Coupling Of FEM Research Articles

Versatile coupling of MPM and FEM: A case study of the stability of vegetated slope

Evaluating root reinforcement in the root–soil composite is challenging due to the complex interactions among its components and the variable configurations of the roots. A proposed FEM-MPM coupled model is dedicated to examining the influence of roots on slope stability. The FEM component employed the Truss structural element type to model the dynamics and physics of the root, coupled with a damaged constitutive model, which sheds light on the effects of orientation, cohesion, and friction on the brittle or progressive failure modes of the root. The MPM counterpart provided the capability for large deformation simulation in the post-failure phase of the slope. The framework’s integration was achieved through a penalty method, correcting the dynamics of its members (translation and orientation) and linking the decay of the root with the plastic behavior of the soil through updated geometrical and mechanical properties. Several geotechnical tests and examples, such as pull-out tests, direct shear tests, and vegetated slope collapse simulations, were conducted to validate and verify the robustness of the proposed approach. The results demonstrate the methodology’s capability to capture the mechanism of root reinforcement in vegetated slope stability.

Numerical Research on Impacting Load and Structural Response for a Model Experiment of High-speed Craft

Abstract High-speed craft generally applies hy droplane boat-type and large power engine to obtain high speed in water as results that significant hydrodynamic nonlinearities, high-speed craft has complex the impact load characteristics and structural response which attract considerable attentions of ship mechanics researchers. This paper studies impacting load and structural response of a high-speed craft by means of numerical approach coupling CFD and FEM. A model experiment of high-speed craft is selected to simulate impact load and structural response, the craft model consists of two ship bodies and a keel beam, a number of pressure sensors and strain gauges are arranged to capture the impacting pres s ure and VBM. A numerical FSI approach coupling CFD and FEM is used to study the model experiment of the high-speed craft. CFD is used to solve the hydrodynamics of the high-speed craft, DFBI and overset grid algorithm are employed to simulate the craft motion. Dy namic FEM is us ed to calculate structural response of high-speed craft, structural VBM is obtained. Two-way FSI is employ ed to realize coupling of CFD and FEM, wave pres s ures and structural displacement are iterated to progress. At last, numerical res ults and experimental res ults including impacting pressure, craft motion and VBM are compared and analyzed, they agree with closely. The numerical approach can be used to study the impacting load and structural respons e for high-speed craft.

Thermal Fracturing in Orthotropic Rocks with Superposition-Based Coupling of PD and FEM

Thermal Fracturing in Orthotropic Rocks with Superposition-Based Coupling of PD and FEM

Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM

Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient for theory and practice, since only a single domain discretisation is needed, it also requires the knowledge of the domain mapping. However, in certain applications, the random domain is only described by its random boundary, while the quantity of interest is defined on a fixed, deterministic subdomain. In this setting, it thus becomes necessary to compute a random domain mapping on the whole domain, such that the domain mapping is the identity on the fixed subdomain and maps the boundary of the chosen fixed, nominal domain on to the random boundary. To overcome the necessity of computing such a mapping, we therefore couple the finite element method on the fixed subdomain with the boundary element method on the random boundary. We verify on one hand the regularity of the solution with respect to the random domain mapping required for many multilevel quadrature methods, such as the multilevel quasi-Monte Carlo quadrature using Halton points, the multilevel sparse anisotropic Gauss–Legendre and Clenshaw–Curtis quadratures and multilevel interlaced polynomial lattice rules. On the other hand, we derive the coupling formulation and show by numerical results that the approach is feasible.

