, the focus of structural stochastic analysis is how to simulate the finite element model or the physical model by the method of approximate model with the requirements of the expected accuracy range. For the higher precision sensitivity coefficients, a large number of finite element simulations would be conducted and this process leads to intensive computation. This paper puts forward a methodology that combines the high dimensional model representation(HDMR) method and the hybrid neural network for the approximate model. The advantage of this method is the determination of coupling characteristics of the input parameters, and the complex multidimensional model could be constructed by the limited sample points. The feasibility of the method was applied to semi-rigid connection with multidimensional parameter, and the efficiency and precision were obviously superior to the traditional approximate method.

Novel metaheuristic classification approach in developing mathematical model-based solutions predicting failure in shallow footing

This study evaluated and compared several novel classification approaches to develop the most reliable stability model-based solution in the prediction of shallow footing’s allowable settlement. By applying the biogeography-based algorithm, this study presents an optimized metaheuristic classification approach with mathematical-based multi-layer perceptron neural network and fuzzy inference system to achieve a better assessment of the recognition of a complex failure phenomenon. By the contribution of a large number of finite element simulation, and considering seven key factors, the settlement of a shallow footing placed on a two-layered soil was measured as the target variable. Then, to change into the classification method, two overall situations of stability or failure were considered for the proposed soil layer. The ensemble of BBO–MLP and BBO–FIS are developed, and the results are evaluated by well-known accuracy indices. The results showed that employing BBO helps both MLP and FIS to have a better analysis. Besides, referring to the obtained total ranking scores of 6, 5, 11, and 8, respectively, for the MLP, FIS, BBO–MLP, and BBO–FIS, the BBO–MLP found to be the most accurate model, followed by BBO–FIS, MLP, and FIS.

Computationally Efficient Tolerance Analysis of the Cogging Torque of Brushless PMSMs

This paper investigates the impact of tolerances related to permanent magnets on the cogging torque performance of Permanent magnet synchronous machines (PMSMs). These machines usually show a considerable sensitivity regarding tolerances for geometric dimensions and material characteristics. A consistent approach is presented in order to minimize the computational effort for evaluating the sensitivity, robustness, or reliability. Thereby, design of experiments is used to minimize the required number of finite element simulations. In this work, a Box–Behnken-based approach is considered. Subsequently, a surrogate modeling technique based on a second-order equation is applied. As a consequence, a reduction of the computational cost by 96% is achieved. The obtained results are compared with outcomes solely derived by means of finite element computations and very good agreement is observed. This is illustrated by providing the probability distribution of the cogging torque for the considered machine design. In addition, the cumulative distribution is presented, which usually is applied for analyzing the reliability. Considering the analysis of the impact of tolerances as part of optimization scenarios increases the number of designs to be analyzed by at least one degree of magnitude. The obtained results look promising for achieving this at feasible computational cost.

Optimization of hot stamping cooling system using segmented model

The quenching operation during the hot stamping process is critical to the final properties of formed parts. Current design for die-cooling system uses gun-drilled straight channels and the optimization of design parameters is based on the results of a large number of finite element simulations. The simulation process will be time consuming if the entire model is used. In this paper, to reduce time cost of the FE simulation, segmented FE models were developed to optimize the geometries of the cooling system and response surface method was used. A typical U-shape component was used in the optimization process. To verify the optimization results with segmented models, simulations with the entire model were carried out. The results show that very good agreement was achieved and the computational time saves up to 92.6% compared with the entire model of the U-shape component.

The Method of Model Approximation for the Analysis of Semi-rigid Connection with Parameter Correlation

The moment-rotation model is the main study of semi-rigid connection, moreover, the sensitivity coefficients of parameters on semi-rigid connection are the precondition of a moment-rotation model. There are two issues in the current research: the defective models would be obtained without considering the correlation among the parameters of the structure; for the higher precision sensitivity coefficients, a large number of finite element simulations would be conducted and this process leads to intensive computation. According to these problems, the sampling of the parameters with considering the correlation and the approximate model which was constructed by numbered finite element simulations and improved chaotic particle swarm algorithm are proposed in this paper. Two mathematical example are conducted and the approximate models represent a high degree of accuracy. A new sensitivity calculation is proposed based on the correlation parameters and the approximate model, the moment-rotation model of extended end plate connection obtained from this algorithm has the properties of high computational efficiency and explicit physical meaning.

