Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.

A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.

Big Model Strategy for Bridge Structural Health Monitoring Based on Data-Driven, Adaptive Method and Convolutional Neural Network (CNN) Group

This study introduces an innovative“Big Model”strategy to enhance Bridge Structural Health Monitoring(SHM)using a Convolutional Neural Network(CNN),time-frequency analysis,and fine element analysis.Leveraging ensemble methods,collaborative learning,and distributed computing,the approach effectively manages the complexity and scale of large-scale bridge data.The CNN employs transfer learning,fine-tuning,and continuous monitoring to optimize models for adaptive and accurate structural health assessments,focusing on extracting meaningful features through time-frequency analysis.By integrating Finite Element Analysis,time-frequency analysis,and CNNs,the strategy provides a comprehensive understanding of bridge health.Utilizing diverse sensor data,sophisticated feature extraction,and advanced CNN architecture,the model is optimized through rigorous preprocessing and hyperparameter tuning.This approach significantly enhances the ability to make accurate predictions,monitor structural health,and support proactive maintenance practices,thereby ensuring the safety and longevity of critical infrastructure.

Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.

Circuit-field coupled finite element analysis method for an electromagnetic acoustic transducer under pulsed voltage excitation

This paper presents an analytical method for electromagnetic acoustic transducers （EMATs） under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation （FFT）. In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting＇s theorem. Then the currents under different frequencies are calculated according to Ohm＇s law and the pulsed current excitation is obtained by inverse fast Fourier transformation （IFFT）. Lastly, the sequentially coupled finite element method （FEM） is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board （PCB） coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Furthermore, the influences of lift-off distances and the non-uniform static magnetic field on the Lorentz force under pulsed voltage excitation are studied.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Numerical analysis of coupled finite element with element-free Galerkin in sheet flexible-die forming

A numerical method for coupled deformation between sheet metal and flexible-die was proposed. Based on the updated Lagrangian （UL） formulation, the elastoplastic deformation of sheet metal was analyzed with finite element method （FEM） and the bulk deformation of flexible-die was analyzed with element-free Galerkin method （EFGM）. The frictional contact between sheet metal and flexible-die was treated by the penalty function method. The sheet elastic flexible-die bulging process was analyzed with the FEM-EFGM program for coupled deformation between sheet metal and bulk flexible-die, called CDSB-FEM-EFGM for short. Compared with finite element code DEFORM-2D and experiment results, the CDSB-FEM-EFGM program is feasible. This method provides a suitable numerical method to analyze sheet flexible-die forming.

ANALYSIS OF THE THERMOPHYSICAL PARAMETERS OF MOIST WOOD PARTICLE MATERIAL IN A COUPLED HEAT AND MASS TRANSFER PROCESS OF FREEZING BY USING FINITE ELEMENT METHOD

The coupled heat and moisture transfer in a freezing process of wood particle material was mathematically modeled in the paper. The models were interactively solved by using the numerical method(the finite element method and the finite difference method). By matching the theoretical calculation to an experiment, the nonlinear problem was analyzed and the variable thermophysical parameters concerned was evaluated. The analysis procedure and the evaluation of the parameters were presented in detail. The result of the study showed that by using the method as described in the paper, it was possible to determine the variable (with respect to temperature, moisture content and freezing state) thermophysical parameters which were unknown or difficult to measure as long as the governing equations for a considered process were available. The method can significantly reduces the experiment efforts for determining thermophysical parameters which arc very complicated to measure. The determined variable of the effective heat conductivity of wood particle material was given in the paper. The error of the numerical calculation was also estimated by the comparison with a matched experiment.

A New Unified Stabilized Mixed Finite Element Method of the Stokes-Darcy Coupled Problem: Isotropic Discretization

In this paper, we develop an a-priori error analysis of a new unified mixed finite element method for the coupling of fluid flow with porous media flow in RN, N ∈ {2,3}, on isotropic meshes. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The approach utilizes a modification of the Darcy problem which allows us to apply a variant nonconforming Crouzeix-Raviart finite element to the whole coupled Stokes-Darcy problem. The well-posedness of the finite element scheme and its convergence analysis are derived. Finally, the numerical experiments are presented, which confirm the excellent stability and accuracy of our method.

