Direct Finite Element Analysis Research Articles

Closed-form effective out-of-plane elastic properties of regular and non-regular hexagonal lattice plates

This study derives closed-form expressions for the effective out-of-plane elastic properties of regular and non-regular hexagonal lattice plates. The derivation utilizes the homogenization method based on equivalent strain energy and the Kirchhoff plate theory. Rigorous accuracy assessments of the closed forms are conducted through comparisons with the existing literature and direct finite element analysis. A detailed parametric study is also conducted using the obtained closed forms to provide insights into the relationships between the effective elastic properties and the unit-cell shape. Lastly, general forms for some effective properties applicable to out-of-plane and in-plane situations are presented for hexagonal lattices.

Surrogate-Based Multi-Objective Optimization of Flux-Focusing Halbach Coaxial Magnetic Gear

Due to their contact-free and low-maintenance features, magnetic gears (MGs) have been increasingly investigated to amplify the torque of electric motors in electric vehicles (EVs). In order to meet the requirements of propelling EVs, it is essential to design an MG with a high torque density. In this paper, a novel flux-focusing Halbach coaxial MG (FFH-CMG) is proposed, which combines the advantages of flux focusing and Halbach permanent magnet (PM) arrays. The proposed structure has a higher torque performance and greater efficiency than conventional structures. A multi-objective design optimization based on a surrogate model is implemented to achieve the maximum volumetric torque density (VTD), torque-per-PM volume (TPMV), and efficiency, as well as the minimum torque ripple, in the proposed FFH-CMG. The employed optimization approach has a higher accuracy and is less time-consuming compared to the conventional optimization methods based on direct finite-element analysis (FEA). The performance of the proposed FFH-CMG is then investigated through 2D-FEA. According to the simulation results, the optimized FFH-CMG can achieve a VTD of 411 kNm/m3, and a TPMV of 830 kNm/m3, which are significantly larger than those of the existing MGs and make the proposed FFH-CMG very suitable for EV applications.

Efficient buckling analysis and optimization method for rotationally periodic stiffened shells accelerated by Bloch wave method

Rotationally periodic stiffened shells have been widely used as load-bearing parts in engineering structures, however, the buckling analysis and optimization of stiffened shells suffer from large computational time owing to the large-scale and complex development tendency of engineering structures. Considering that most of the traditional equivalent buckling analysis methods do not retain the features of stiffeners and cannot capture local buckling, their prediction accuracies in buckling load and mode are not high enough although they can reduce the analysis cost. In this paper, an efficient buckling analysis and optimization method is proposed for rotationally periodic stiffened shells accelerated by Bloch wave method. Firstly, the derivation of Bloch wave boundary conditions for buckling analysis of the substructure is presented, along with the corresponding numerical implementation procedure. Based on the buckling analysis method accelerated by Bloch wave method, the Kriging-based Efficient Global Optimization method is used to improve the optimization efficiency. Then, typical examples are carried out for the buckling analyses of stiffened cylindrical shells with various grid patterns including orthogonal grids, triangle grids, rotated triangle grids, mixed triangle grids and hierarchical orthogonal grids, as well as the integrally stiffened shell with non-straight generatrix. Compared with buckling results from the direct finite element analysis, the proposed method achieves high prediction accuracy in buckling load and remarkable improvement in modelling and analysis efficiency simultaneously. Particularly, the proposed method succeeds in capturing both local buckling mode and global buckling mode. Finally, the optimization design of the integrally stiffened shell with non-straight generatrix is carried out based on the proposed method aiming at maximizing the buckling load. Results indicate that the proposed method can reduce the total optimization time significantly and improve the buckling load by 94.5%, contributing to providing meaningful references for the design large-scale engineering structures.

Second‐order defeaturing estimator of manufacturing‐induced porosity on structural elasticity

AbstractManufactured metallic components often contain nonuniformly distributed pores of complex morphologies. Since such porosity defects have a significant influence on material behaviors and affect the usage in high‐performance applications, it is significant to understand the impact of porosity characteristics on the behaviors of components. In this work, a gradient‐enhanced porosity defeaturing estimator, which allows for the modeling of pore geometry and spatial distribution, is proposed within a general elastostatic framework. In this approach, the first‐order shape sensitivity is implemented to account for the change in the elastic quantity of interests to variations of pore sizes and shapes, which is then supplemented by a second‐order shape sensitivity whose mixed partial derivative quantifies the interactions between pores in proximity. The efficacy of the proposed method comes from its posterior manner that it only relies on field solutions of reference models where pores are suppressed. In this context, meshing difficulty and solution convergence issues are avoided, which would otherwise arise in a direct finite element analysis on porous structures. The impact of porosity on structural elastic performance is approximated using a second‐order Taylor expansion where the topological difference between the porous and reference domains is estimated by topological sensitivity; the field variables on pore boundaries are approximated as explicit functions of design variables using exterior formulations. Numerical results show that the elastic performances of components are influenced by the existence of pores. The pore‐to‐pore interactions are significant when pores are close by.