Identification of material properties using nanoindentation and surrogate modeling

In theory, identification of material properties of microscopic materials, such as thin film or single crystal, could be carried out with physical experimentation followed by simulation and optimization to fit the simulation result to the experimental data. However, the optimization with a number of finite element simulations tends to be computationally expensive. This paper proposes an identification methodology based on nanoindentation that aims at achieving a small number of finite element simulations. The methodology is based on the construction of a surrogate model using artificial neural-networks. A sampling scheme is proposed to improve the quality of the surrogate model. In addition, the differential evolution algorithm is applied to identify the material parameters that match the surrogate model with the experimental data. The proposed methodology is demonstrated with the nanoindentation of an aluminum matrix in a die cast aluminum alloy. The result indicates that the methodology has good computational efficiency and accuracy.

Polymer based aerospace structures under high velocity impact applications; experimental, constitutive and finite element analysis

Polymethyl methacrylate (PMMA) and Polycarbonate (PC) are two famous optically clear thermoplastic polymers widely used in various aeronautical and astronatucial applications. Owing to their exceptional transparency, process shape adaptability, low density and high impact strength they find particular attention in aerospace industry where they are used to manufacture air craft canopies, windshields, impact resistant windows, visors and safety glasses. The design and manufacturing of the satisfied polymeric structures involve accurate modeling of the material behavior and detailed analysis of their service behavior under extreme loading conditions. In order to evaluate the material behavior under these loading conditions, extensive work in terms of experimental characterization and material constitutive modeling is required. A systematic research methodology including the material characterization, material constitutive modeling, constitutive model implementing and finite element prediction of mechanical behaviors is proposed in this work. The material characterization tests were performed by means of universal testing machine and Split Hopkinson pressure bar (SHPB) setup. On the basis of performed tests and using phenomenological approach, a constitutive model was proposed to successfully predict the entire deformation behavior of polymers under various loading conditions with sufficient accuracy. The model was implemented numerically by establishing a User-defined material subroutine (UMAT) in explicit Finite element (FE) solver LS-DYNA. The model successfully ascertained the dynamic behavior of PMMA based aircraft windshield and PC based astronaut helmet visor under application of high velocity projectile impact. A number of FE simulations were carried out to determine the critical impact energy, maximum deformation and stress level in these structures. The simulations results help to evaluate various design approaches to optimize the structural response prior to preliminary experimentations and therefore provide an alternative to costly and time consuming extensive experimental tests.

CAD Based Drilling Simulations for Al7075

Drilling is considered to be one of the mostly used processes for holemaking. Researchers have followed three different approaches for its simulation i.e. analytic, experimental and numerical. Nowadays the direct access of scientists to the Application Programming Interface (API) of several CAD systems led to an increased number of finite element simulations based on CAD 3D models of drilling tools. The present paper uses a CAD system and via its API a kinematic model is created. Different tool parameters and cutting conditions are introduced; a series of 3D solid models for the tool, the workpieces and the undeformed chips are created and the resulted thrust forces are predicted in both the main edges and the chisel edge. The proposed methodology is experimentally verified using Al7075 for the workpiece and HSS for the tool material. In addition, it provides the basis for a series of new applications in other manufacturing processes based on CAD created geometries.

Finite Element Simulation of Orthogonal Cutting Process for Steel

The process of orthogonal metal cutting is analysed using the commercial FEA package ABAQUS/Explicit. The focus of the results presented in this paper is on the effect of friction and rake angle on the cutting forces in a metal cutting process. A number of finite element simulations have been done with the Johnson-Cook Damage model being used to initiate the damage and simulate chip separation from the workpiece .A tool rake angle varying from 20ᵒ to 30ᵒ and have been considered in the simulations. The results of these simulations provide insight as to how cutting forces are influenced by rake angle.