Coupled Large Scale Hydromechanical Modelling for Caprock Failure Risk Assessment of Gas Storage in Aquifer

The rapidly increasing demand for the consumption of natural gas has attracted the interests to store natural gas in aquifer reservoir. However, natural gas injected into the aquifer reservoir, which could cause ground surface deformation and mechanical integrity destruction of caprock. Taking the aquifer gas storage of S trap as the research object, according to the geological structure and hydrogeological information, a coupling large-scale hydromechanical model is established to evaluate the damage risk of the gas reservoir in S aquifer. The proposed methodology is based on the development of fluid-solid coupling and application of FEM. The different failure mechanisms of S aquifer gas storage caprock can be evaluated on the basis of the tensile failure criterion and Mohr-Coulomb shear failure criterion. To analyze the change of caprock in gas injection and production process more clearly, a reference model is defined as an ideal calculation condition to discuss the mechanical response, pore pressure variation, and surface deformation characteristics of the caprock during injection and production. On this basis, the second scheme of sensitivity analysis is defined. The pressure injection rate, reservoir parameters, in situ stress, and other factors are considered, respectively, and the influence of different input parameters on mechanical stability and surface deformation of caprock is analyzed. Finally, the mechanical stability is analyzed and combined the above two criteria to predict the upper limit injection pressure of S. Simulation results show that the permeability and in situ stress have a significant influence on ground surface deformation and mechanical integrity of caprock, but Young’s modulus and Poisson’s ratio can be ignored; the upper limit pressure coefficient of S is 1.908.

Multi-scale mechanics of sand based on FEM-DEM coupling method

Multiscale mechanics is one of the important mechanical behaviors of granular materials. To perform an efficient calculation of the multiscale mechanics of granular materials based on the coupling of FEM and DEM, a GPU-based solver named as Coupling Simulator (CoSim) is developed. Taking sand as the example of granular materials, triaxial tests are performed to verify the reliability of the multiscale simulation. Firstly, based on the laboratory tests, a parameter inversion method is introduced to obtain the contact parameters of the particles composing the RVE of the sand sample. Then the parameters and RVE sample are used for multi-scale simulation of the triaxial test. The numerical results show that the stress-strain relationship and deformation characteristics are corresponding well with that of the laboratory tests on the macro-scale. According the numerical tests, the meso-mechanical behaviors at different positions of the sample varies greatly, but the deformation and stress evolution of the sample on macro scale are all closely related. Unlike the shear bands where both of the volume expansion and dramatic adjustment of the meso-structure take place, a numerical invalidation of Gaussian points around the shear bands is induced by the volume expansion with no or very slight adjustment of the meso-structure takes place. Finally, the strength reduction method is induced to the multi-scale algorithm and is used for the stability analysis of a sand slope. The numerical results show that both of the factor of stability (FOS) and the obtained slide face are corresponding well with that of the limit equilibrium method. So, the developed GPU-based FEM-DEM coupling code can better be used for the multi-scale simulation of granular materials and geotechnical engineering.

Hydro-structure coupling of CFD and FEM - Quasi-static approach

The present article deals with the coupling of hydrodynamic loading, modelled by OpenFOAM Finite Volume (FV) framework for Computational Fluid Dynamics (CFD), and the structural response, modelled by the general 3D Finite Element (FE) approach. The overall methodology and the numerical approaches which are discussed are very general and remain valid for any type of hydro-structure interaction problems, but here the main concern is on marine structures (ships, off-shore platforms …) where the loading is induced by water waves. In the present work, the accent is placed on the linear quasi static structural response which is the problem belonging to the one-way coupling procedures. Particularly, this means that the hydrodynamic and structural simulations can be performed independently of each other. The main technical issue becomes the consistent transfer of the hydrodynamic loads from the hydrodynamic CFD mesh to the structural FE mesh. This paper presents a novel methodology of the load transfer based on the projection method for the specific application to FV hydrodynamic and FE structural coupling. Validation tests are performed on a simple fixed vertical cylinder in presence of waves and on a more practical case of container ship in large waves demonstrating the robustness and accuracy of the method.

Verification of Tire Hydroplaning Phenomenon Using Coupled FSI Simulation by CFD and FEM

Hydroplaning phenomenon is one of the major factors that must be considered to ensure safe driving on wet road surfaces. In this paper, the approach to numerical simulation of the physical hydroplaning characteristics using patterned tire is described. A detailed 3-D patterned tire model is constructed by in-house modeling program and the water flow is considered as incompressible. The complex tire material compositions are effectively modeled using composites, and rubber properties generalize the Mooney-Rivlin model. The finite element method (FEM) and the advanced finite volume method (FVM) are used for structural and for fluid-tire interaction analysis, respectively. Performance prediction of hydroplaning via coupling of computational fluid dynamics (CFD) and FEM has delivered a detailed insight into the local mechanisms and root causes of hydroplaning. Numerical examples were verified by comparing the experimental test results and it is confirmed to indicate similar correlation tendency and high reliability. The effect of driving velocity, pattern groove size, and pattern direction on hydroplaning phenomenon of tire is discussed and logical results were obtained.

