Large-scale Finite Element Research Articles

A theoretical framework for predicting the heterogeneous stiffness map of brain white matter tissue

Finding the stiffness map of biological tissues is of great importance in evaluating their healthy or pathological conditions. However, due to the heterogeneity and anisotropy of biological fibrous tissues, this task presents challenges and significant uncertainty when characterized only by single-mode loading experiments. In this study, we propose a new theoretical framework to map the stiffness landscape of fibrous tissues, specifically focusing on brain white matter tissue. Initially, a finite element (FE) model of the fibrous tissue was subjected to six loading cases, and their corresponding stress-strain curves were characterized. By employing multiobjective optimization, the material constants of an equivalent anisotropic material model were inversely extracted to best fit all six loading modes simultaneously. Subsequently, large-scale FE simulations were conducted, incorporating various fiber volume fractions and orientations, to train a convolutional neural network capable of predicting the equivalent anisotropic material properties solely based on the fibrous architecture of any given tissue. The proposed method, leveraging brain fiber tractography, was applied to a localized volume of white matter, demonstrating its effectiveness in precisely mapping the anisotropic behavior of fibrous tissue. In the long-term, the proposed method may find applications in traumatic brain injury, brain folding studies, and neurodegenerative diseases, where accurately capturing the material behavior of the tissue is crucial for simulations and experiments.

Quantitative guided wave imaging with shear horizontal waves and deep convolutional descent full waveform inversion

Effectively determining the size and thickness distributions of corrosion damages is a vital problem in nondestructive testing (NDT). In this article, a new approach is introduced that employs magnetostrictive transducers (MST) to excite the first dispersive shear horizontal mode (SH1), and utilizes the DCD-FWI (deep convolutional descent full waveform inversion) to provide comprehensive thickness mapping in just 1 s. Compared with traditional imaging techniques, DCD-FWI network is an intrinsically full waveform inversion (FWI) based method, which yields reliable imaging results in large scale finite element simulations. Moreover, the shorter wavelength and resistance to water loading of SH guided waves bring about reliable imaging results. Combined with these advantages, the high energy transfer efficiency of the MST enhances the proposed method's robustness, as demonstrated by guided wave tomography experiments on aluminum plates.

Modal analysis of honeycomb panel satellite structure based on MSC Apex

Modal analysis plays an important role in the process of Satellite structure development. In this paper, the honeycomb sandwich plate and the satellite structure are taken as the research objects, and the corresponding finite element models are established. The analysis results of the actual modeling of honeycomb plate and the equivalent modeling of sandwich sandwich plate are obtained, and the fundamental frequency deviation of the whole satellite structure is discussed when the equivalent correction coefficient γ of honeycomb plate is different. The results show that the maximum relative error of the modal frequency between the equivalent method of sandwich sandwich plate and the actual modeling is 2.8%. Therefore, the equivalent method can be applied to large-scale finite element analysis and calculation, and the calculation efficiency can be improved. When the value of γ is 0.4∼0.6, the vibration modes of the whole satellite structure are basically consistent, and the maximum fundamental frequency difference is 10%. The results can evaluate the accuracy of the sandwich sandwich plate equivalent method for satellite mechanical analysis.

Liquefaction-induced large deformation method with automatic time-step mapping and interfacial interpolation improvement: Case study of the San Fernando dam

This study constructed the u-p equation for saturated soil in the meshfree global weak form within the arbitrary Lagrangian-Eulerian (ALE) framework to solve the problem of liquefaction-induced large deformation induced by strong seismic loading. The interpolation improvement in the near-interface zone was achieved using domain truncation optimization and the local nodal refinement algorithm, and the relative error of the shape function was proposed as the judgment criterion for radial basis function (RBF) field variable mapping. Finally, a high precision meshfree liquefaction-induced large deformation method (MFLLDM) with automatic time step mapping and interfacial zone interpolation improvement was established. The MFLLDM achieved the efficient dynamic updating of soil stress state and pore pressure information in space during the deformation process and more accurately depicted the localized large shear deformation characteristics of the soil in the near-interface zone. The proposed method was integrated into a custom-built large-scale finite element method (FEM) computing system (GEODYNA), based on object-oriented and super element program design technology. This enabled the efficient coupled analysis of MFLLDM in the liquefied-induced large deformation zone and FEM in the small deformation zone. Numerical consolidation examples were used to validate the accuracy, convergence, and applicability of the soil elasto-plastic model for MFLLDM. The method was then used to simulate the liquefaction damage of the San Fernando dam, which reproduced the development process of large slip deformation and high-water pressure ratio for the upstream dam slope.

