Conventional Finite Element Analysis Research Articles

Stability design of cold-formed high and ultra-high strength steel thin-walled box sections using effective stress-strain model

This paper proposes an effective stress-strain model for integrated analysis and design of cold-formed steel structures with thin-walled sections. The study focuses on square and rectangular hollow sections made from high and ultra-high strength steel. Initially, a shell-finite element model (SFEM) was developed and validated using experimental data, specifically for cold-formed members subjected to axial compression. Subsequently, a comprehensive parametric study is conducted to establish the stress-strain relationship model through nonlinear finite element analysis. The proposed model incorporates material nonlinearity, cold-forming effect, local plate imperfection, and residual stresses into a unified stress-strain curve, leading to advanced structural analysis and design of cold-formed structures using simple one-dimensional beam-column element. Subsequently, the proposed method is then implemented in the conventional finite beam-column element analysis, demonstrating consistent agreement with both experimental tests and sophisticated finite shell element results. Finally, the robustness and validation of the proposed method are established, and its application is exemplified through the design of a modular integrated construction (MiC) structure. This study highlights the versatility and reliability of the proposed approach for the analysis and design of cold-formed steel structures.

Strain regularisation using a non-local method in Coupled Eulerian-Lagrangian analyses

Conventional finite element analyses generally suffer from mesh dependency when considering softening effects. Non-local strain regularisation techniques have been developed to address this issue, which are generally complex to implement. In view of this, this paper introduces an more efficient procedure for implementation of a non-local method in Abaqus for Coupled Eulerian-Lagrangian (CEL) large deformation finite element undrained analyses. Results from a series of biaxial compression simulations demonstrate that the non-local method with a strain-softening Tresca model in CEL avoids mesh dependency. Owing to the stationary Eulerian element and the built-in mapping algorithm in CEL, high computational efficiency is achieved, adding no more than 12% to the computational cost. Guidance is provided on selection of internal length scales, element sizes and the search radius to ensure efficient non-local calculations, and it is shown that a softening scaling rule can also be used to allow use of practical mesh densities for some boundary value problems. Simulations of a number of classical geotechnical problems demonstrate the type of boundary value problems where the non-local method can effectively mitigate the mesh dependency, whilst also highlighting that the method fails to control the strain localisation that develops at soil-structure interfaces due to geometrical issues.

Applications of Computer Vision-Based Structural Monitoring on Long-Span Bridges in Turkey.

Structural displacement monitoring is one of the major tasks of structural health monitoring and it is a significant challenge for research and engineering practices relating to large-scale civil structures. While computer vision-based structural monitoring has gained traction, current practices largely focus on laboratory experiments, small-scale structures, or close-range applications. This paper demonstrates its applications on three landmark long-span suspension bridges in Turkey: the First Bosphorus Bridge, the Second Bosphorus Bridge, and the Osman Gazi Bridge, among the longest landmark bridges in the world, with main spans of 1074 m, 1090 m, and 1550 m, respectively. The presented studies achieved non-contact displacement monitoring from a distance of 600 m, 755 m, and 1350 m for the respective bridges. The presented concepts, analysis, and results provide an overview of long-span bridge monitoring using computer vision-based monitoring. The results are assessed with conventional monitoring approaches and finite element analysis based on observed traffic conditions. Both displacements and dynamic frequencies align well with these conventional techniques and finite element analyses. This study also highlights the challenges of computer vision-based structural monitoring of long-span bridges and presents considerations such as the encountered adverse environmental factors, target and algorithm selection, and potential directions of future studies.

