Structure Interaction Problems Research Articles

A theoretical investigation of the frisbee motion of red blood cells in shear flow

The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.

Numerical Modeling of the Fluid-Porohyperelastic Structure Interaction

We consider a moving domain, fluid-porohyperelastic structure interaction problem in a dual-mixed formulation. The fluid is described using the Navier--Stokes equations, and the porohyperelastic structure is described using the Biot equations. To solve this problem numerically, we propose two novel, partitioned, loosely coupled methods based on the generalized Robin boundary conditions. In the first partitioned method, the Navier--Stokes problem is solved separately from the Biot problem. In the second proposed method, the problem is further split by separating the Biot problem into a mechanics subproblem and a Darcy subproblem. We derive the energy estimates for the proposed methods on a simplified, linear problem and show that the first partitioned method is unconditionally stable. The second partitioned method is shown to be energy-stable if the structure is viscoelastic and if certain conditions on the problem parameters and the time step are satisfied. The performance of both methods is investigated in the numerical examples.

Observability and unique continuation of the adjoint of a linearized simplified compressible fluid-structure model in a 2d channel

We consider a compressible fluid structure interaction model in a 2D channel with a simplified expression of the net force acting on the structure appearing at the fluid boundary. Concerning the structure we will consider a damped Euler-Bernoulli beam located on a portion of the boundary. In the present article we establish an observability inequality for the adjoint of the linearized fluid structure interaction problem under consideration which in principle is equivalent with the null controllability of the linearized system. As a corollary of the derived observability inequality we also obtain a unique continuation property for the adjoint problem.

Parallel time-stepping for fluid–structure interactions

We present a parallel time-stepping method for fluid–structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space is based on equal order finite element for all variables and a variant of the Crank-Nicolson scheme is used as second order time integrator. To accelerate the solution of the systems, we analyze a parallel-in time method. For different numerical test cases in 2d and in 3d we present the efficiency of the resulting solution approach. We also discuss some challenges and limitations that are connected to the special structure of fluid–structure interaction problem. In particular, we will investigate stability and dissipation effects of the time integration and their influence on the convergence of the parareal method. It turns out that especially processes based on an internal dynamics (e.g.driven by the vortex street around an elastic obstacle) cause great difficulties. Configurations however, which are driven by oscillatory problem data, are well-suited for parallel time stepping and allow for substantial speedups.

A [formula omitted]SPH–SPIM coupled method for fluid–structure interaction problems

In this work, the fluid–structure interaction (FSI) problems have been studied by coupling the δ Smoothed Particle Hydrodynamics (δSPH) with the Smoothed Point Interpolation Method (SPIM), which is abbreviated as δSPH–SPIM coupled method. SPIM is used for structure dynamics owing to its good performance for large deformation analysis of solids. For the fluid solver, in order to further reduce the unphysical noise in pressure field, the δSPH (where the density diffusion term is added into the continuity equation) is adopted. Inspired by the particle-element method, a new interpolation scheme is proposed for the coupling force calculation and transfer, which does not require the fluid and solid spacing to be the same. The coupled method has been verified by hydrostatic water column on an elastic plate, and has been applied to solve the problems of high speed water entry of an elastic wedge as well as dam-break flow.

Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space

Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static analysis is accurate enough, as the rocking motion is the dominant mode of their interaction with the surrounding soil (i.e. soil–structure interaction problem). In this study, the soil–structure interaction problems are extended to consider the effect of elastic non-homogeneities as well as changing the elasticity constants with depth in an exponential manner for the rocking loads. This paper analytically investigates the mixed boundary value problem regarding the forced rocking interaction of a rigid foundation embedded in a finite depth of an exponentially graded transversely isotropic half-space. The potential function method accompanied by Hankel integral transforms is applied to solve the system of the equations of motion of the media. Due to integral transforms used in the solving procedure, the mixed boundary value problem raised may be apt to be transformed to dual integral equations, which in turn, could be reduced to Fredholm integral equation of the second kind. To evaluate the solution of the integral equations, a robust numerical procedure has been developed for different anisotropic materials. Regarding the complicated integrand functions, the integrals are numerically and graphically presented to cover the effect of degree of change of material properties that plays a key role.