Tomography-based digital twin of Nd-Fe-B permanent magnets

Many functional materials have been designed at the multiscale level. To properly simulate their physical properties, large and sophisticated computer models that can replicate microstructural features with nanometer-scale accuracy are required. This is the case for permanent magnets, which exhibit a long-standing problem of a significant offset between the simulated and experimental coercivities. To overcome this problem and resolve the Brown paradox, we propose an approach to construct large-scale finite element models based on the tomographic data from scanning electron microscopy. Our approach reconstructs a polycrystalline microstructure with actual shape, size, and packing of the grains as well as the individual regions of thin intergranular phase separated by triple junctions. Such a micromagnetic model can reproduce the experimental coercivity of ultrafine-grained Nd-Fe-B magnets along with its mechanism according to the angular dependence of coercivity. Furthermore, a remarkable role of thin triple junctions as nucleation centers for magnetization reversal is revealed. The developed digital twins of Nd-Fe-B permanent magnets can assist their optimization toward the ultimate coercivity, while the proposed tomography-based approach can be applied to a wide range of polycrystalline materials.

Research on seismic performance of corrugated web rigid structures

Abstract: Corrugated web H-beam refers to a steel beam with a wavy shape along its length, which is extensively utilized in various parts of building structures such as beams, columns, and walls. It serves the purpose of connection and support, while the corrugated or folded design enhances the shear resistance and out-of-plane stiffness of the web to some extent. However, despite their advantages including high strength, stiffness, and lightweight construction, relevant regulations stipulate that these members can only be used in lower-intensity applications or higher-intensity scenarios if specific conditions are met. One crucial condition is that the ratio between the design value of axial force subjected to seismic action and the product of the member's flange section area and steel's tensile strength should not exceed 0.4. In this study, we aim to further investigate the seismic characteristics and applicable intensity of corrugated steel structures under earthquakes through large-scale finite element ABAQUS simulations. We will observe dynamic characteristics and failure modes of corrugated rigid frame structures using elastic-plastic time-history analysis methods as well as examine plastic deformation features of steel beam members under low cyclic loads via hysteretic analysis methods. The findings demonstrate that when properly designed with reasonable beam spans, corrugated web rigid frame structures can still be employed in high-intensity areas above 7 degrees even when subjected to an axial compression ratio up to 0.5.

Sensitivity Analysis of Transient Forced Response of Mistuned Bladed Disks Under Complex Excitation and Varying Rotation Speed

Abstract During accelerations and decelerations of gas-turbine engines, the transient vibration effects in bladed disk vibration become significant and the transient response needs to be efficiently and accurately assessed. This paper develops an effective method for efficient calculations of the sensitivity of the transient vibration response for a mistuned-bladed disk under varying rotation speeds. The sensitivities are calculated concerning two major factors: (i) the blade mistuning and (ii) the rotor acceleration/deceleration rates. The method uses the large-scale finite element modeling of the bladed disk to accurately describe the dynamic properties of the mistuned bladed disk. The method can be applied for a case when the loading is the transient load, with the amplitude and frequency spectrum changing with rotation speed. The dependency of the modal characteristics on the rotation speed is included in the formulation of the sensitivity analysis method. Efficient reduced order models are used to reduce the computational cost, which can adapt to the effects of the varying rotation speed on the natural frequencies and mode shapes of the mistuned bladed disk under transient conditions. The expressions for the sensitivities are derived analytically which provides high accuracy and speed of the calculations. The method has been implemented in a computer code and thoroughly verified using a set of test cases. The studies of transient forced response sensitivity have been performed for realistic bladed disk models.

