Hybrid Finite Element Approach Research Articles

Modeling liquefaction-induced runout of a tailings dam using a hybrid finite element and material point method approach

Modeling liquefaction-induced runout of a tailings dam using a hybrid finite element and material point method approach

Custom Transient Finite Element for the Modelling of Ultrasonic Control Methods for Downhole Well Integrity

The transient spectral element method can be understood as a specific high-order finite element method that is particularly accurate and fast with a low memory footprint, hence enabling 3D ultrasonic testing simulations on a standard PC. However, particular care must be taken in its settings when seeking both practicality and performance. In comparison, fast semi-analytical simulation using ray tracing is easily accessible to nondestructive testing experts, through the CIVA simulation software. Although this approximate model effectively deals with a wide range of industrial applications, it reaches its limits in certain cases, particularly at relatively low frequencies involving resonance phenomena. To deal with these challenging inspection configurations, CEA-List is working on dedicated finite element models in the CIVA framework to meet specific needs in a compromise between efficiency and accuracy. The case study considered in partnership with SLB perfectly illustrates the benefits of developing such a modelling approach. SLB provides cased-well imaging services using ultrasonic resonance methods to evaluate oil and gas well integrity. Defective cased wells have irregularities, such as corroded casings with pitting, localized cement debonding and channelings. Simulated ultrasonic signals of the actual wells are useful to understand the measurements and are available by finite element modelling with sufficient accuracy. However, the associated computational costs for numerous model cases limit the building of the model database as the digital twin of the actual well logging. The development strategy of dedicated hybrid finite element applications adopted by CEA-List is presented in broad outline. Cross-model comparisons on a reference configuration of pristine cases are presented, highlighting the effective limits of standard CIVA ray models. The contribution offered by the new hybrid finite element approach is then discussed. We discuss the evolution of model functionalities to handle geometries that differ from the canonical case (interface defects, loss of thickness in arbitrary geometries, etc.) from the perspective of a digital twin of this control.

Damage Quantification and Identification in Structural Joints through Ultrasonic Guided Wave-Based Features and an Inverse Bayesian Scheme.

In this paper, defect detection and identification in aluminium joints is investigated based on guided wave monitoring. Guided wave testing is first performed on the selected damage feature from experiments, namely, the scattering coefficient, to prove the feasibility of damage identification. A Bayesian framework based on the selected damage feature for damage identification of three-dimensional joints of arbitrary shape and finite size is then presented. This framework accounts for both modelling and experimental uncertainties. A hybrid wave and finite element approach (WFE) is adopted to predict the scattering coefficients numerically corresponding to different size defects in joints. Moreover, the proposed approach leverages a kriging surrogate model in combination with WFE to formulate a prediction equation that links scattering coefficients to defect size. This equation replaces WFE as the forward model in probabilistic inference, resulting in a significant enhancement in computational efficiency. Finally, numerical and experimental case studies are used to validate the damage identification scheme. An investigation into how the location of sensors can impact the identified results is provided as well.

Investigation of hydraulic fracture branching in porous media with a hybrid finite element and peridynamic approach

Simulation of complex fracture patterns in porous media can help understand and improve hydraulic fracturing processes, with potential for significant impact on enhancing oil and gas recovery. In this paper, a fully coupled hydraulic fracture propagation simulation method employing a hybrid finite element method (FEM) and peridynamic (PD) approach is presented. Considering the ability of PD in solving discontinuous problems, the area where cracks can potentially occur is discretised by PD and the crack-free area is discretised by FEM. The solid deformation and fracture propagation are captured by PD and FEM, while the fluid flow in both the reservoir and fracture is simulated with FEM. The whole process is solved in a monolithic way with an implicit scheme. The presented method demonstrates the capability of modelling complex dynamic crack propagation via benchmark examples. Branching phenomenon is then investigated with the proposed model. It is found that faster loading rate, lower-energy release rate, and more brittle and impermeable media will cause crack branching more easily.

Accelerated design of architectured ceramics with tunable thermal resistance via a hybrid machine learning and finite element approach

Topologically interlocked architectures can transform brittle ceramics into tougher materials, while making the material design procedure a cumbersome task since modeling the whole architectural design space is not efficient and, to a degree, is not viable. We propose an approach to design architectured ceramics using machine learning (ML), trained by finite element analysis data and together with a self-learning algorithm, to discover high-performance architectured ceramics in thermomechanical environments. First, topologically interlocked panels are parametrically generated. Then, a limited number of designed architectured ceramics subjected to a thermal load is studied. Finally, the multilinear perceptron is employed to train the ML model in order to predict the thermomechanical performance of architectured panels with varied interlocking angles and number of blocks. The developed feed-forward artificial neural network framework can boost the architectured ceramic design efficiency and open up new avenues for controllability of the functionality for various high-temperature applications. This study demonstrates that the architectured ceramic panels with the ML-assisted engineered patterns show improvement up to 30% in frictional energy dissipation and 7% in the sliding distance of the tiles and 80% reduction in the strain energy, leading to a higher safety factor and the structural failure delay compared to the plain ceramics.