About Application of the Overset Grid Method for Fluid Structure Interaction Problems in 3D Codes Based on Modification of Godunov Scheme Uniform for Both CFD and CSD

About Application of the Overset Grid Method for Fluid Structure Interaction Problems in 3D Codes Based on Modification of Godunov Scheme Uniform for Both CFD and CSD

Numerical simulation of level ice–structure interaction using damage-based erosion model

In this study, a numerical analysis technique was developed to simulate the collision between level ice and a rigid structure. The traditional Drucker–Prager plasticity model was combined with damage mechanics to simulate the material behavior of ice and linked with the element erosion technique to analyze the fracture behavior of level ice colliding with the structure. To consider the fluid force acting on broken ice flakes, both hydrostatic pressure and drag force were considered. To validate the effectiveness of the proposed technique, a numerical analysis of the four-point bending test was performed, and the results were compared with the experimental results obtained by the in situ bending test. The proposed analysis technique was applied to the level ice–structure interaction problem, and the ice resistance experienced by the moving structure was numerically calculated. The ice resistances acting on the rigid structure under several different forward speeds were obtained and compared with the model test results. Moreover, the level ice fracture pattern, which depended on the forward speed of the structure, was investigated.

A New Development of a Shadow Density Filter for Manufacturing Constraint and Its Applications to Multiphysics Topology Optimization

Abstract The present research develops a new shadow filter and presents its usage for structural topology optimization (TO) considering the molding manufacturability. It is important to consider manufacturing methods in designing products. Some geometrical features not allowing molded parts should be removed. In addition, it has been an important issue to efficiently impose these manufacturing constraints in TO. For this purpose, the present research emulates implementation of shadowing of products and applies the shadow images as pseudo-density variables in TO. The use of this shadow density filter ensures that the optimized layouts comply with the conditions of the manufacturing constraints. Various manufacturing conditions can be imposed depending on the direction and the position of the light. Several numerical examples of compliance minimization problem, conjugate heat transfer problem, and fluid–structure interaction problem are solved to demonstrate the validity and effectiveness of the present shadow density filters, and their performances are compared.

A coupled 3D isogeometric/least-square MPS approach for modeling fluid–structure interactions

A two-way coupling method of the three-dimensional (3D) isogeometric approach and the least-square moving particle semi-implicit method (LSMPS) is presented for handling the fluid–structure interaction problems. This method takes advantages of isogeometric analysis (IGA) for structure deformation, e.g. the exact representation of the structure geometry and high accuracy for solution fields with relatively few elements, and that of the LSMPS method for fluid flow, e.g. its consistent discretization for both internal particles and boundary conditions. When the fluid is solved by the LSMPS method, the NURBS (Non-Uniform Rational B-Splines) surfaces provide boundary conditions for the LSMPS method. Afterward, the pressure on the NURBS surface is first evaluated from the pressure and the corresponding derivatives at the LSMPS particles by using the Taylor series expansion, and then integrated to determine the pressure force at the virtual points on the NURBS surface by using the Newton–Cotes method. Subsequently, the pressure forces at the virtual points are distributed onto the control nodes (i.e. control points) of the IGA elements so that the structure deformation can be analyzed by using the IGA method. The coupling algorithm is based on a Lagrangian framework and can handle the boundary conditions and the fluid–structure interactions accurately and easily. Finally, three examples, i.e. fluid flowing in a rigid pipe, fluid-tank, and fluid-torus interactions in the elastic regime, are simulated to demonstrate the accuracy and validity of the proposed coupling method.