A structural reanalysis assisted harmony search for the optimal design of structures

Structural optimization usually requires a large amount of time-consuming structural analyses to evaluate the feasibility of the designs, which obstructs its application in large-scale problems. This study proposed a structural reanalysis-assisted harmony search (RAHS) algorithm for structural optimization. The RAHS utilizes the combined approximation (CA) technique instead of direct finite element analysis to evaluate the performances of the modified structures generated in iterations. Different from existing approaches, the proposed RAHS will update the reanalysis design point set and select the best reanalysis design point based on the similarity of the design vectors to improve the accuracy of the CA in a large search space. The RAHS also develops a diversity-based error criterion to accommodate the accuracy requirements of CA in different search phases of the harmony search. Five benchmark examples are utilized to examine the performances of the proposed RAHS. The results demonstrate that the Cosine distance outperforms the other four design point selection approaches, and the diversity-based error criterion can significantly reduce the computational cost. Compared with the penalty-based method and the improved Deb rule, the number of FE-based structural analyses can be lessened by about 90% and 50%, respectively, while yielding similar optimal designs.

Adapting a continuous flow cryostat and a plate DAC to do high pressure Raman experiments at low temperatures

We present a method for modifying a continuous flow cryostat and a steel plate DAC (Diamond Anvil Cell) to perform high pressure micro-Raman experiments at low temperatures. Despite using a steel DAC with a lower specific heat capacity (∼335 J/kg K), this setup can routinely perform high pressure (∼10GPa) measurements at temperatures as low as 26K. This adaptation is appropriate for varying the temperature of the sample while keeping it at a constant pressure. We determined that the temperature variation across the sample chamber is about 1K using both direct temperature measurements and finite element analysis of the heat transport across the DAC. We present Raman spectroscopy results on elemental selenium at high pressures and low temperatures using our modified setup.

Assessment of the global stability of three-limbed steel tube latticed column using finite element modelling

In order to study the stability performance of the three-limbed steel tube latticed column, the finite element numerical analysis method based on the structural stability theory is adopted. Firstly, the linear analysis of the three-limbed steel tube latticed column without diagonal lacing bar is carried out, and the calculation method of elastic buckling load considering the influence of shear deformation is obtained. Then, the elastic buckling analysis and elastoplastic buckling analysis three-limbed steel tube latticed column with diagonal lacing bar are carried out. The elastic buckling load and elastoplastic buckling load of three-limbed steel tube latticed column with diagonal lacing bar are studied when only the global initial geometric defects, only the member initial geometric defects, and both kinds of defects are considered at the same time. The results show that the direct finite element analysis method can be used to calculate the elastic buckling load of three-limbed steel tube latticed column with diagonal lacing bar, and the error is 6.67%. In the elastic analysis of three-limbed steel tube latticed column with diagonal lacing bar, the column global stability mainly depends on the global initial geometric defects, and the member initial geometric defect is negligible. And when two kinds of defects are applied at the same time, the structural buckling load is reduced by less than 0.20% compared to the global initial geometric defects. In the elastoplastic analysis, the column global stability is determined by both the global initial geometric defect and the member initial geometric defect. When both defects are applied at the same time, the structural buckling load decreases by less than 0.65% compared to the global initial geometric defect only, and 7.60% compared to the member initial geometric defects only. It can be concluded that there is little difference in the overall stability bearing capacity between the two kinds of defects.

