a higher order time integration algorithm for the simulation of nonlinear fluid structure interaction abstract in this paper higher order time integration schemes are applied to nonlinear fluid structure interaction fsi simulations for a given accuracy we investigate the efficiency of higher order time integration schemes compared to lower order methods in the partitioned fsi simulations on a one dimensional piston problem a mixed implicit explicit imex time integration scheme is employed the implicit scheme is used to integrate the fluid and structural dynamics whereas an explicit runge kutta scheme integrates the coupling terms the resulting imex scheme retains the order of the implicit and explicit schemes in the imex scheme considered the implicit scheme consists of an explicit first stage singly diagonally implicit runge kutta esdirk scheme which is a multi stage l stable scheme

semidiscrete finite element approximations of a linear fluid structure interaction problem semidiscrete finite element approximations of a linear fluid structure interaction problem are studied first results concerning a divergence free weak formulation of the interaction problem are reviewed next semidiscrete finite element approximations are defined and the existence of finite element solutions is proved with the help of an auxiliary discretely divergence free formulation a discrete inf sup condition is verified and the existence of a finite element pressure is established strong a priori estimates for the finite element solutions are also derived then by passing to the limit in the finite element approximations the existence of a strong solution is demonstrated and semidiscrete error estimates are obtained

quasi newton methods for implicit black box fsi coupling abstract in this paper we introduce a new multi vector update quasi newton mvqn method for implicit coupling of partitioned transient fsi solvers the new quasi newton method facilitates the use of black box field solvers and under certain circumstances can be demonstrated to provide newton like convergence behaviour for strongly coupled fsi benchmark problems we demonstrate the superior convergence behaviour and robust nature of the mvqn method compared to other well known quasi newton coupling schemes including the least squares reduced order modelling ibqn ls scheme the classical rank 1 update broyden s method and fixed point iterations with dynamic relaxation the quasi newton methods are analysed on a suite of strongly coupled fsi problems including but not limited to internal incompressible flow through a flexible tube where the solid density is an order of magnitude lower than the fluid density

a new approach to inversion based feedforward control design for nonlinear systems the finite time transition between stationary setpoints of nonlinear siso systems is considered as a scenario for the presentation of a new design approach for inversion based feedforward control design techniques which are based on a stable system inversion result in input trajectories with pre and or post actuation intervals the presented approach treats the considered transition task as a two point boundary value problem bvp and yields causal feedforward trajectories which are constant outside the transition interval the main idea of this approach is to provide free parameters in the desired output trajectory to solve the bvp of the internal dynamics thereby a standard matlab function can be used for the numerical solution of the bvp feedforward control design techniques are illustrated by simulation results for a simple example

conservative tightly coupled simulations of stochastic multiscale systems multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations the fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain including subdomains represented by deterministic solvers when the constituent processes take place in nonoverlapping subdomains system behavior can be modeled via a domain decomposition approach that couples separate components at the interfaces between these subdomains its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength we propose a conservative domain decomposition algorithm in which tight coupling is achieved by employing either picard s or newton s iterative method coupled diffusion equations one of which has a gaussian white noise source term provide a computational testbed for analysis of these two coupling strategies fully converged implicit coupling with newton s method typically outperforms its picard counterpart especially at high noise levels this is because the number of newton iterations scales linearly with the amplitude of the gaussian noise while the number of picard iterations can scale superlinearly at large time intervals between two subsequent inter solver communications the solution error for single iteration explicit picard s coupling can be several orders of magnitude higher than that for implicit coupling increasing the explicit coupling s communication frequency reduces this difference but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error depending on the communication frequency of the latter and the noise strength this trend carries over into higher dimensions although at high noise strength explicit coupling may be the only computationally viable option

nonlinear minimum time control with pre and post actuation this article studies the time optimal output transition problem to change the system output from an initial value y t y for all time t 0 to a final value y t y for all time t t for invertible nonlinear systems the main contribution of the article is to show that the use of pre and post actuation input outside the transition interval i t 0 t can reduce the transition time t beyond the standard bang bang type inputs for optimal state transition the advantage of using pre and post actuation is demonstrated with an illustrative nonlinear example

generalized bang bang control for feedforward constrained regulation in the behavioral framework for continuous time linear scalar systems simple sufficient conditions for the solution of the minimum time rest to rest feedforward constrained control problem are provided the investigation of the time optimal input output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure the resulting optimal input is composed of sequences of bang bang functions and linear combinations of the modes associated to the zero dynamics this signal behavior constitutes a generalized bang bang control that can be fruitfully exploited for feedforward constrained regulation using discretization an arbitrarily good approximation of the optimal generalized bang bang control is found by solving a sequence of linear programming problems numerical examples are included

algorithms for strong coupling procedures abstract this paper considers algorithms for computing the response of a coupled problem with a partitioned approach one important example treated here is fluid structure interaction fsi often procedures or even software exists to solve each sub problem separately and one wants to couple both this setting seems to allow only the so called weak coupling which is not sufficient for some problems the so called strong coupling is often a totally implicit formulation where the system components are evaluated at the same time level this usually requires an iterative procedure the fsi problem is cast as an abstract differential algebraic equation dae for which the coupling procedures are developed with the partitioned approach one simple and frequently used computational procedure is similar to a block gauss seidel iteration it is shown why this approach may experience difficulties and how they may be circumvented with newton like methods still staying in the partitioned framework the functional and software engineering requirements for the simulation interface are described and analysed some simple coupled example problems demonstrate how the proposed procedures work