Load history estimation for ballistic impacts with bullet-splash

The paper validates two simplified approaches to simulate the interactions between impactor and target during the so-called bullet splash phenomenon, i.e., the full fragmentation of the impactor without any penetration of the target. The approaches are based on treating the interactions between impactor and target as the deflection of a fluid flow; in one case the load history is estimated by the mass distribution of the bullet and its impact velocity; in the second case the interaction is simulated by means of an arbitrary Lagrangian Eulerian formulation. The two methods are applied and experimentally validated to simulate a monolithic .308 rifle bullet impacting on a high strength steel plate. The results demonstrate the suitability of the load history method for large scale finite element explicit simulations for the assessment of ballistic protection systems.

Finite Element Analysis of Steel Truss Bridge Structure Based on ANSYS

With the rapid development of bridge engineering in China, steel truss bridge is widely used with many advantages such as clear force of the structure itself, easy to analyze, and low requirement for foundation. In this paper, the finite element analysis method is adopted to analyze the stress and deformation distribution of steel truss bridge on the platform of ANSYS, a large-scale finite element analysis software. In the static analysis, by applying the vehicle load, the operation mode of the structure is simulated, and the cloud diagrams of its displacement and stress are derived. The dangerous areas of the bridge are identified to provide a reference basis for the design of steel truss bridges.

Geomechanical reservoir modelling with Thermodynamics-based Artificial Neural Networks (TANNs)

Geological subsurface storage is a promising strategy for large-scale, cost-efficient energy storage systems. Stress sensitivity has notably influence on the long-term stability and serviceability of subsurface reservoirs set for energy storage use. The evolution of the field stress of stress-sensitive reservoirs and the associated structural deformation, often a consequence of fluid production and injection, can cause significant changes to the reservoir stress-dependent properties [1]. These properties include pore and void compressibility, and porosity. For fractured and faulted reservoirs, field stress variation may also impact fracture conductivity, alter pre-existing fractures, and reactivate faults [4].
 Current geomechanical reservoir simulators incorporate the evolution of the reservoir mechanical state by means of material constitutive modelling, typically within a Finite Element Modelling (FEM) framework. In efforts to honour the heterogeneity and multi-scale nature of subsurface reservoirs, multi-scale solution methods are commonly adopted. For a reservoir multi-scale simulation, the micro-scale problem must be iteratively solved for different input parameters, render-ing the solution method computationally exhaustive, particularly for two-way coupled problems.
 The combination of machine learning-based solution methods and FEM frameworks can address the computational inefficiency of conventional multi-scale reservoir modelling schemes. In principle, a machine learning algorithm trained to learn the constitutive behaviour of a material can replace in-built material constitutive models in a FEM framework. We resort to Thermodynamics-based Artificial Neural Networks (TANNs), a physics-based data-driven machine learning algorithm introduced in [5] for material constitutive modelling. TANNs have been shown to guarantee the thermodynamic consistency of learnt material constitutive models. The first and second laws of thermodynamics are directly encoded in the architecture of TANNs through the definition of two scalar functions, an energy potential and a dissipation function, and the computation of their differentials [3].
 TANNs can be incorporated in FEM tools, in what is referred to as TANNxFEM in [6]. We present the application of the TANNxFEM framework to geomechanical reservoir modelling. This work aims to introduce a computationally efficient reservoir modelling framework, for which uncertainty quantification is possible. The proposed framework can maximise the use of information inherently contained in high-dimensional data, and significantly reduce computation demands necessary for accurate statistical evaluation, while warranting physical and geological realism.
 TANNs are first trained on analytical material data, computed by numerical integration of an incremental, thermodynamically consistent material model presented in [2]. The trained TANNs are then imported into a user material subroutine for the finite element package Abaqus. Through an input file, the parameters of the trained neural network are read as a set of material properties. The material subroutine then evaluates the incorporated trained neural network to construct the stress and elasticity tensors necessary for large-scale finite element reservoir simulation. The above proposed framework is validated against a large-scale finite element simulation with a user material subroutine implementing the constitutive model used to first generate the training data for TANNs. The free-energy, dissipation, and the stress-strain response of the two finite element simulations are compared for model verification.