Coupling of FEM and ordinary state-based peridynamics for brittle failure analysis in 3D

This paper presents a method to couple FEM meshes with ordinary state-based peridynamic grids. It generates a computational tool that is as efficient as computer methods based on classical continuum mechanics and as flexible as peridynamics in dealing with crack propagation. Moreover, it removes most of the problems due to the surface effects typical of nonlocal methods such as OSB-PD. The adaptive dynamic relaxation approach is used to solve linear elastic and crack propagation problems. The method is successfully applied to a complex crack propagation case in 3 D and is able to accurately reproduce the shape of the experimentally observed crack.

Coupling of FEM and DEM simulations to consider dynamic deformations under particle load

Coupled FEM–DEM simulations enable the direct analysis of the load, the deformation and the stresses inside machine parts which interact with bulk materials. The analysis of large deformations of elastic parts is interesting as the deformation will significantly influence the bulk material behaviour. In this paper a bidirectional coupling method for the FEM software $$\hbox {ANSYS}^\circledR $$ Classic and the DEM software $$\hbox {LIGGGHTS}^\circledR $$ is presented. The coupling algorithm was verified and validated using a modified draw down test rig. The results from the experimental investigations and the FEM–DEM simulations are compared. A very good correlation between experiments and simulations could be found.

On the coupling of DPG and BEM

In this talk we present results of our recent work [2]: We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of standard Galerkin boundary elements. The procedure (i) is somehow a natural approach, because the DPG method can also be equivalently written as a least-squares problem. However, the implementation involves, besides the computation of discrete boundary integral operators, the evaluation of non-local norms, which is not needed for the methods (ii). The derivation of the procedures (ii) relies on either one or both equations of the Calderon system and their analysis makes use of various ideas resp. results for the coupling of FEM and BEM [1, 3, 4]. The stability of these methods hinges on an additional parameter, i.e., a scaling of the trial-to-test operator or the test functions. Nevertheless, numerical experiments indicate that the stability does not depend on this parameter. An essential feature of the methods (i)–(ii) is that, despite the use of boundary integral equations, optimal test functions have to be computed only locally. We apply our findings to a standard transmission problem in full space and present numerical examples to validate our theory.

Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements

We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the condition number of the preconditioned system stays uniformly bounded, independently of the refinement level and the local mesh‐size of the underlying adaptively refined triangulations. Although the focus is on the nonsymmetric Johnson–Nédélec one‐equation coupling, the principle ideas also apply to other formulations like the symmetric FEM‐BEM coupling. Numerical experiments underline our theoretical findings. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 603–632, 2017

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

Time‐dependent fluid‐structure interaction

The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of the central importance in detecting and identifying submerged objects. The problem is generally referred to as a fluid‐structure interaction and is mathematically formulated as a time‐dependent transmission problem. In this paper, we consider a typical fluid‐structure interaction problem by using a coupling procedure that reduces the problem to a nonlocal initial‐boundary problem in the elastic body with a system of integral equations on the interface between the domains occupied by the elastic body and the fluid. We analyze this nonlocal problem by the Lubich approach via the Laplace transform, an essential feature of which is that it works directly on data in the time domain rather than in the transformed domain. Our results may serve as a mathematical foundation for treating time‐dependent fluid‐structure interaction problems by convolution quadrature coupling of FEM and BEM. Copyright © 2015 John Wiley & Sons, Ltd.

