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.

Finite Element Simulation of Radial Tire Building and Shaping Processes Using an Elasto-Viscoplastic Model

The comprehensive tire building and shaping processes are investigated through the finite element method(FEM)in this article.The mechanical properties of the uncured rubber from different tire components are investigated through cyclic loading-unloading experiments under different strain rates.Based on the experiments,an elastoviscoplastic constitutive model is adopted to describe themechanical behaviors of the uncured rubber.The distinct mechanical properties,including the stress level,hysteresis and residual strain,of the uncured rubber can all be well characterized.The whole tire building process(including component winding,rubber bladder inflation,component stitching and carcass band folding-back)and the shaping process are simulated using this constitutive model.The simulated green tire profile is in good agreement with the actual profile obtained through 3D scanning.The deformation and stress of the rubber components and the cord reinforcements during production can be obtained fromthe FE simulation,which is helpful for judging the rationality of the tire construction design.Finally,the influence of the parameter“drum width”is investigated,and the simulated result is found to be consistent with the experimental observations,which verifies the effectiveness of the simulation.The established simulation strategy provides some guiding significance for the improvement of tire design parameters and the elimination of tire production defects.

Phase-field modeling of dendritic growth under forced flow based on adaptive finite element method

A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

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.

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

Multiple linear system techniques for 3D finite element method modeling of direct current resistivity

The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.

The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives

In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.

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.

The Modeling of 2D Controlled Source Audio Magnetotelluric (Csamt) Responses Using Finite Element Method

This paper presents the modeling of 2D CSAMT responses generated by horizontal electric dipole using the separation of primary and secondary field technique. The primary field is calculated using 1D analytical solution for homogeneous earth and it is used to calculate the secondary electric field in the inhomogeneous Helmholtz Equation. Calculation of Helmholtz Equation is carried out using the finite element method. Validation of this modeling is conducted by comparison of numerical results with 1D analytical response for the case of homogeneous and layered earth. The comparison of CSAMT responses are also provided for 2D cases of vertical contact and anomalous conductive body with the 2D magnetotelluric (MT) responses. The results of this study are expected to provide better interpretation of the 2D CSAMT data.

Finite element method for coupled diffusion-deformation theory in polymeric gel based on slip-link model

A polymeric gel is an aggregate of polymers and solvent molecules, which can retain its shape after a large deformation. The deformation behavior of polymeric gels was often described based on the Flory-Rehner free energy function without considering the influence of chain entanglements on the mechanical behavior of gels. In this paper,a new hybrid free energy function for gels is formulated by combining the EdwardsVilgis slip-link model and the Flory-Huggins mixing model to quantify the time-dependent concurrent process of large deformation and mass transport. The finite element method is developed to analyze examples of swelling-induced deformation. Simulation results are compared with available experimental data and show good agreement. The influence of entanglements on the time-dependent deformation behavior of gels is also demonstrated.The study of large deformation kinetics of polymeric gel is useful for diverse applications.

Optimal design of automotive body B-pillar using simplified finite element model of body-in-prime combined with an optimization procedure

Optimization of an automotive body structure faces the difficulty of having too many design variables and a too large design search space. A simplified model of body-in-prime(BIP) can solve this difficulty by reducing the number of design variables. In this study, to achieve lighter weight and higher stiffness, the simplified model of BIP was developed and combined with an optimization procedure;consequently, optimal designs of automotive body B-pillar were produced. B-pillar was divided into four quarters and each quarter was modelled by one simplified beam. In the optimization procedure, depth, width, and thickness of the simplified beams were considered as the design variables.Weight, bending and torsional stiffness were also considered as objective functions. The optimization procedure is composed of six stages: designing the experiments, calculating grey relational grade, calculating signal-to noise ratio,finding an optimum design using Taguchi grey relational analysis, performing sensitivity analysis using analysis of variance(ANOVA) and performing non-dominated sorting and multi-criteria decision making. The results show that the width of lower B-pillar has the highest effect(about 55%) and the obtained optimum design point could reduce the weight of B-pillar by about 40% without reducing the BIP stiffness by more than 1.47%.

Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.

SEMI-ANALYTICAL FINITE ELEMENT METHOD FOR FICTITIOUS CRACK MODEL IN FRACTURE MECHANICS OF CONCRETE

Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.

COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES

Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.

STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS

The aim of the paper is to discover the general creep mechanisms for the short fiber reinforcement matrix composites (MMCs) under uniaxial stress states and to build a relationship between the macroscopic steady creep behavior and the material micro geometric parameters. The unit cell models were used to calculate the macroscopic creep behavior with different micro geometric parameters of fibers on different loading directions. The influence of the geometric parameters of the fibers and loading directions on the macroscopic creep behavior had been obtained, and described quantitatively. The matrix/fiber interface had been considered by a third layer, matrix/fiber interlayer, in the unit cells with different creep properties and thickness. Based on the numerical results of the unit cell models, a statistic model had been presented for the plane randomly-distributed-fiber MMCs. The fiber breakage had been taken into account in the statistic model for it starts experimentally early in the creep life. With the distribution of the geometric parameters of the fibers, the results of the statistic model agree well with the experiments. With the statistic model, the influence of the geometric parameters and the breakage of the fibers as well as the properties and thickness of, the interlayer on the macroscopic steady creep rate have been discussed.

Development of a nonlinear 3D solid finite element model for the calculation of bending moments of flexural members

A numerical model is developed in this paper to calculate the bending moments of flexural members through integration in 3D solid finite element analyses according to the nonlinear constitutive model of concrete and the elastoplastic constitutive model of steel,utilizing the stress condition of the cross-section,considering the destruction characteristic of reinforced concrete members,and based on the plane cross-section assumption.The results of this model give good agreement with those of the classical method.Consequently,we can also deduce the corresponding numerical expression for eccentrically loaded members according to the analysis method.

Finite Element Analysis in Combination with Perfectly Matched Layer to the Numerical Modeling of Acoustic Devices in Piezoelectric Materials

The characterization of finite length Surface Acoustic Wave (SAW) and Bulk acoustic Wave (BAW) resonators is addressed here. The Finite Element Analysis (FEA) induces artificial wave reflections at the edges of the mesh. In fact, these ones do not contribute in practice to the corresponding experimental response. The Perfectly Matched Layer (PML) method, allows to suppress the boundary reflections. In this work, we first demonstrate the basis of PML adapted to FEA formalism. Next, the results of such a method are depicted allowing a discussion on the behavior of finite acoustic resonators.

FINITE ELEMENTAN ALYSIS FOR THE UNSTEADY NEARSHORECIR CULATION DUE TO WAVE－CURRENT INTER－ACTION（I）──NUMERICAL MODEL

In lhis paper, a numerical model for predicting the unsteady nearshore circulationdue to wave-current interaction was proposed. In addition io the traditional continuity,momentunm and energy. equations, the dispersion and refraction relations were includedin the governing equalions. Moreover, the effects of lateral shears, wind, radiation andbottom stresses were analysed in the governing equalions. Therefore, we expect thatthis model may more completely and exactly reflect the law of ware-currentinteraction. In part (II) we will adopt the selective lumping two-step explicit finite elementmethod to solve the model, and some examples will be presented.