Real-Time 3D Liver Tumor Localization via Combined Optical Surface Imaging and an X-Ray Projection from Arbitrary Imaging Angles

A deep learning (DL)-based, deformable registration-driven liver tumor localization technique was developed for onboard deformable motion tracking. The technique (Surf-X360-Bio) uses in-room optical surface imaging and an x-ray projection at an arbitrary scan angle to solve volumetric liver and liver tumor motion in real-time. Surf-X360-Bio solves the volumetric motion of the liver and localizes the liver tumor, through deforming liver and liver tumor meshes segmented on prior 4D-CTs/CBCTs. It uses real-time onboard information from an optical surface image and a simultaneously-acquired x-ray projection (from an arbitrary scan angle). Surf-X360-Bio localizes tumors via two steps: liver boundary motion estimation and intra-liver motion derivation. Surf-X360-Bio first estimates liver boundary motion by a patient-specific surface imaging model (Surf), utilizing the correlation between the external body surface motion and the internal liver boundary motion. As the correlation can be imperfect, the residual motion estimation errors were corrected by a patient-specific, angle-agnostic x-ray imaging model (X360). X360 deformed the liver boundary to match motion-related imaging features encoded in an arbitrarily-angled x-ray projection, using the Surf output for initialization. X360 adopted a geometry-aware learning module to extract and adapt to angle-varying features of arbitrarily-angled x-ray images, by calculating the projection system matrix of each x-ray image on-the-fly during model training and inference. After the liver boundary motion estimation by Surf and X360, intra-liver deformation was solved by a biomechanical model (Bio) to propagate the liver boundary motion inside to localize the tumors. The DL-based Bio model used domain knowledge of tissue biomechanics and finite element analysis (FEA) to solve intra-liver motion, with a much faster speed than conventional FEA methods to meet the real-time constraint. Surf-X360-Bio was evaluated using a dataset of 34 liver patients. Liver tumor localization accuracy was evaluated by the Dice similarity coefficient (DSC), the 95-percentile Hausdorff distance (HD95), and the center-of-mass error (COME). Using 3,306 motion scenarios spanning the 360 degree x-ray scan angles for each testing patient, Surf-X360-Bio localized the liver tumors to 0.81 (mean) ± 0.16 (s.d.) in DSC, 2.5 ± 1.7 mm in HD95, and 2.1 ± 1.8 mm in COME. In comparison, the prior reference image without deformable registration-driven localization yielded 0.42 ± 0.29 in DSC, 8.1 ± 5.2 mm in HD95, and 8.5 ± 5.2 mm in COME. Via Surf-X360-Bio, the overall inference time was below 230 ms for each case. Combining optical surface imaging and x-ray imaging, Surf-X360-Bio achieved fast (<250 ms inference time), accurate (mean error < 2.1 mm), and robust liver tumor localizations at arbitrary x-ray scan angles for real-time, marker-less 3D deformable motion tracking.

Shear Lag Analysis of Simply Supported Box Girders Considering Axial Equilibrium and Shear Deformation

The conventional methods used to analyze the shear lag effect in simply supported box girders assume that the neutral axis of the section coincides with the centroid, which does not strictly satisfy the axial equilibrium condition. To address this problem, this study proposes an analysis method in which three independent functions for the shear lag are employed to define the different shear lag strengths of the top slab, the bottom slab, and the cantilever slab. To fulfill the axial equilibrium condition of the box girder and to automatically locate the neutral axis position, the longitudinal displacement of the web is introduced. The shear deformation of the box girder is also considered. The governing differential equations and corresponding boundary conditions for displacement variables such as deflection and rotation of the box girder are derived through the application of the principle of virtual work. The differential equations are solved by utilizing the boundary conditions to obtain the analytical expressions of the shear lag function, longitudinal displacement of the web, rotation, deflection, and neutral axis position. Furthermore, after performing the finite element analysis, the effectiveness of the proposed method is verified by comparing the results with those obtained from conventional methods and finite element analysis. Furthermore, the influence of the axial equilibrium condition is quantified on axial force and stress difference ratios under three methods. Finally, extensive parametric analysis is carried out to investigate the effect of different parameter ratios on the ratios of the stress difference of the flanges. The results show that when the axial equilibrium condition is not considered, the axial stresses in the upper flange of the simply supported box girder are underestimated, especially at the intersection of the top, cantilever slab, and web, and the axial stresses in the lower flange are overestimated. As a result, the method in this study is able to calculate the axial stresses and deflections on simply supported box girders more accurately.