External loads identification and shape sensing on an aluminum wing box: An integrated approach

The recent development of the Structural Health Monitoring (SHM) framework has required the simultaneous development of the tools fundamentals for its realization. The shape sensing methods and the loads identification ones have established themselves as crucial tools for the monitoring of aerospace structures. The two families of methods have been developed separately, although the possibility to achieve the knowledge of the displacement field and of the external loads together can enable a further progress in the SHM. In this paper, an integrated approach to simultaneously preform loads identification and shape sensing from discrete strain measurements is proposed. The methods is based on a two-steps process. The first step involves the identification of continuously distributed and concentrated external loads from discrete strain measurements. This step is achieved by discretizing the loads with Finite Elements (FE) and by computing the coefficients of influence between the nodal values of the loads and the discrete strain measurements. The second step reduces the shape sensing inverse problem to a simple direct Finite Element Analysis. The loads identified in the previous step are applied to a refined FE model of the structure and the displacement field is easily obtained through a direct FE analysis. This investigation proves that the two-steps method can accurately identify the loads and the displacement field of a wing box subject to an aerodynamic pressure distribution and a set of concentrated forces, when a sufficient number of strain information is available. When the number of discrete strain measurements decreases or the strains are affected by measurement error, the loads are poorly predicted but the method is still capable of an extremely accurate displacements reconstruction.

Non-intrusive coupling of a 3-D Generalized Finite Element Method and Abaqus for the multiscale analysis of localized defects and structural features

This paper presents a multiscale computational framework able to resolve localized defects and features such as cracks and welds in large structures. It couples Abaqus models and 3-D Generalized Finite Element (GFEM) discretizations enriched with numerically-defined functions – the GFEM with global-local enrichments (GFEMgl). The structural-scale problem is modeled in Abaqus using a coarse, 3-D mesh, suitable for capturing the global response of the structure. The GFEMgl is used to accurately model localized features of interest that are otherwise ignored by Abaqus models. The GFEMgl utilizes enrichment functions provided by the solution of, potentially multiple, local problems solved in parallel. The coupling between Abaqus and GFEMgl models is handled by the Iterative Global-Local method (IGL). The proposed multiscale framework – denoted by the acronym IGL-GFEMgl in this work – is non-intrusive in the sense that the interactions between Abaqus and the GFEMgl solver require no modifications of Abaqus or knowledge about its implementation of the FEM. Numerical examples of a specimen undergoing localized plasticity, a hat-stiffened panel with a large number of spot welds, and a T-joint structure subjected to mixed-mode fatigue crack propagation are presented to demonstrate the accuracy and applicability of the proposed framework. The results show that the IGL-GFEMgl can achieve nearly the same accuracy as a Direct Finite Element Analysis (DFEA) while leveraging methodologies and algorithms implemented in commercial and research software. Moreover, it is also shown that the user time spent on model preparation can be greatly reduced when dealing with complex problems.

Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method.

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

Direct Finite Element Analysis of the Stress Evolution and Interaction in Resistance Spot Welding with Multiple Processes and Multiple Spots Based on Reverse Engineering Technology

The current work achieved quantitative analysis of stress evolution and interaction in continuous spot welding processes that consider the stamping dimensional deviation. The reverse component that contains the stamping dimensional deviation was first established with reverse engineering technology. Then the two spot welding processes with twenty weld spots were simulated by the direct finite element analysis method. Welding experiment was conducted, and the actual residual deformation was measured by a 3D laser scanning system to validate the finite element model. The measured deformation shows good agreement with the simulated one. After that, the stress evolution was analyzed through the transient stress at a single spot weld and the peak stress during the entire welding process. The stress interaction between the spot welds in the same process and in the different processes was also analyzed. The results show that the stress interaction depends on the distance between the spot welds, the distribution of the spot welds, and the structure of the sheet metal parts. It is difficult to generalize a universal theorem to predict stress interaction. The value of the current research lies in its achievement in quantitative analysis of the stress evolution and interaction in components containing stamping dimensional deviation with direct finite element analysis, which can be extended to other complex components.

A Comparative and Review Study on Shape and Stress Sensing of Flat/Curved Shell Geometries Using C0-Continuous Family of iFEM Elements.