Three‐dimensional simulations of tensile cracks in geomaterials by coupling meshless and finite element method

SummaryFailure in geotechnical engineering is often related to tension‐induced cracking in geomaterials. In this paper, a coupled meshless method and FEM is developed to analyze the problem of three‐dimensional cracking. The radial point interpolation method (RPIM) is used to model cracks in the smeared crack framework with an isotropic damage model. The identification of the meshless region is based on the stress state computed by FEM, and the adaptive coupling of RPIM and FEM is achieved by a direct algorithm. Mesh‐bias dependency, which poses difficulties in FEM‐based cracking simulations, is circumvented by a crack tracking algorithm. The performance of our scheme is demonstrated by two numerical examples, that is, the four‐point bending test on concrete beam and the surface cracks caused by tunnel excavation. Copyright © 2014 John Wiley & Sons, Ltd.

The Coupling of NBEM and FEM for Quasilinear Problems in a Bounded or Unbounded Domain with a Concave Angle

Based on the Kirchhoff transformation and the natural boundary element method, we investigate a coupled natural boundary element method and finite element method for quasi-linear problems in a bounded or unbounded domain with a concave angle. By the principle of the natural boundary reduction, we obtain natural integral equation on circular arc artificial boundaries, and get the coupled variational problem and its numerical method. Moreover, the convergence of approximate solutions and error estimates are obtained. Finally, some numerical examples are presented to show the feasibility of our method. Our work can be viewed as an extension of the existing work of H.D. Han et al..

Analysis of Magnetic Field for Power Transmission Line With Multiple AC Singular Currents by Coupling of Fourier Series Expansion and FEM

The central characteristic of line current problems with AC power transmission lines and overhead trolley lines are that the source region of conductors is extremely small compared with the entire analytical region. This is a problem with singular point sources in two-dimensional space that creates computational difficulties whit the standard finite element method. This paper proposes an accurate and efficient method for magnetic field calculations for such electric lines, which couples the analytical method and finite element formulation. The analytical solution is expressed as a Fourier series. Unknowns of finite elements at the boundary between the current and finite element regions are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a three-phase two-circuit transmission line. The results are compared with the measured one.

Realtime Two‐Way Coupling of Meshless Fluids and Nonlinear FEM

AbstractIn this paper, we present a novel method to couple Smoothed Particle Hydrodynamics (SPH) and nonlinear FEM to animate the interaction of fluids and deformable solids in real time. To accurately model the coupling, we generate proxy particles over the boundary of deformable solids to facilitate the interaction with fluid particles, and develop an efficient method to distribute the coupling forces of proxy particles to FEM nodal points. Specifically, we employ the Total Lagrangian Explicit Dynamics (TLED) finite element algorithm for nonlinear FEM because of many of its attractive properties such as supporting massive parallelism, avoiding dynamic update of stiffness matrix computation, and efficient solver. Based on a predictor‐corrector scheme for both velocity and position, different normal and tangential conditions can be realized even for shell‐like thin solids. Our coupling method is entirely implemented on modern GPUs using CUDA. We demonstrate the advantage of our two‐way coupling method in computer animation via various virtual scenarios.

Coupling of FEM and BEM for a transmission problem with nonlinear interface conditions. Hierarchical and residual error indicators

In this paper we consider the coupling of finite elements and boundary elements for a transmission problem with a nonlinear transmission condition. We first consider the uniform h-version and show how to linearise the resulting systems by Newtonʼs method. Next we derive a posteriori error estimates of hierarchical and residual type and implement corresponding adaptive procedures. Our results show that for the nonlinear transmission problem optimal mesh refinements are obtained with our error controlled approach.

Nonsymmetric coupling of BEM and mixed FEM on polyhedral interfaces

In this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderon projector to obtain a symmetric coupled system, we propose methods with only one integral equation. The system can be considered as a further generalization of the Johnson-Nedelec coupling of BEM—FEM to the case of mixed formulations in the bounded domain. Using some recent analytical tools we are able to prove stability and convergence of Galerkin methods with very general conditions on the discrete spaces and no restriction relating the finite and boundary element spaces. This can be done for general Lipschitz interfaces and in particular, the coupling boundary can be taken to be a Lipschitz polyhedron. Both the indirect and the direct approaches for the boundary integral formulation are explored.