A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors

The effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu–Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains of the beam, which are allowed to be discontinuous across elements. This approach turns out to significantly improve the computational efficiency and the accuracy of the results. We consider a beam formulation with extensible directors, where cross-sectional strains are enriched to avoid Poisson locking by an enhanced assumed strain method. In numerical examples, we show the superior per degree-of-freedom accuracy of IGA over conventional finite element analysis, due to the higher order continuity in the displacement field. We further verify the efficient rotational coupling between beams, as well as the path-independence of the results.

Effective Scheme for Inductive Wireless Power Coil Design Using Scan-and-Zoom Optimization

In inductive power transfer (IPT) systems, the coil design is crucial since the power transfer efficiency (PTE) of IPT depends on the coil characteristics such as geometric shape, diameter, wire thickness, etc. The most commonly used technique for the coil is finite element analysis (FEA). Nevertheless, if there are more than two parameters to be designed, FEA design requires a long simulation time since the coil design problem is separated into a series of single-parameter optimization problems. Another issue of conventional FEA is difficulty in interfacing with circuit simulation. To mitigate this issue, a novel co-simulation framework of MATLAB/ANSYS Maxwell is proposed in this paper. In MATLAB, multi-dimensional optimization algorithms like scan-and-zoom are employed to determine geometric parameters to achieve high PTE and minimize the number of FEA executions while Maxwell serves to extract the circuit parameters from the geometric parameters and enhance the accuracy of calculation. The 100 W prototype IPT system is built to verify the proposed coil design scheme in this paper. The performance comparisons with the conventional methods in terms of design accuracy, simulation time, and application flexibility are performed on a pair of designed single-layer circular coils.

A Linear Hybrid Model for Analytical Magnetic Field Analysis in Flux-Switching Permanent-Magnet Machine

A hybrid model for the flux-switching permanent-magnet (FSPM) machine is proposed in this paper. In this hybrid model, the air-gap magnetic field in FSPM machine is investigated from the perspective of the stator modulation effect and rotor modulation effect. The stator modulation is discussed from the perspective of equivalent air-gap in the stator slots and permanent-magnets (PMs). The rotor modulation effect is divided to two aspects, namely the effect on the magnetomotive force (MMF) and the effect on stator modulation effect. Different from the conventional model where the stator modulation effect and the rotor modulation are independent of each other, stator modulation effect in the proposed model is coupled with the rotor modulation effect by the minimal reluctance principle. Therefore, MMF and the stator modulation effect in FSPM machine become susceptible to rotor positions with the influence of the rotor modulation effect. Air-gap flux density in FSPM machine is calculated by this hybrid model and compared with those by conventional model and finite element analysis (FEA). Finally, the effectiveness of the proposed hybrid model is validated by comparison of the electromotive force with FEA and experimental results.

Time-Domain Homogenized Finite Eddy Current Analysis Using Recursive Convolution Method

This paper presents a novel method for effectively and accurately performing time-domain homogenized finite element analysis of multi-turn coil windings. In this method, the macroscopic complex permeability is represented by a partial fraction form, and then inverse Laplace transformation is performed using the recursive convolution method. The proposed method is approximately 100 times faster than conventional finite element analysis, with good agreement between the obtained results. Moreover, the results obtained by the proposed method were also in good agreement with those obtained by measurement.

