An enriched space-time finite element method for fluid-structure interaction - Part II: Thin flexible structures

Enriched finite element methods have gained traction in recent years for modeling problems with material interfaces and cracks. By means of enrichment functions that incorporate a priori behavior about the solution, these methods decouple the finite element (FE) discretization from the geometric configuration of such discontinuities. Taking advantage of this greater flexibility, recent studies have proposed the adoption of Non-Uniform Rational B-Splines (NURBS) to preserve the interfaces' exact geometries throughout the analysis. In this article, we investigate NURBS-based geometries in the context of the Discontinuity-Enriched Finite Element Method (DE-FEM) based on linear field approximations. While optimal convergence is retained for problems with weak discontinuities without singularities, representing exact geometry via NURBS does not yield noticeable improvements when extracting stress intensity factors of cracked specimens. For low-order elements, we conclude that the benefits of exact geometry representation do not outweigh the increased complexity in formulation and implementation. The choice of linear FEs hinders the accuracy of the proposed formulation, suggesting that its full potential may only be unleashed by increasing the field representation order.

In this work, the functionally graded magneto-electro-elastic (FG-MEE) structures were used to study mechanical performance under a thermal environment using the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM). Through enhancing the traditional solution space of the finite element method (FEM), additional degrees of freedom are introduced without modifying the mesh structure. Therefore, as a class of higher-order finite element methods, field variables with high gradients can be captured without a relatively finer mesh. The accuracy of TMEM-EFEM is improved by using interpolation covers. The feasibility of TMEM-EFEM is proven by numerical examples. The proposed TMEM-EFEM is proven to be accurate under the relatively coarse mesh. Through numerical examples, the high accuracy of TMEM-EFEM is demonstrated. Therefore, TMEM-EFEM can be a good alternative for the statics study of FG-MEE structures.

An enriched finite element method with interpolation cover functions for acoustic analysis in high frequencies

The present study introduces a Gauss-Seidel fluid-structure interaction (FSI) method including the flow solver, structural statics solver and a fast data transfer technique, for the research of structural deformation and flow field variation of rotor blades under the combined influence of steady aerodynamic and centrifugal forces. The FSI method is illustrated and validated by the static aeroelasticity analysis of a transonic compressor rotor blade, NASA Rotor 37. An improved local interpolation with data reduction (LIWDR) algorithm is introduced for fast data transfer on the fluid-solid interface of blade. The results of FSI calculation of NASA Rotor 37 show that when compared with the radial basis function (RBF) based interpolation algorithm, LIWDR meets the interpolation accuracy requirements, while the calculation cost can be greatly improved. The data transmission time is only about 1% of that of RBF. Moreover, the iteration step of steady flow computation within one single FSI has little impact on the converged aerodynamic and structural results. The aerodynamic load-caused deformation accounts for nearly 50% of the total. The effects of blade deformation on the variations of aerodynamic performance are given, demonstrating that when static aeroelasticity is taken into account, the choke mass flow rate increases and the peak adiabatic efficiency slightly decreases. The impact mechanisms on performance variations are presented in detail.

Magneto-electro-elastic (MEE) composites have promising application prospects due to the rapid response to the excitation of external electric or magnetic fields. Finite element simulation of the multi-physics coupling problems in MEE-based structures is significant. The enriched finite element method (EFEM) is derived from the standard finite element method (FEM), with finite element shape functions improved by interpolation covers. Considering the complex mechanical-electro-magnetic multi-physics coupling mechanism of MEE-based structures, the mechanical-electro-magnetic coupling enriched finite element method (MEM-EFEM) was proposed. The method is well worked for investigating the mechanical-electro-magnetic multi-physics coupling issues to calculate the generalized displacement (displacement components, electric and magnetic potential) with 3-node triangular elements. In a set of numerical experiments involving the static analysis of MEE-based structures, MEM-EFEM outperforms the regular FEM. When it comes to the same solution accuracy level, the number of elements used by MEM-EFEM is lower than that of the standard FEM, suggesting that MEM-EFEM has better convergence and accuracy on this subject. Besides, the MEM-EFEM solution accuracy can be enhanced by mesh refinement. Overall, the MEM-EFEM has the potential to be used in engineering practice to solve the static responses of MEE-based structures on mechanical-electro-magnetic multi-physics coupling issues.

Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases or first order of trigonometric functions) is relatively large. Consequently, the present EFEM with a quadric polynomial enrichment function shows more powerful capacities in elastodynamic analysis than the other considered numerical techniques. More importantly, the attractive monotonic convergence property can be broadly realized by the present approach with the typical two-step Bathe temporal discretization technique. Three representative numerical experiments are conducted in this work to verify the abilities of the present approach in elastodynamic analysis.