In this study, we methodologically compare and review the accuracy and performance of C0-continuous flat and curved inverse-shell elements (i.e., iMIN3, iQS4, and iCS8) for inverse finite element method (iFEM) in terms of shape, strain, and stress monitoring, and damage detection on various plane and curved geometries subjected to different loading and constraint conditions. For this purpose, four different benchmark problems are proposed, namely, a tapered plate, a quarter of a cylindrical shell, a stiffened curved plate, and a curved plate with a degraded material region in stiffness, representing a damage. The complexity of these test cases is increased systematically to reveal the advantages and shortcomings of the elements under different sensor density deployments. The reference displacement solutions and strain-sensor data used in the benchmark problems are established numerically, utilizing direct finite element analysis. After performing shape-, strain-, and stress-sensing analyses, the reference solutions are compared to the reconstructed solutions of iMIN3, iQS4, and iCS8 models. For plane geometries with sparse sensor configurations, these three elements provide rather close reconstructed-displacement fields with slightly more accurate stress sensing using iCS8 than when using iMIN3/iQS4. It is demonstrated on the curved geometry that the cross-diagonal meshing of a quadrilateral element pattern (e.g., leading to four iMIN3 elements) improves the accuracy of the displacement reconstruction as compared to a single-diagonal meshing strategy (e.g., two iMIN3 elements in a quad-shape element) utilizing iMIN3 element. Nevertheless, regardless of any geometry, sensor density, and meshing strategy, iQS4 has better shape and stress-sensing than iMIN3. As the complexity of the problem is elevated, the predictive capabilities of iCS8 element become obviously superior to that of flat inverse-shell elements (e.g., iMIN3 and iQS4) in terms of both shape sensing and damage detection. Comprehensively speaking, we envisage that the set of scrupulously selected test cases proposed herein can be reliable benchmarks for testing/validating/comparing for the features of newly developed inverse elements.

Factor analysis of deformation in resistance spot welding of complex steel sheets based on reverse engineering technology and direct finite element analysis

Abstract Direct finite element analysis of continuous spot welding was implemented with reverse geometric models of the actual stamping parts that comprise the back-side panel. This reverse panel showed apparent gaps after assembly and yielded to the electrodes and fixtures during welding, causing significant deformations. We acquired the total residual deformation in continuous simulation through a 3-D comparison between the original panel and the final deformed panel. This total deformation indicates that the deformations in the two processes offset with each other. We also performed a spot welding experiment and measured the actual residual deformation to validate the total deformation in simulation. They show good agreement in terms of deformation trend and magnitude. Finally, we designed seven comparative simulations to investigate the influence of the clamping pressure, electrode force, and spot welding sequence on the residual deformation. The results show that the sole increase of clamping pressure causes a deformation reduction in plate P4, while that of electrode force causes a deformation increase in P3. When the welding sequences of processes 1 and 2 are both reversed, the plate with the lowest deformation changes from P4 to P3. The final deformations in parts with multiple processes and multiple spot welds result from nonlinear interaction among many factors. The influence of a single factor change on the final deformation will be balanced by the remaining factors. This is why the fluctuations in total deformation are not significant between the standard simulation and each of the seven comparative simulations. The value of this article lies in the parameters optimization of spot welding based on reverse engineering and direct finite element analysis.

Multiscale Analysis of Heterostructured Electropermanent Magnet in Magnetic Actuators

In this work, a multiscale analysis of an electropermanent magnet in an actuator is carried out. The electropermanent magnet is heterostructured magnet composed of hard and soft ferromagnetic materials. Due to the soft ferromagnetic material (i.e., iron), the magnetic field of the magnet can be controlled by external current in a winding around the magnet. It is expected that the electropermanent magnet can enhance the mechanical force performance of magnetic actuators. For the fast and efficient analysis of the heterostructured electropermanent magnet, its multiscale analysis is proposed in this work. Through the microscale analysis, the homogenized effective magnetic permeability and residual magnetic flux density of the magnet are calculated by applying asymptotic homogenization method. The computed effective properties are utilized in the macroscale actuator model, and consequently the magnetic field distribution and magnetic force in actuators are calculated. The accuracy and computational benefit of the proposed multiscale analysis are validated by comparing the analysis result obtained by direct finite element analysis of heterostructured electropermanent magnet.

Investigating the influence of interface in a three phase composite using variational asymptotic method based homogenization technique

A computational framework based on Variational Asymptotic Method (VAM) has been developed to determine the thermomechanical properties of carbon coated inclusion in three phase Metal Matrix Composites (MMCs). In the model perfect bonding traction and displacement continuity conditions have been assumed between the matrix-interface and interface-inclusion boundaries. Both periodic and random distribution of inclusions have been considered in the study. Simulation results corresponding to homogenized effective properties and local fields have been compared with results from direct Finite Element Analysis (FEA) simulations. Results show good agreement between the model predictions and the FEA simulations. As an application, the framework has been used to investigate the influence of interface volume fraction, stiffness and shape on the overall homogenized properties and the local fields in a three phase composite.