Structural Integrity Analysis of Containers Lost at Sea Using Finite Element Method

Unlike traditional transportation,container transportation is a relatively new logistics transportation mode.Shipping containers lost at sea have raised safety concerns.In this study,finite element analysis of containers subjected to hydrostatic pressure,using commercial software ANSYS APDL was performed.A computer model that can reasonably predict the state of an ISO cargo shipping container was developed.The von Mises stress distribution of the container was determined and the yield strength was adopted as the failure criterion.Numerical investigations showed that the conventional ship container cannot withstand hydrostatic pressure in deep water conditions.A strengthened container option was considered for the container to retain its structural integrity in water conditions.

Mixed Finite Volume Element Method for Vibration Equations of Beam with Structural Damping

In this paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate variables, the original fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed. Numerical examples are provided to confirm the theoretical results. In the end, we test the value of δ to observe its influence on the model.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

Conversion between solid and beam element solutions of finite element method based on meta-modeling theory:development and application to a ramp tunnel structure

In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.

Geotechnical particle finite element method for modeling of soilstructure interaction under large deformation conditions

The possibilities of the particle finite element method(PFEM)for modeling geotechnical problems are increasingly evident.PFEM is a numerical approach to solve large displacement and large strain continuum problems that are beyond the capabilities of classical finite element method(FEM).In PFEM,the computational domain is reconfigured for optimal solution by frequent remeshing and boundary updating.PFEM inherits many concepts,such as a Lagrangian description of continuum,from classic geomechanical FEM.This familiarity with more popular numerical methods facilitates learning and application.This work focuses on G-PFEM,a code specifically developed for the use of PFEM in geotechnical problems.The article has two purposes.The first is to give the reader an overview of the capabilities and main features of the current version of the G-PFEM and the second is to illustrate some of the newer developments of the code.G-PFEM can solve coupled hydro-mechanical static and dynamic problems involving the interaction of solid and/or deformable bodies.Realistic constitutive models for geomaterials are available,including features,such as structure and destructuration,which result in brittle response.The solutions are robust,solidly underpinned by numerical technology including mixedfield formulations,robust and mesh-independent integration of elastoplastic constitutive models and a rigorous and flexible treatment of contact interactions.The novel features presented in this work include the contact domain technique,a natural way to capture contact interactions and impose contact constraints between different continuum bodies,as well as a new simplified formulation for dynamic impact problems.The code performance is showcased by the simulation of several soil-structure interaction problems selected to highlight the novel code features:a rigid footing insertion in soft rock,pipeline insertion and subsequent lateral displacement on over-consolidated clay,screw-pile pull-out and the dynamic impact of a free-falling spherical penetrometer into clay.

Full－range nonlinear analysis of fatigue behaviors of reinforced concrete structures by finite element method

The offshore reinforced concrete structures are always subject to cyclic load, such as wave load.In this paper a new finite element analysis model is developed to analyze the stress and strain state of reinforced concrete structures including offshore concrete structures, subject to any number of the cyclic load. On the basis of the anal ysis of the experimental data,this model simplifies the number of cycles-total cyclic strain curve of concrete as three straight line segments,and it is assumed that the stress-strain curves of different cycles in each segment are the same, thus the elastoplastic analysis is only needed for the first cycle of each segment, and the stress or strain corresponding to any number of cycles can be obtained by superposition of stress or strain obtained by the above e lastoplastic analysis based on the cyclic numbers in each segment.This model spends less computer time,and can obtain the stress and strain states of the structures after any number of cycles.The endochronic-damage and ideal offshore concrete platform subject to cyclic loading are experimented and analyzed by the finite element method based on the model proposed in this paper. The results between the experiment and the finite element analysis are in good agreement,which demonstrates the validity and accuracy of the proposed model.

THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS

In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.

ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem

A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.