Extended variable-time-step Adams–Bashforth–Moulton method for strongly coupled fluid–structure interaction simulation

An extended variable-time-step Adams–Bashforth–Moulton (ABM) method is presented for obtaining the solution of six-degrees-of-freedom (6DoF) rigid body motion. This second-order method involves the use of one predictor and several correctors, thus requiring an iteration process during each time step. Aitken’s dynamic under-relaxation (ADUR) scheme is used to reduce the time to convergence. The initial value of the under-relaxation factor at each time step is evaluated from the values of the two previous time steps, the predictor, and the first corrector. Cooperating with the incompressible two-phase flow solver included in OpenFOAM®, the present method is capable of simulating fluid–structure interaction (FSI) problems, in which strong coupling is ensured through the outer loop of the PIMPLE algorithm. Various interface capture schemes as well as mesh motion schemes are considered. Several two- and three-dimensional cases of multi-DoF are simulated, and the recommended iteration stop condition is summarised. Finally, the method is employed to reproduce an experiment that investigates the interaction between a dam-break flow and a floating box. Satisfactory overall agreement between the numerical and experimental results is observed, which demonstrates that the method is suitable for simulating FSI problems in ocean engineering.

Modelling horizontally loaded reinforced-concrete piles in a geotechnical centrifuge

The design of pile foundations to accommodate horizontal loads is a complex soil−structure interaction problem. Current small-scale laboratory testing of pile foundations is mostly focused on metal piles, which raises the question of the validity of results from these tests, and the principles derived, for the use of analysing and designing reinforced-concrete piles, where not only the soil, but also the piles exhibit highly non-linear material behaviour. This paper describes centrifuge tests that were conducted on scaled aluminium and reinforced-concrete single piles, subjected to lateral loading, with the aim of establishing the suitability of using aluminium alloys for modelling scaled reinforced-concrete piles. With responses similar to literature, both pile types proved to model the behaviour of laterally loaded piles well as far as bending and deflection at low loads are concerned. At larger loads, the reinforced-concrete pile cracked, resulting in non-linear material response, which contributed significantly to the difference in the behaviour between the piles studied. It was observed that the behaviour of reinforced-concrete piles under serviceability loads would not be captured using materials that cannot replicate the reduction in stiffness resulting from crack formation in concrete.

PISA design model for monopiles for offshore wind turbines: application to a stiff glacial clay till

Offshore wind turbines in shallow coastal waters are typically supported on monopile foundations. Although three-dimensional (3D) finite-element methods are available for the design of monopiles in this context, much of the routine design work is currently conducted using simplified one-dimensional (1D) models based on the p–y method. The p–y method was originally developed for the relatively large embedded length-to-diameter ratio (L/D) piles that are typically employed in offshore oil and gas structures. Concerns exist, however, that this analysis approach may not be appropriate for monopiles with the relatively low values of L/D that are typically adopted for offshore wind turbine structures. This paper describes a new 1D design model for monopile foundations; the model is specifically formulated for offshore wind turbine applications, although the general approach could be adopted for other applications. The model draws on the conventional p–y approach, but extends it to include additional components of soil reaction that act on the pile. The 1D model is calibrated using a set of bespoke 3D finite-element analyses of monopile performance, for pile characteristics and loading conditions that span a predefined design space. The calibrated 1D model provides results that match those obtained from the 3D finite-element calibration analysis, but at a fraction of the computational cost. Moreover, within the calibration space, the 1D model is capable of delivering high-fidelity computations of monopile performance that can be used directly for design purposes. This 1D modelling approach is demonstrated for monopiles installed in a stiff, overconsolidated glacial clay till with a typical North Sea strength and stiffness profile. Although the current form of the model has been developed for homogeneous soil and monotonic loading, it forms a basis from which extensions for soil layering and cyclic loading can be developed. The general approach can be applied to other foundation and soil–structure interaction problems, in which bespoke calibration of a simplified model can lead to more efficient design.