Finite element geotechnical analysis incorporating deep learning-based soil model

Owing to the complicated mechanical behaviors of soils, their constitutive models often involve obscureformulations and suffer from poor applicability in engineering practice. In this study, a novel framework for the finite element (FE) analysis of geotechnical engineering problems is proposed, in which a deep learning (DL) model is employed to depict the constitutive behaviors of soils, circumventing the difficulties associated with conventional approaches. The DL model can incorporate different neural network architectures and is trained with stress–strain data, obtained either experimentally or numerically, before being integrated into the FE solver for analyzing various boundary value problems (BVPs). During the FE solution, the DL model receives strains at the Gauss integration points and returns the predicted stresses to advance the computation. The applicability and capacity of the framework were demonstrated by analyzing three BVPs, in which different geometries, meshes, and boundary conditions were considered. It was shown that the framework is capable of reproducing satisfactory solutions without resorting to any constitutive theory. Furthermore, the use of the DL model not only avoids the stress integration of the conventional FE analysis, but also leads to better computational efficiency.

A novel pre-processing modelling method for the finite element analysis of the thermal deformation of large structures in the erection stage

The manufacturing process of ships and offshore structures comprises several stages, which include plate cutting, sub-assembly, block assembly, pre-erection, and erection. Accuracy and quality control management are crucial issues in the manufacturing process. Welding-induced distortion and deformation complicate the assembly stage in shipyards. Through conventional finite element (FE) analysis, the manufacturing process can be predicted and controlled up to the sub-assembly stage; however, applying the FE method to the stages between block assembly and erection is difficult. In this study, a new FE analysis method for predicting welding-induced thermal deformation of large blocks, which was difficult to predict with traditional methods, was proposed. In addition, based on this result, we developed a novel pre-processing modelling system that can automatically extract the erection weld lines and automatically divide blocks, which are necessary for the thermal deformation analysis of large blocks. Validation experiments confirmed the applicability of the proposed method to the shaft alignment of a container ship and LNG carrier, with industrial accuracy and quality control in the manufacturing process. Compared with existing methods, the proposed method increases the accuracy of the analysis and reduces the total pre-processing time.

Machine-Learning-Enabled Design and Manipulation of a Microfluidic Concentration Gradient Generator.

Microfluidics concentration gradient generators have been widely applied in chemical and biological fields. However, the current gradient generators still have some limitations. In this work, we presented a microfluidic concentration gradient generator with its corresponding manipulation process to generate an arbitrary concentration gradient. Machine-learning techniques and interpolation algorithms were implemented to help researchers instantly analyze the current concentration profile of the gradient generator with different inlet configurations. The proposed method has a 93.71% accuracy rate with a 300× acceleration effect compared to the conventional finite element analysis. In addition, our method shows the potential application of the design automation and computer-aided design of microfluidics by leveraging both artificial neural networks and computer science algorithms.

High-Fidelity Induction Motor Simulation Model Based on Finite Element Analysis

This article proposes a new high-fidelity simulation model of an induction motor (IM) based on finite-element analysis (FEA). The proposed model enables fast and accurate IM simulation with the inverter circuit model and control algorithm. That is, the proposed model can represent non-ideal features of IM, such as magnetic saturation, spatial harmonics, skew, and saturation-induced saliency in high accuracy. To construct the proposed model, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> equivalent circuit of the squirrel cage rotor is introduced. Based on this, the static FEA is conducted which can accelerate the model construction compared to the conventional time-stepping FEA technique. Then, a flux-based IM model is established, which has advantages on speed, accuracy, and memory size in the simulation. To verify the effectiveness of the proposed model, the models are constructed for two commercial IMs used for the industrial drive. IM control algorithms are tested in various operating conditions on the proposed model. The results are compared with the time-stepping FEA and the experiment for the verification of the proposed model.

Variational Autoencoder-Based Metamodeling for Multi-Objective Topology Optimization of Electrical Machines

Conventional magneto-static finite element (FE) analysis of electrical machine design is time-consuming and computationally expensive. Since each machine topology has a distinct set of parameters, design optimization is commonly performed independently. This article presents a novel method for predicting key performance indicators (KPIs) of differently parameterized electrical machine topologies at the same time by mapping a high-dimensional integrated design parameters in a lower-dimensional latent space using a variational autoencoder (VAE). After training, via a latent space, the decoder and multi-layer neural network will function as meta-models for sampling new designs and predicting associated KPIs, respectively. This enables parameter-based concurrent multi-topology optimization.