Constitutive modeling of orthotropic nonlinear mechanical behavior of hardened 3D printed concrete

3D printing of concrete is a promising construction technology, offering the potential to build geometrically complex structures without the use of cost-intensive formwork. The layer-wise deposit of filaments during the 3D printing process results in an intrinsic orthotropic mechanical behavior in the hardened state. Beyond that, the material behavior of 3D printed concrete (3DPC) is governed by a highly nonlinear behavior, characterized by irreversible deformations, strain hardening, strain softening and a degradation of the material stiffness. In this contribution, a new constitutive model for describing the orthotropic and highly nonlinear material behavior of 3DPC will be presented. It is formulated by the extension of a well-established isotropic damage plasticity model for concrete to orthotropic material behavior by linear mapping of the stress tensor into a fictitious isotropic configuration. The performance of the new model will be evaluated by finite element simulations of three-point bending tests of 3DPC samples, performed for different orientations of the loading direction relative to the printing direction and comparison with experimental results. In addition, the applicability of the model to replicate the mechanical behavior of 3DPC, manufactured by the alternative 3D printing process of binder jetting of cementitious powders, will be demonstrated by 3D finite element simulations of an arch structure with varying orientations of the loading direction relative to the layering. Overall, the proposed model provides a computationally efficient modeling approach for large-scale finite element simulations of 3DPC structures, being a promising alternative to complex and computationally expensive finite element models considering distinct interfacial planes.

Techniques to embed channels in finite element shallow water equation models

Two new and novel techniques to efficiently represent channels in large-scale finite element shallow water equation models are introduced. The first enables the discontinuous representation of bathymetric depth by allowing nodes along a discontinuity to have two land surface elevations, one representing the bottom of the discontinuity and the other the top of the discontinuity. Elemental integration proceeds using the nodal depth corresponding to whether the element is on the upper or lower side of the discontinuity and enables efficient treatment of steep sided features in a two-dimensional horizontal discretization. The second technique consolidates nodal equations at paired nodes across a channel. Doing this eliminates cross-channel variability and consequently eliminates the across-channel Courant-Friedrichs-Lewy stability constraint on the model time step. Together the two techniques allow channels of various sizes as well as other instances of steep topography to be embedded seamlessly, efficiently and in a fully coupled manner within an otherwise two-dimensional horizontal spatial discretization. This new capability is especially useful in the interface zone subject to both coastal and hydrological influences as it effectively captures bi-directional channelized flow, bi-directional flow between the channel and the floodplain, and coupled flow when the channel and floodplain are fully submerged. This paper describes the methodological development and presents a series of tests that verify the performance of this novel solution approach.

A Problem-Independent Machine Learning (PIML) enhanced substructure-based approach for large-scale structural analysis and topology optimization of linear elastic structures

Structural analysis for structures composed of highly heterogeneous materials which often involves the solution of large-scale linear algebraic equations is very time-consuming even within the linear elastic regime. Furthermore, the tremendous computational cost of iterative large-scale finite element analysis also prevents the widespread use of topology optimization as a powerful design tool especially when the desired design resolution is very high. In order to break the bottleneck hindering the efficient solutions of large-scale structural analysis and design optimization problems, in the present article, a general machine learning (ML) enhanced substructure-based framework is proposed. The essential idea is resorting to the classical substructure-based finite element analysis approach and establishing an implicit mapping between the parameters characterizing the material distribution within a substructure and the corresponding condensed stiffness matrix/numerical shape functions through offline trained deep neural networks. In contrast to most of the existing ML enhanced approaches, the proposed framework is truly independent of the forms of structural geometry, boundary condition and external load, and can be applied to solve various boundary value problems governing by the same type of partial differential equation once the offline training is completed. Armed with modern artificial intelligence techniques, the proposed approach in some sense revives the classical substructure approach in finite element analysis. Compared with the traditional paradigm, it can achieve 104–105 times solution efficiency for tested large-scale examples with satisfactory accuracy. The effectiveness of the approach was also validated for the non-adjoint topology optimization problems, i.e., 3D compliant mechanism design. Finally, to demonstrate the proposed approach’s capability in dealing with extremely large-scale three-dimensional problems, a three-dimensional topology optimization problem with about 109 design variables and 3×109 degrees of freedom (Dofs) is solved on a laptop without resorting to any parallel computing techniques.