Numerical simulation of fluid–structure interaction with SPH method

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian, particle method, which combines the advantages of Euler and Lagrangian method and has special advantages in simulating violent non-linear fluid–structure interaction problems. In this study, an improved SPH method is used to simulate four fluid–structure interaction cases. Firstly, the violent flow in the mould filling process is simulated to validate that the SPH model can obtain accurate flow patterns with any complex solid boundaries. Secondly, the dam-break flow against a vertical wall is simulated, and the pressure curves are compared with the experiment. Then liquid sloshing problems under different external excitations are simulated, and the complex coupling characteristics can be captured. Finally, the interactions between fluid and floating bodies are researched. The obtained numerical results show good agreement with the results from other sources, and clearly demonstrate the effectiveness of the presented SPH method in modelling fluid–structure interaction problems.

Finite Element Modeling of Soil Structure Interaction System with Interface: A Review

Non-linear analysis of soil structure interaction problem is still an active field of research due to development of useful interface element between the soil–soil and soil–structure. In this paper a focused review on coupled finite element modeling of soil structure interaction (SSI) system with soil non-linearity and interface element modeling is discussed. The non-linearity in soil is reviewed with various available constitutive models, whereas the Interface modeling is reviewed with zero thickness and thin layer elements, which is proposed by many researchers from 1970 to till date with special emphasis on behavior of superstructure. Further the paper discusses on the occurrence of ill conditioning due to significance of interface thickness and selection of normal and tangential stiffness during interface modeling. In addition to above, some special interface element (different degree of freedom on top and bottom face of element) in non-linear SSI is also reviewed. Therefore the attention is on advantages and disadvantages of the discussed methods according to their applicability, accuracy and caliber to idealize the superstructure and soil.

Existence of global weak solutions for the high frequency and small displacement oscillation fluid–structure interaction systems

The purpose of this paper is to study the fluid–structure interaction (FSI) problem which is a simplified model to describe high frequency and small displacement oscillation of elastic structure in fluids. The elastic structure displacement is modeled by a fourth‐order nonlinear hyperbolic square equations, the motion of fluid is modeled by the time‐dependent incompressible Navier–Stokes equations. We prove the existence of at least one weak solution (global in time) to this problem by compactness method. The result both holds for two‐dimensional and three‐dimensional cases.

An explicit MPS/FEM coupling algorithm for three-dimensional fluid-structure interaction analysis

Currently, accurate simulations of fluid structure interaction (FSI) problems still remain a challenging task in the academic community. The purpose of this work is to develop a three-dimensional (3D) coupling algorithm to achieve the end, where the explicit moving particle simulation method (MPS) and the finite element method (FEM) are respectively employed to account for fluid flows and structural deformation. The developed coupling algorithm inherits the advantages of the aforementioned methods, while also addressing their shortcomings. We start by extending a newly proposed ghost cell boundary (GCB) model, which has proved to be an effective method to deal with the wall boundary of complicated shapes, to three dimensions. For the problems of interest, the finite elements for structural discretization serve as ghost cells for interaction force calculation, thereby providing an easy and natural way for the construction of ghost cells. The interactions between fluids and structures are dealt with using an integral version of the MPS model, and the resultant interaction forces calculated at integration points of a cell are distributed to finite element nodes for the update of nodal kinematics in the context of an explicit time integration scheme. The effectiveness and accuracy of the 3D GCB model are validated via two numerical examples, i.e., the dam break test and the water flow in a rotating gear test. Afterwards, the developed coupling algorithm is applied to two common FSI problems, i.e., the dam break tests with respective an elastic obstacle and an elastic gate. The good agreements between our simulation results and the existing data in literature demonstrate the accuracy and capacity of the developed coupling algorithm in solving FSI problems.