A 2-D Hybrid FE Model With Double Air Gap Elements for Eccentric Magnetic Harmonic Gears

Eccentric magnetic harmonic gears with high gear ratios exhibit high torque densities. However, the revolution and rotation of the eccentric rotor increase the magnetic field analysis complexity. This paper presents a hybrid finite element approach of magnetic field analysis for magnetic harmonic gears. The eccentric air gap region has been divided into three parts: two uniform layers, adjoining the stator and the rotor respectively, are treated as air gap elements; one non-uniform middle layer, as a variable air gap permeance, is discretized by FE meshes similar to the stator and the rotor. Mesh reconstruction can be avoided because the annular cylindrical rings of the two air gap elements are introduced. The mixed eccentric motion of the rotor can be easily treated. In order to save the computational time an equivalent motion mode is introduced and the sliding surface technique is applied by which the coefficient calculation of the air gap elements only needs to be done once wherever the rotor moves. The torques are calculated from the flux densities of the air gap elements. A prototype test confirms the validity of the prediction, and the accuracy of the obtained results is evaluated with FEM.

On the efficient optimization of optical properties of particulate monolayers by a hybrid finite element approach

This article addresses the numerical simulation and optimization of the optical properties of mono-layered nano-particulate films. The particular optical property of interest is the so-called haze factor, for which a model close to an experimental setup is derived. The numerical solution becomes very involved due to the resulting size of computational domain in comparison to the wave length, rendering the direct simulation method infeasible. As a remedy, a hybrid method is suggested, which in essence consistently combines analytical solutions for the far field with finite element-based solutions for the near field. Using a series of algebraic reformulations, a model with an off- and online component is developed, which results in the computational complexity being reduced by several orders of magnitude. Based on the suggested hybrid numerical scheme, which is not limited to the haze factor as objective function, structural optimization problems covering geometrical and topological parametrizations are formulated. These allow the influence of different particle arrangements to be studied. The article is complemented by several numerical experiments underlining the strength of the method.

A hybrid fundamental-solution-based 8-node element for axisymmetric elasticity problems

A novel hybrid finite element approach using fundamental solutions in conjunction with the boundary integration is proposed for the analysis of axisymmetric elasticity problems. In the formulation two displacement fields are independently assumed within the element domain and at the element boundary, which combines the advantages of conventional finite and boundary element methods. The resulting system of algebraic equations is symmetric and positive definite, which reduces the spatial dimension of the problem by one. It offers great flexibility in generating the mesh with arbitrary higher-order elements. Firstly, the proposed approach is validated by the analytical solution of a thick-walled hollow cylinder. A good agreement is observed. Meantime, the optimal number and location of source points for fundamental solutions as well as sensitivity to mesh distortion are studied. Finally, two more numerical examples including a flange and a wheel are provided. Compared to ABAQUS, the proposed approach exhibits higher efficiency, better convergence rate and strong capability to capture geometric singularities.

Finite element prediction of stress transfer in h-BN sheet nanocomposites

PurposeThe purpose of this paper is to implement a micromechanical hybrid finite element approach in order to investigate the stress transfer behavior of composites reinforced with hexagonal boron nitride (h-BN) nanosheets.Design/methodology/approachFor the analysis of the problem, a three-dimensional representative volume element, consisting of three phases, has been used. The reinforcement is modeled discretely using spring elements of specific stiffness while the matrix material is modeled as a continuum medium using solid finite elements. The third phase, the intermediate one, known as the interface, has been simulated by appropriate stiffness variations which define a heterogeneous region affecting the stress transfer characteristics of the nanocomposite.FindingsThe results show a good agreement with corresponding ones from the literature and also the effect of a number of factors is indicated in stress transfer efficiency.Originality/valueThis is the first time that such a modeling is employed in the stress transfer examination of h-BN nanocomposites.

Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach

The purpose of this study is to calculate the torsional rigidity and maximum shear stresses of arbitrarily shaped orthotropic composite or functionally graded material sections on the basis of a hybrid finite element approach. A hybrid finite element based on a Hellinger–Reissner functional is presented. A set of numerical examples is solved to verify the proposed method, and a parametrical study is also performed.