Computational homogenization of additively manufactured lightweight structures with multiscale topology optimization

Abstract Topology optimization (TO) is an optimal design method to obtain an efficient structure with minimal usage of material by satisfying two conflicting objectives of weight reduction and structural safety. Owing to the recent advances in additive manufacturing technology, TO has been developed in connection with the use of microscale lattices, of which complicated geometries require considerable computational loads to verify their structural performance. This study aims to develop an efficient computational method to analyze a complex TO model. Computational homogenization was then developed for efficient computation of the TO model that contains a number of microscale lattices. The proposed homogenization scheme was then applied to perform three-dimensional (3D) finite element analysis (FEA) on various TO models with three scales (i.e., macroscale, microscale, and multiscale TOs). The homogenized FEAs were conducted to verify the static and dynamic deformation behaviors of three optimized meta-sandwich beams, and their results and computational efficiency were compared with those from full solid FEAs. Experimental verification revealed that the proposed homogenized FEA provided more reliable results and better computational efficiency for the microscale and multiscale TO models, whereas the conventional solid FEA was advantageous for the macroscale TO model. To apply the proposed simulation strategy to a more complex 3D geometry, three TO models were calculated for a 3D block under a compression load. The simulation strategy combining the full solid and homogenized FEAs was then applied to analyze the static and dynamic deformation behaviors of various TO models, which provided reliable predictions of the experimentally observed behaviors within an acceptable computational time.

Deep Learning-Accelerated Designs of Tunable Magneto-Mechanical Metamaterials.

Metamaterials are artificially structured materials with unusual properties, such as negative Poisson's ratio, acoustic band gap, and energy absorption. However, metamaterials made of conventional materials lack tunability after fabrication. Thus, active metamaterials using magneto-mechanical actuation for untethered, fast, and reversible shape configurations are developed to tune the mechanical response and property of metamaterials. Although the magneto-mechanical metamaterials have shown promising capabilities in tunable mechanical stiffness, acoustic band gaps, and electromagnetic behaviors, the existing demonstrations rely on the forward design methods based on experience or simulations, by which the metamaterial properties are revealed only after the design. Considering the massive design space due to the material and structural programmability, a robust inverse design strategy is desired to create the magneto-mechanical metamaterials with preferred tunable properties. In this work, we develop an inverse design framework where a deep residual network replaces the conventional finite-element analysis for acceleration, realizing metamaterials with predetermined global strains under magnetic actuations. For validation, a direct-ink-writing printing method of the magnetic soft materials is adopted to fabricate the designed complex metamaterials. The deep learning-accelerated design framework opens avenues for the designs of magneto-mechanical metamaterials and other active metamaterials with target mechanical, acoustic, thermal, and electromagnetic properties.

Nonlinear Response Prediction of Spar Platform in Deep Water Using an Artificial Neural Network

The finite element method (FEM) is an essential method for predicting the response of the spar platform considering all nonlinear variables. Although FEM is an extremely laborious and time-consuming process for predicting platform responses using hydrodynamic loads, artificial neural networks (ANNs) can predict the response quickly, as required for platform management to either linger or stop the production of oil and gas. The application of ANN approaches to estimate the wave height and period from the expected wind forces is investigated in this paper. The ANN model can also predict the nonlinear responses of the spar platform subjected to the structural parameter as well as the wave height and wave period. The backpropagation technique depletes feed-forward neural networks, allowing the network to be trained. Following the formation of the neural network, rapid reactions from a freshly anticipated wind force are obtained. The results are validated via a comparison with results from a conventional finite element analysis. The findings demonstrate that the artificial neural network (ANN) technique is effective and is able to significantly reduce the required time to make predictions when compared to the conventional FEM.