A New Method to Determine Material Parameters from Machining Simulations Using Inverse Identification

Realistic simulations of machining processes require a correct description of the material behaviour. Due to the large strains and strain rates in the shear zone, the conditions during machining are difficult to reproduce in material testing so that extrapolation from testing data is often necessary. One way to circumvent this problem is to use inverse identification methods and to match machining simulations with experiments by varying the material parameters.The inverse identification process, however, is time-consuming because standard optimisation methods like evolutionary algorithms or Newton methods usually need a large number of finite element simulations. In this contribution, we use a new parameter identification method to identify Johnson-Cook material parameters from machining simulations. Target simulations with known parameters are used instead of experimental results since material parameters can be varied. The method is able to correctly reproduce the target simulations for different target materials with a small number of FEM simulations, identifying five parameters of the Johnson-Cook law.

Multiroller straightening analytical model of H-beam

H-beams are currently the largest output section steel in the world. Straightening is an important finishing step in the manufacturing process and directly determines the ultimate straightness of the beams. To analyse the straightening process, a multiroller straightening analytical model of an H-beam was established and is based on the pure bending springback equation of the symmetrical section curved beam. The purpose of the establishment of the model is to calculate the exit residual deflection by inputting the reduction rules and ultimately get the best reduction rules. In the model, the concept of plastic region ratio is proposed. The larger are the plastic region ratios, the easier are the initial curvatures unified, and the fewer straightening roller systems are required, however the greater is the residual stresses. Another innovation of this paper is the definition of a cosine function to express the relationship between reduction and curvature. The function of curvature, which plays an important role in the analytical model, was developed by a large number of finite element simulation and numerical fittings. The principle of the multiroller straightening process is clearly reflected by the analytical model in the theoretical analysis. By contrast, the theoretical calculation results of the analytical model are consistent with the finite element simulation results and the field data. It is suggested that the multiroller straightening analytical model of an H-beam is a theoretical foundation to optimise the straightener parameters and the reduction rules with higher accuracy.

Inverse parameter identification with finite element simulations using knowledge-based descriptors

Material parameters can be determined from complex engineering processes by inverse methods: A simulation model (usually using finite elements) of the process is used, and its parameters are varied systematically until agreement between simulation and experiment is achieved. Using standard methods like the Levenberg–Marquardt algorithm or evolutionary techniques has the disadvantage of needing a large number of simulations. Here we present a new method to solve the problem of inverse identification. The material behaviour is described using auxilliary quantities, called descriptors, that are closely related to observable quantities, for example the force in a deformation process. Choosing appropriate descriptors allows to determine them rapidly using a scaling procedure. Calculating material parameters from descriptors involves inverse parameter identification methods, but no finite element simulations are needed for this step. The method is described theoretically and is numerically investigated using two examples: Forging of an elasto-plastic specimen and deformation of a hyperfoam material. The number of finite element simulations needed to identify material parameters and the total computing time are strongly reduced compared to standard methods.

Characterization of nonlinear shear properties for composite materials using digital image correlation and finite element analysis

Abstract A method for accurate assessment of nonlinear shear stress–strain relations of composite materials is developed in this work using short-beam shear (SBS) tests. The method is based on a combination of a finite element model (FEM) for stress calculation and a digital image correlation (DIC) technique for full-field measurement of deformation. An inverse problem of generating shear stress–strain curves is solved using an iterative procedure which starts with a beam theory-based closed-form approximation of shear stresses, and updates the stresses through a number of finite element simulations. The method is demonstrated on unidirectional carbon/epoxy SBS specimens. Experimentally-generated strain fields are compared with FEM-computed strain fields to verify accuracy of the developed method. Shear stress–strain data are compared with V-notched beam test results for further verification.

Determination of shear creep compliance of linear viscoelastic solids by instrumented indentation when the contact area has a single maximum

Abstract