A hybrid finite element and surrogate modelling approach for simulation and monitoring supported TBM steering

The paper proposes a novel computational method for real-time simulation and monitoring-based predictions during the construction of machine-driven tunnels to support decisions concerning the steering of tunnel boring machines (TBMs). The proposed technique combines the capacity of a process-oriented 3D simulation model for mechanized tunnelling to accurately describe the complex geological and mechanical interactions of the tunnelling process with the computational efficiency of surrogate (or meta) models based on artificial neural networks. The process-oriented 3D simulation model with updated model parameters based on acquired monitoring data during the advancement process is used in combination with surrogate models to determine optimal tunnel machine-related parameters such that tunnelling-induced settlements are kept below a tolerated level within the forthcoming process steps. The performance of the proposed strategy is applied to the Wehrhahn-line metro project in Düsseldorf, Germany and compared with a recently developed approach for real-time steering of TBMs, in which only surrogate models are used.

Finite element prediction of stress transfer in graphene nanocomposites: The interface effect

A micromechanical hybrid finite element approach is implemented in this study, in order to evaluate the stress transfer characteristics in graphene-based nanocomposites. Three-dimensional representative volume elements, consisting of two different parts, have been used during the analysis. The matrix material that is modeled as continuum (solid finite elements), and the graphene sheet that is modeled discretely (spring based elements). Between these two constituents, an interfacial region is taking place, simulated by appropriate stiffness variations, defining a heterogeneous region that affects the stress transfer behavior of the composite. Our simulations show good agreement with existing studies of the open literature and indicate the effect of a number of factors in stress transfer efficiency.

Full-waveform inversion in three-dimensional PML-truncated elastic media

We are concerned with high-fidelity subsurface imaging of the soil, which commonly arises in geotechnical site characterization and geophysical explorations. Specifically, we attempt to image the spatial distribution of the Lamé parameters in semi-infinite, three-dimensional, arbitrarily heterogeneous formations, using surficial measurements of the soil’s response to probing elastic waves. We use the complete waveform response of the medium to drive the inverse problem , by using a partial-differential-equation (PDE)-constrained optimization approach, directly in the time-domain, to minimize the misfit between the observed response of the medium at select measurement locations, and a computed response corresponding to a trial distribution of the Lamé parameters. We discuss strategies that lend algorithmic robustness to our proposed inversion scheme. To limit the computational domain to the size of interest, we employ perfectly-matched-layers (PMLs). In order to resolve the forward problem, we use a recently developed hybrid finite element approach, where a displacement–stress formulation for the PML is coupled to a standard displacement-only formulation for the interior domain, thus leading to a computationally cost-efficient scheme. Time-integration is accomplished by using an explicit Runge–Kutta scheme, which is well-suited for large-scale problems on parallel computers. We verify the accuracy of the material gradients obtained via our proposed scheme, and report numerical results demonstrating successful reconstruction of the two Lamé parameters for both smooth and sharp profiles.

Numerical simulation of a phase transition problem with natural convection using hybrid FEM/EFGM technique

Purpose – The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid takes place within a square enclosure in the presence of natural convection. Design/methodology/approach – The physical problem, described with non-linear partial differential equations, is simulated using a hybrid finite element and element free Galerkin method (FEM/EFGM) approach. In energy conservation equation, the fixed-domain, effective heat capacity method is used to take into account the latent heat of phase change. The governing partial differential equations are solved with a meshfree, EFGM near the phase transition front while in the region away from the front with uniform nodal distribution; problem is simulated with traditional FEM. Findings – A sensitivity analysis of characteristic dimensionless numbers Rayleigh number (Ra), Prandtl number (Pr), Stefan number (ste) is presented in order to investigate their impact on thermal and flow fields. Typically computational times of EFGM are higher than that of FEM. Therefore, by using EFGM only in that portion of physical problem where phase transition occurs, the hybrid FEM/EFGM strategy employed in present paper could reduce the computational time of EFGM while still retaining its accuracy. Also, the consistent performance of the results obtained with this hybrid approach is validated with those already available in literature for some special cases. Originality/value – The hybrid methodology adopted in this paper, is quite new for solving such type of phase transition problem.

Modeling of crack density in ceramic matrix composites

The feasibility of utilizing the shear lag theory to estimate crack density in fabric reinforced composites was investigated. A geometric model was constructed for the fabric and meshed using a hybrid finite element approach. The small segment of the yarn and the surrounding matrix enclosed within each element were treated as a unidirectional composite and the shear lag theory was used to estimate the crack density. Model results were compared to experimental data for a 5-harness satin melt-infiltrated SiC/SiC composite under tension and showed a pattern similar to experimental data with the model starting to accumulate cracks at a stress corresponding to the point of departure from linearity in the stress–strain curve while cracks were experimentally observed around 60 MPa higher. The model and experimental data had a similar value for the crack density at the saturation level. Sensitivity analysis showed that the crack density was highly sensitive to the fiber volume fraction in the load direction followed by the weave angle of the crimped segments of the yarns and the interfacial shear strength between the fibers and the matrix.