Mathematical Modeling and Numerical Simulation of Coupled Mass Transfer and Mechanical Processes in Ceramic Ware at Industrial Drying

An algorithm for numerical simulation of transient moisture content fields and mechanical processes in ceramic ware at drying in industrial aggregates is developed. It is based on mathematical models of the mass transfer and mechanical behavior in the ceramic bodies, data for the drying regime and physical properties of the material as function of water content. The models allow variations of the drying conditions in order to choice the most efficient regime at existing or design dryers. The algorithm is applied for a direct coupled finite element analysis of wet bricks behavior in continuous working drying installation. The shrinkage mode, modulus of elasticity, Poisson ratio, modulus of rupture, effective mass transfer coefficient and critical moisture content are determined by experimental tests of the material. They are used to simulate numerically three-dimensional moisture, stress and strain fields in ceramic bodies at the existing drying regime. Ways for improvement of the models and their application for estimation of the potential for energy savings in industrial dryers are discussed.

Applicability of two-step homogenization to high-crimp woven composites

This paper examines applicability of a two-step homogenization approach to carbon/epoxy 3D woven composites. The first step of this approach involves microscale homogenization of the reinforcement consisting of wavy bundles of fibers. Finite Element Analysis (FEA) is used to obtain homogenized properties of explicitly modeled and homogenized wavy tows with fiber volume fraction of 70%. Two geometric parameters are investigated: crimp ratio and wavelength normalized by fiber diameter. Effective elastic properties are shown to be sensitive to the normalized wavelength parameter up to the value 50 at which point they reach asymptotic values and the separation of scales can be claimed.The resulting homogenized properties of the wavy tows are used to calculate the effective elastic properties of one high-crimp and two low-crimp 3D woven composites using FEA. The results of the numerical two-step homogenization are compared with experimental data and a simple Voigt model. Good correlation is observed between experimental results and the homogenization based on direct FEA. The considered Voigt approximation may be used as a reasonable first order estimate for Young’s moduli in low-crimp woven composites.

Deconvolution of the elastic properties of bivalve shell nanocomposites from direct measurement and finite element analysis

Abstract

Effect of stamping dimensional deviations on residual stresses and deformation of resistance spot welded steel sheets

Direct finite element analysis that takes stamping dimensional deviations into account was achieved based on coupled electro-thermo-mechanical method and reverse engineering in the current research. The two continuous resistance spot welding processes of the reverse established back side panel were simulated. Its residual stresses and deformation were compared with those of the ideal back side panel. Large distortion presents in the reverse back side panel while only slight deformation exists in the ideal one. The former is validated to be closer to the deformation of the actual welded back side panel. The peak residual stresses after processes 1 and 2 remain almost unchanged in the reverse back side panel while those in the ideal one show an increasing trend. The final residual stresses of the reverse and the ideal back side panel are both high but the former is lower than the later. The stamping dimensional deviations are responsible for these differences. They lead to obvious attenuation of geometric features and large assembly clearances in the reverse back side panel. These assembly clearances allow large deformations of the stamping parts during the welding process. Meanwhile, these clearances make it relatively freer for the heated sheet metal to expand thermally in the thickness direction, resulting in less or even no residual stress in this direction. These clearances also promote the release of the thickness-direction component of the tensile residual stress in the extension direction of sheet by allowing deformation in the thickness direction.

A two-scale generalized FEM for the evaluation of stress intensity factors at spot welds subjected to thermomechanical loads

This paper presents a two-scale Generalized Finite Element Method with global-local enrichments (GFEMgl) for the evaluation of stress intensity factors (SIFs) at spot welds subjected to thermomechanical loads. The method uses the solution of local boundary value problems as enrichment functions for the global/structural model and can provide accurate solutions on coarse meshes adopted at the structural scale. The faying surface and spot welds are represented by special enrichment functions instead of meshes fitting the weld geometry. This greatly simplifies the model generation process in comparison with a Direct Finite Element Analysis DFEA. Numerical experiments show that the proposed GFEMgl is able to capture the strong gradients and singularities near the spot weld edge. It can provide accurate solutions and SIFs comparable to a 3-D DFEA while requiring significantly less computational resources and user time. The robustness of the method is demonstrated through examples involving spot welds with irregular shapes and built-up panels subjected to sharp thermal fluxes.