Block-partitioned Rayleigh–Ritz method for efficient eigenpair reanalysis of large-scale finite element models

Abstract In this manuscript, we propose a new effective method for eigenpair reanalysis of large-scale finite element (FE) models. Our method utilizes the matrix block-partitioning algorithm in the Rayleigh–Ritz approach and expresses the Ritz basis matrix using thousands of block matrices of very small size. To avoid significant computational costs from the projection procedure, we derive a new formulation that uses tiny block computations instead of global matrix computations. Additionally, we present an algorithm that recognizes which blocks are changed in the modified FE model to achieve computational cost savings when computing new eigenpairs. Through selective updating for the recognized blocks, we can effectively construct the new Ritz basis matrix and the new reduced mass and stiffness matrices corresponding to the modified FE model. To demonstrate the performance of our proposed method, we solve several practical engineering problems and compare the results with those of the combined approximation method, the most well-known eigenpair reanalysis method, and ARPACK, an eigenvalue solver embedded in many numerical programs.

A Fast Frequency Sweep approach for performance-based optimization of earthquake-resistant irregular large-scale buildings

Performance-Based Design (PBD) optimization of buildings subjected to seismic excitations has increasingly been applied to regular small-scale structural systems to minimize initial or life-cycle costs. Nonetheless, a comprehensive bibliographic survey reveals that studies dealing with irregular buildings are scarce, although they can present higher seismic vulnerability than regular buildings. Specifically, the PBD optimization of irregular buildings represented by large-scale finite element (FE) models, and considering dozens of discrete design variables, cannot be found to the best of the authors’ knowledge. Hence, this paper presents an original framework for the PBD optimization of irregular buildings subjected to seismic excitations, handling thousands of DOFs and dozens of discrete design variables. To relieve the computational burden, enabling the problem to be solved, a Model Order Reduction (MOR) strategy based on the Well-Conditioned Asymptotic Waveform Evaluation (WCAWE) approach is combined with a hybrid optimization algorithm, which integrates a local optimizer with a restart strategy. The former is employed to speed up the frequency-domain response, while the latter allows for tackling a non-convex and multimodal objective function with many discrete variables. The procedure is adaptatively devised to operate in a robust and fully black-box approach. The application case consists of a stiffness in-plane irregular H-shape building with 16,452 active DOFs and 34 discrete design variables. The proposed scheme largely reduces the computational burden, leading to speed-up factors (SUF) up to 19 times compared to direct frequency-domain solutions.

Neural network modelling of mechanical joints for the application in large-scale crash analyses

This paper presents an artificial neural network (NN) modelling approach to represent a connector model in large-scale finite element explicit crash simulations. The NN model was established to describe the local force–deformation response of point connectors in automotive applications, namely self-piercing rivets and flow-drill-screws. The study is limited to two-sheet connections and to the use of feedforward NNs. Successive loading and unloading of the joints is not studied. Various architectures and complexities of the feedforward NNs were evaluated and trained based on data generated from a constraint model found in the literature. This forms a proof of concept for implementing a modelling technique not based on physics-motivated constitutive equations. The impact of the network complexity and training data diversity was investigated. The NN model was implemented as a cohesive zone model for incremental force prediction in an explicit finite element code. In order to have a wide selection of joint types, five different joint configurations including self-piercing rivets (SPR) and flow-drill screws (FDS) were investigated. Numerical results from the NN model were compared to physical tests from all joint configurations. It was shown that a rather basic machine learning technique like a feedforward NN was able to reproduce path-dependent force–deformation behaviour for the application in explicit FE solvers.

Elucidating non-uniform assembling effect in large-scale PEM fuel cell by coupling mechanics and performance models

The assembly of proton exchange membrane (PEM) fuel cell has a significant influence on contact pressure of BP and GDL, which affects key parameters of GDL including contact resistance, porosity, and permeability. In this study, a large-scale finite element method (FEM) PEM fuel cell model is developed considering realistic assembly, which is assembled by 14 bolts. The contact pressure at the interface of GDL and BP is converted into non-uniform contact resistance incorporated into a self-developed “3D + 1D” full PEM fuel cell multi-phase model with the active area of 108 cm2. The “3D + 1D” model simplifies part of components along through-plane direction into 1D model to improve calculation efficiency and stability. The results show that the performance reduces slightly when considering non-uniform contact resistance compared with that considering uniform contact resistance. The uniformity of current density and temperature distributions reduces evidently when considering non-uniform contact resistance affecting the performance and durability, which demonstrates the necessity of treatment of non-uniform contact resistance. Furthermore, the effects of porosity and permeability of deformed GDL under different preloading torques on performance are investigated. It is found that the contact resistance reduces first and then flats as the preloading torques increase, which results in the same trend of electronic ohmic loss, while the concentration loss nearly linearly increases. The simulation shows that the PEM fuel cell shows the best performance when the preloading torque is 3 Nm. This study provides some meaningful guidance for PEM fuel cell stack assembly.