ABSTRACTThis paper proposes an enriched equilibrium finite element method (EFEM) for addressing crack problems within the framework of linear elastic fracture mechanics and complementary energy principle. The key ingredient of enriched EFEM is to construct the equilibrated stress field using equilibrated tractions along with asymptotic enrichment. Specifically, an auxiliary field is employed to capture the asymptotic singular behavior of the near‐tip stress field, while the traction‐based equilibrium finite element accounts for the residual terms. The remarkable property of the proposed enriched EFEM is that the stress intensity factors (SIFs) and the stress fields are directly obtained with high accuracy, even on a very coarse mesh. Moreover, in combination with the compatible solution acquired by the enriched finite element method (FEM), strict estimation of the discretization error is obtained for crack problems by dual analysis. Numerical examples are finally conducted to verify the performance of the proposed method on strict error estimation and accurate computation of the SIFs.

Extended finite element modeling of deformable porous media with arbitrary interfaces

An enriched finite element method is presented to numerically solve the eigenvalue problem on electromagnetic waveguides governed by the Helmholtz equation. In this work, a highly efficient, simple and precise higher order subparametric method was developed using a 2D automated mesh generator performed with JuliaFEM. The transcendence computerized discretization code in Julia is developed for the present work. For curved waveguide structures, meshes with one side and curving higher orders are proposed with triangular elements with parabolic arcs. The technique is shown for distinct waveguide constructions, and the results are compared with the strongest numerical or analytical results available. The results demonstrate that the proposed methodology is effective and accurate for generating finite element simulations for complex structures with black holes and irregular topology due to no curvature loss. This article presents a finding cutoff frequency performed with JuliaFEM—an open-source program. Analysis results produced by commercial software are considered for the comparison and show that the calculation results between the two programs do not differ significantly. This procedure can be used to achieve the most effective transmission of energy for electromagnetic applications.

This paper presents a novel numerical method for simulating the transport and dispersion of pollutants in the Mediterranean sea. The governing mathematical equations consist of a barotropic ocean model with friction terms, bathymetric forces, Coriolis and wind stresses coupled to an advection–diffusion equation with anisotropic dispersion tensor and source terms. The proposed numerical solver uses a multilevel adaptive semi-Lagrangian finite element method that combines various techniques, including the modified method of characteristics, finite element discretization, coupled projection scheme based on a rotational pressure correction algorithm, and an adaptive L2-projection. The approach employs the gradient of the concentration as an error indicator for enrichment adaptations and increasing the number of quadrature points where needed without refining the mesh. The method is shown to provide accurate and efficient simulations for pollution transport in the Mediterranean sea. The proposed approach distinguishes itself from the well-established adaptive finite element methods for incompressible viscous flows by retaining the same structure and dimension of linear systems during the adaptation process.

Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads

This work is concerned with the modelling of the interaction of fluid flow with flexible solid structures. The fluid flow considered is governed by the incompressible Navier-Stokes equations and modelled with stabilised low order velocity-pressure finite elements. The governing equation of fluid movement is described by an arbitrary Lagrangian-Eulerian (ALE) strategy. The structure is represented by means of an appropriate standard finite element formulation. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface. The resulting strongly coupled set of non-linear equations is solved by means of a partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates the full linearization of the overall incremental problem.

Interactive method for computation of viscous flow with recirculation

A numerical simulation method for parachute Fluid-Structure Interaction (FSI) problem using Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is proposed. This method could be used in both coupling computation of parachute FSI and flow field analysis. Both flat circular parachute and conical parachute are modeled and simulated by this new method. Flow field characteristics at various angles of attack are further simulated for the conical parachute model. Comparison with the space-time FSI technique shows that this method also provides similar and reasonable results.

Glaucoma, an irreversible ocular disease with a risk of blindness, is often treated with glaucoma drainage device (GDD) implantation as a last resort. The study on the impact of passive valve GDD implantation on aqueous humor (AH) dynamics is of great significance for supplementing numerical simulation methods for GDDs and exploring novel glaucoma treatment approaches. Therefore, this study employed a porous region method to simulate the regulatory role of the trabecular meshwork in intraocular pressure (IOP), establishing a glaucoma model. Based on this, a multi-outlet, passive valve GDD was designed and virtually implanted, with the post-implantation flow field simulated using mesh deformation, overset mesh, and fluid–structure interaction methods. Results indicate that by adjusting the structural parameters of the GDD, IOP can be maintained within an acceptable range. The thickness (h) of the upper component has a more significant impact on the IOP and outlet flow distribution ratio than the distance (d) between the drainage tube's central axis and the drainage groove. Both increases in h and d lead to increased IOP, gradually approaching pre-implantation levels. The fissure region formed by the deformation of the upper component and the trabecular meshwork region work together to regulate IOP in the simulation. However, the fissure region shows a greater height near the center of the shunting tube, potentially imposing additional mechanical stress on ocular tissues, reaching up to 5.8 μm for a GDD with h = 10 and d = 160 μm. Additionally, wall shear stress on the iris near the shunting tube inlet is relatively high, reaching values of 6.24 × 10−4 Pa under the same conditions. In conclusion, the designed GDD effectively controls postoperative IOP. Studying AH regulation performance after GDD implantation provides a foundation for the personalized customization of passive valve-type GDDs.