Development of a hybrid model based on mesh and meshfree methods and its application to fluid–elastic structure interaction for free surface waves

In this paper, a hybrid scheme, Fluid–Fluid–Elastic Structure (FFES) model was developed in the time domain to address the wave breaking impact on the structure. The model is developed based on the partitioned approach with different governing equations that describe various regions of the model domain. The fluid–fluid model denotes that two different fluid models were used to describe fluid in the actual physical domain. The method is a physics-based approximation to reduce the computational time, i.e. in the far-field inviscid fluid (fully nonlinear potential flow theory model), and near to the structure, viscous fluid (Navier Stokes model) is used. The coupled model then interacts with the elastic structure (based on Euler–Bernoulli beam theory). The system of equations is strongly coupled both in space and time. The Fluid–Fluid coupling uses an implicit predictor–corrector scheme, and the fluid–structure coupling works based on an iterative scheme. This approach makes the method more robust and for future extension. Three different possibilities for introducing the coupling was identified and implemented. The model was validated against results from the analytical solution and literature. The method proposed is a reliable, robust, and efficient alternative for simulating fluid–structure interaction problems.

Dry-friction-induced self-excitation of a rectangular liquid-filled tank

The self-excitation of spring–mass system subjected to dry friction has been studied for decades because of its interesting and complex nonlinear dynamics behaviors. In this paper, a fluid–structure interaction problem, which describes the dry-friction-induced self-excitation of a rectangular liquid-filled tank, is proposed here about how the liquid sloshing affects the tank’s motion. To study responses of both the tank and liquid in depth, an equivalent pendulum model is developed to consider the coupling effects of structure elasticity, liquid sloshing, and dry friction. Another model based on smoothed particle hydrodynamics (SPH) method is also built for studying the liquid behavior while sloshing. The multidimensional-mode convergence is first analyzed, and then, the parameter analysis on the mode and frequency of the tank–spring–liquid–belt coupled system is analytically and numerically conducted. With the increasing liquid, the first two modes of the system approach the structure frequency and liquid frequency, respectively, at first, and then, the tendency converts for the intersection of the structure frequency and liquid frequency. Based on Lyapunov stability theorem, the periodic motion of the liquid-filled tank, including the stick–slip phase and slip phase, is both caused by Hopf bifurcation of equilibrium point. The sloshing effect results in a comparatively smaller bifurcation point. When there is no liquid or a little liquid in tank, the system experiences a subcritical Hopf bifurcation. If the liquid mass is heavy enough, the subcritical Hopf bifurcation converts to the supercritical Hopf bifurcation. During the self-excitation motion, liquid in tank sometimes sloshes linearly with small-amplitude free-surface deformation based on SPH simulation and sometimes sloshes violently with impacting, turning, breaking, and merging. Results by equivalent model show that the swing range of the equivalent pendulum can even reach ± 25.0° at this time. Hence, the dry-friction-induced self-excitation of the liquid-filled tank with lots of interesting nonlinear dynamics behaviors is tightly parameter-related. Results show that the equivalent pendulum model and SPH model match each other well and have different advantages on handling the nonlinear dynamical behaviors of such systems.

A coupled Smoothed Particle Hydrodynamics-Volume Compensated Particle Method (SPH-VCPM) for Fluid Structure Interaction (FSI) modelling

A new unified particle model that couples the Smoothed Particle Hydrodynamics (SPH) and a discontinuous approach known as the Volume Compensated Particle Method (VCPM) is developed to solve Fluid Structure Interaction (FSI) problems involving large deformation. Unlike the model that couples the Smoothed Particle Hydrodynamics and the Discrete Element Method (i.e. SPH-DEM) in which the applicable Poisson's ratio of the solid material should be less than certain critical values, the current unified particle model is able to model solid materials of large Poisson's ratio by using only axial interaction between solid particles. The coupling between SPH and VCPM is accomplished by treating the solid particles of VCPM at the solid-fluid interface as dummy particles in SPH. This paper presents the first SPH-VCPM coupled method for FSI with comprehensive validations. The VCPM solver is firstly verified for solving static and dynamic solid mechanics problems. Then, the proposed solver is used to solve several FSI problems involving free surface, i.e. water column on an Aluminum plate, flow under an elastic gate, dam break problems involving flexible structures and deformation of flexible structure in a rolling oil tank. The SPH-VCPM results match well with the published numerical results obtained from the literature.