Investigation of stress transfer in carbon nanotube reinforced composites using a multi-scale finite element approach

This paper describes a micromechanical hybrid finite element approach to study the stress transfer in single-walled carbon nanotube reinforced composites. A three-dimensional representative volume element of composite has been considered in this analysis. The nanotube is modeled taking into account its atomistic microstructure. The matrix material is modeled as continuum utilizing appropriate solid finite elements. Spring-based elements are used to describe the behavior of the single-walled carbon nanotubes. The interfacial effects between the two materials are simulated by appropriate stiffness variations defining a heterogeneous region. The model presents a reasonable behavior, with respect to composite effective mechanical properties, comparing with results available in the literature. The effects of carbon nanotube volume fraction, interfacial stiffness and elastic modulus of matrix on stresses are analyzed in details.

SPECIAL CIRCULAR HOLE ELEMENTS FOR THERMAL ANALYSIS IN CELLULAR SOLIDS WITH MULTIPLE CIRCULAR HOLES

This paper presents a new hybrid finite element approach with fundamental solutions (HFS-FEM) as a trial function for modeling thermal behavior in perforated or cellular solids containing multiple randomly distributed circular holes with arbitrary sizes and locations, using special elements to reduce mesh effort. Based on the independent intra-element field in the element consisting of fundamental solutions and the frame field defined on the element boundary, the approach has characteristic features of elementary boundary integrals and versatile element construction by virtue of combining the new hybrid functional. Special purpose hole elements and regular elements are constructed using the special fundamental solution satisfying the specified hole boundary conditions and the conventional fundamental solution, respectively, such that the circular hole region can be modeled with a much smaller number of elements. Numerical examples including problems with single, double and randomly distributed multiple holes are considered and the results demonstrate the versatility, accuracy, and efficiency of the approach presented.

A new hybrid finite element approach for plane piezoelectricity with defects

In this paper, a new type of hybrid fundamental solution-based finite element method (HFS-FEM) is developed for analyzing plane piezoelectric problems with defects by employing fundamental solutions (or Green’s functions) as internal interpolation functions. The hybrid method is formulated based on two independent assumptions: an intra-element field covering the element domain and an inter-element frame field along the element boundary. Both general elements and a special element with a central elliptical hole or crack are developed in this work. The fundamental solutions of piezoelectricity derived from the elegant Stroh formalism are employed to approximate the intra-element displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. By using Stroh formalism, the computation and implementation of the method are considerably simplified in comparison with methods using Lekhnitskii’s formalism. The special-purpose hole element developed in this work can be used efficiently to model defects such as voids or cracks embedded in piezoelectric materials. Numerical examples are presented to assess the performance of the new method by comparing it with analytical or numerical results from the literature.

A new hybrid finite element approach for three-dimensional elastic problems

A new fundamental solution based finite element method (HFS-FEM) is presented for analyzing three-dimensional (3D) elastic problems with body forces in this paper. It begins with deriving formulations of 3D HFS-FEM for elastic problems without body force and then the body force term is handled by means of the method of particular solution and radial basis function approximation. In our analysis, the homogeneous solution is obtained using the proposed HFS-FEM and the particular solution associated with the body force is approximated by radial basis functions. Several standard tests and numerical examples are considered to assess the capability and performance of the proposed method and elements. It is found that, comparing with conventional FEM (ABAQUS), the proposed method can achieve higher accuracy and efficiency when same element meshes are used. It is also found that the elements associated with this method are not very sensitive to mesh distortion and can be employed for problems involving nearly incompressible materials. This new method seems to be promising to deal with problems involving generalized body force, complex geometry, stress concentration and multi-materials.

A hybrid finite element approach to modeling sound radiation from circular and rectangular ducts

A numerical model based on a hybrid finite element method is developed that seeks to join sound pressure fields in interior and exterior regions. The hybrid method is applied to the analysis of sound radiation from open pipes, or ducts, and uses mode matching to couple a finite element discretization of the region surrounding the open end of the duct to wave based modal expansions for adjoining interior and exterior regions. The hybrid method facilitates the analysis of ducts of arbitrary but uniform cross section as well the study of conical flanges and here a modal expansion based on spherical harmonics is applied. Predictions are benchmarked against analytic solutions for the limiting cases of flanged and unflanged circular ducts and excellent agreement between the two methods is observed. Predictions are also presented for flanged and unflanged rectangular ducts, and because the hybrid method retains the sparse banded and symmetric matrices of the traditional finite element method, it is shown that predictions can be obtained within an acceptable time frame even for a three dimensional problem.