Estimation of Soil–Structure Model Parameters for the Millikan Library Building Using a Sequential Bayesian Finite Element Model Updating Technique

We present a finite element model updating technique for soil–structure system identification of the Millikan Library building using the seismic data recorded during the 2002 Yorba Linda earthquake. A detailed finite element (FE) model of the Millikan Library building is developed in OpenSees and updated using a sequential Bayesian estimation approach for joint parameter and input identification. A two-step system identification approach is devised. First, the fixed-base structural model is updated to estimate the structural model parameters (including effective elastic modulus of structural components, distributed floor mass, and Rayleigh damping parameters) and some uncertain components of the foundation-level motion. Then, the identified structural model is used for soil–structure model updating wherein the Rayleigh damping parameters, the stiffness and viscosity of the soil subsystem (modeled using a substructure approach), and the foundation input motions (FIMs) are estimated. The identified model parameters are compared with state-of-practice recommendations. While a specific application is made for the Millikan Library, the present work offers a framework for integrating large-scale FE models with measurement data for model inversion. By utilizing this framework for different civil structures and earthquake records, key structural model parameters can be estimated from the real-world recorded data, which can subsequently be used for assessing and improving, as necessary, state-of-the-art seismic analysis and structural modeling techniques. This paper presents an effort towards using real-world measurements for large-scale FE model updating in the soil and structure, uniform soil time domain for joint parameter and input estimation, and thus paves the way for future applications in system identification, health monitoring, and diagnosis of civil structures.

Fine-grained heterogeneous parallel direct solver for finite element problems

The improvement of computational effectiveness is a vital issue in the field of large-scale finite element analysis. The performance is fundamentally determined by the efficiency of solving sparse linear system equations using the implicit finite element method. This paper presents a direct linear solver based on heterogeneous hybrid parallel computing on CPUs and GPUs. This can efficiently utilize computing resources of multiple devices to achieve performance improvement. Initially, we partition the elimination tree into several subtrees to accomplish the task decomposition. Based on this, we build a dynamic programming mathematical model to balance the computational load of the various devices. Then, we develop a numerical decomposition strategy by combining node parallelism and tree parallelism for the CPUs. In addition, efficient numerical decomposition is achieved on the GPU through batch processing and maximizing the overlap between computations and data transfers. Numerical experiments show that, compared with MKL PARDISO, the performance of numerical factorization can be improved by up to 10 times by using CPU and dual-path GPU hybrid calculations, and the computation time of simulation can be reduced by one-third for the multicondition analysis of Body In White and by 20% for the large-scale nonlinear finite element deformation analysis.

Combined digital twin and hierarchical deep learning approach for intelligent damage identification in cable dome structure

Accurate identification of structural damage is the most critical step in structural health monitoring. Traditional damage identification strategies are easily interfered by environmental and human factors, resulting in low-accuracy of identification. In this light, a combined digital twin (DT) and hierarchical deep learning (DL) approach for intelligent damage identification in cable dome structures is proposed in this paper. Based on actual engineering cases, a DT model that accurately maps the physical structure of the cable dome is constructed using APDL based on data. A cable dome structure damage sample database is then automatically established through the large-scale finite element analysis of DT. Finally, the damage features of the data samples are extracted using the hierarchical DL framework proposed in this study. Accuracy verification based on cable force confirms that the established DT model can accurately reflect the mechanical state of the physical structure. The identification results of the trained network on a test set demonstrate that the proposed framework can intelligently identify the damage type, damage location, and damage degree in the cable dome structure with a high accuracy and strong robustness. The proposed intelligent damage identification approach is feasible and reliable and can provide a new basis for structural damage identification with broad application prospects.