Investigation on the mechanical properties of TPMS porous structures fabricated by laser powder bed fusion

With the rapid development in additive manufacturing (AM), graded triply periodic minimal surface (TPMS) lattice structures are brought into focus for various multi-functional applications. However, the simulation of TPMS structures includes excessive data and long computing processes due to the complexity of TPMS structures. Therefore, we used an equivalent entity (EE) modelling approach based on homogenisation method: namely a simple solid block replaces the complex TPMS structures during the simulation of mechanical properties. Two cases, including homogenous structures (Case I) and graded structures (Case II), are proposed to verify the feasibility of the EE model. The as-built samples of these structures show a high relative density of 99.92%. Following the experiments conducted on the two cases, the EE model has similar simulation results including mechanical behaviour (stiffness and strength) and stress distribution, compared with the conventional finite element analysis (CFEA) model, while the EE model has a ~ 96.40% decrease in the number of elements and a ~ 99.80% decrease in the calculation time. This EE model method has significant implications for the graded TPMS structure design process.

A data-driven approach for fatigue life of water intake risers

Water intake risers are novel concept for cooling water transport from the sea to the floating facilities. The fatigue performance is key to design of the water intake risers. In this paper, the fatigue performance of a bundle of water intake risers is investigated for the first time using full-scale field measurements in combination with a finite element model. Through this approach, a data-driven model is developed to assess the fatigue damage of water intake risers. A fatigue analysis framework is proposed to calculate the bending stress along the risers based on the measured rotations at two locations of the risers. Compared to the conventional finite element analysis, this framework provides a more accurate and time-efficient solution for fatigue estimation, which helps the structural integrity of the water intake risers over their life cycle.

Vibration analysis of permanent magnet synchronous motor using coupled finite element analysis and optimized meshless method

Conventional finite element analysis (FEA) performed in electromagnetic-vibration coupling calculation of motor suffers from several significant drawbacks, such as large memory space, high computational cost and heavy reliance on mesh quality for accurate solution. With the traditional meshless method, special attention needs to be paid to correctly impose the boundary condition like FEA. Besides, the matrix is easily prone to be ill-conditioned due to introducing large amount of higher-order basis functions. We propose a novel multi-physical coupling method combining FEA and optimized meshless method. The proposed methodology is further evaluated on the vibration analysis of a 12-slot 10-pole permanent magnet synchronous motor (PMSM). Firstly, 2D stator electromagnetic force is simulated and derived based on the local Jacobian derivative method through FEA. The electromagnetic force spectrum is calculated using FFT analysis and further imported into commercial meshless structural simulation software SimSolid for stator harmonic response analysis. Correct force boundary condition and data mapping between meshless and FEA simulation interface are key to the accuracy of the proposed combined multi-physical modeling methodology. This is achieved by introducing new high-dimensional ramp function in the transition region between FEA and meshless domains, which are defined with the shape functions composed of the FEA and meshless method. This function satisfies the continuity and consistency of the displacement function and ensures the convergence of coupled FEA-meshless method. Subsequently, construction of basis function is key to the establishment of convention meshless discrete equation for the elastic problem of rotating machinery. This is designed by using moving least square theory in cylindrical coordinate system. A harmonic response with meshless method is analyzed by using the mode superposition method to obtain detailed mode shape data, acceleration and displacement distribution of stator. Finally, the tangential continuity and robustness are not well considered in the traditional simulation with FEA coupled meshless method. To mitigate this problem, we propose an optimized meshless method based on modified local basis functions to recalculate the harmonic response motion. Then, the coupling electromagnetic-vibration simulation results of traditional coupled FEA-meshless method, optimized coupled FEA-meshless method and complete FEA coupled method are compared. It is worth noting that the optimized method significantly improves accuracy, robustness and computational speed at the same time. In short, the proposed electromagnetic-structure coupling calculation method provides a novel alternative for the multi-physical coupling calculation of rotating machinery combining FEA and meshless simulation methods.