a partitioned strongly coupled fluid structure interaction method to model heart valve dynamics a new method for the calculation of fluid structure interaction fsi of highly flexible bodies is presented this innovative algorithm demonstrates the strong coupling of a commercial computational fluid dynamics code with an in house coded structural solver the strong response of the pressure distribution to the displacement can be approximated by a reduced order model for the fluid solver the jacobian of this reduced order model is then used in the structural solver to obtain a stable and full implicit iteration scheme the method is demonstrated on a 2d model of a flexible aortic valve during the cardiac cycle furthermore the model is able to calculate shear stresses on the leaflet

noncausal inverses for linear systems suppose we are to guide a plant with a square transfer matrix through a series of way points this can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof our technique is to compute 1 a noncausal particular solution based on the desired trajectory over each segment and the movement from one segment to the next and this particular solution consists of a particular control and a particular state trajectory and 2 a regulator to handle modeling errors disturbances etc we concentrate on the particular solution

combined interface boundary condition method for fluid rigid body interaction abstract this research is motivated by the recent work which has presented a new loosely coupled partitioned algorithm for fluid structure interaction fsi r jaiman p geubelle e loth x jiao combined interface boundary condition method for unsteady fluid structure interaction comput methods appl mech engrg 200 2011 27 39 the loosely coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition cibc method in this method correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter that plays an important part in the stability and accuracy of the coupled system the structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem this handling asks for the structural traction before it is corrected by the cibc method in this paper a new formulation for the cibc method is developed to repair the aforementioned inconvenience after simple manipulation the structural traction ratio is removed in constructing the traction correction therefore the structural traction is no more needed in cibc correction terms meantime the ratio t is employed to tune the interfacial corrections instead of the coupling parameter an arbitrary lagrangian eulerian finite element method is used to analyze fsi the characteristic based split cbs scheme is employed to solve incompressible navier stokes equations while the equation for rigid body dynamics is solved by newmark method a numerical technique called moving submesh approach is performed for the mesh deformation for respecting geometric conservation law a mass source term is implanted into the cbs scheme on the moving mesh several numerical examples are tested to validate the proposed methodology for fluid rigid body interaction the obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully

brief paper on the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two sided laplace transform in this paper the two sided laplace transform a classical but not very common mathematical tool is revived to express the stable inversion for linear nonminimum phase systems that was recently proposed from the viewpoint of state space representations it is demonstrated that those two different expressions for the stable inversion are mathematically equivalent simple examples are presented to illustrate the two sided laplace transform as a direct and intuitive approach to stable inversion the two sided laplace transform approach is also applied to the development of an iterative learning control for nonminimum phase systems that needs neither a precise inversion model nor fourier transform computations but instead requires only measuring the system response with time reversals

brief paper inversion of sampled data system approximates the continuous time counterpart in a noncausal framework although correspondence between the poles of a continuous time and sampled data system with a piecewise constant input is simple and desirable from the stability viewpoint the relationship between zeros is intricate inversion of a sampled data system is mostly unstable irrespective of the stability of the continuous time counterpart this makes it difficult to apply inversion based control techniques such as perfect tracking transient response shaping or iterative learning control to sampled data systems although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros whether the inversion of sampled data systems approximates the continuous time counterpart or not as the sample period is shortened is still to be determined this article gives a positive conclusion to this problem

a computational strategy for thermo poroelastic structures with a time space interface coupling this paper deals with a computational strategy suitable for the simulation of multiphysics problems based on the large time increment latin method the simulation of such problems must encounter the possible different time and space scales which usually arise with the different physics herein we focus on using different time and space discretizations for each physics by introducing an interface with its own discretization the feasibility of both a time and space couplings is exemplified on a nonlinear 3 physics strongly coupled problem the thermal fluid structure interaction in a thermo poroelastic structure

stable inversion and parameter variations abstract as part of the process of automatically guiding an aircraft we have been successful in using stable inversion to compute a desired bounded state trajectory and corresponding bounded control in addition to this feedforward control we must also construct a regulator to address modeling errors and disturbances with respect to modeling errors we find that the stable inversion procedures used are so accurate that the regulator can assume a simple form say a linear regulator about the desired trajectory we show that under the appropriate assumptions the bounded state trajectory and bounded control computed through stable inversion depend continuously on the parameters of the system this is a consequence of a mathematical result that we prove about the continuous dependence of the particular solution of a time varying nonlinear system driven by a bounded input this is distinct from the usual continuous dependence of the initial value problem for systems

a general framework for approximated model stable inversion abstract in this paper we propose an approximated method for the design of feedforward actions based on model stable inversion in the proposed framework the solution of the model stable inversion is approximated in the least squares sense by a suitable combination of any arbitrary set of basis functions the paper makes use of operator theory to derive a closed form formula to compute such approximation and to provide boundedness properties for the computed solution simulations are provided to show the effectiveness of the proposed method with different families of basis functions

a stable second order scheme for fluid structure interaction with strong added mass effects abstract in this paper we present a stable second order time accurate scheme for solving fluid structure interaction problems the scheme uses so called combined field with explicit interface cfei advancing formulation based on the arbitrary lagrangian eulerian approach with finite element procedure although loosely coupled partitioned schemes are often popular choices for simulating fsi problems these schemes may suffer from inherent instability at low structure to fluid density ratios we show that our second order scheme is stable for any mass density ratio and hence is able to handle strong added mass effects energy based stability proof relies heavily on the connections among extrapolation formula trapezoidal scheme for second order equation and backward difference method for first order equation numerical accuracy and stability of the scheme is assessed with the aid of two dimensional fluid structure interaction problems of increasing complexity we confirm second order temporal accuracy by numerical experiments on an elastic semi circular cylinder problem we verify the accuracy of coupled solutions with respect to the benchmark solutions of a cylinder elastic bar and the navier stokes flow system to study the stability of the proposed scheme for strong added mass effects we present new results using the combined field formulation for flexible flapping motion of a thin membrane structure with low mass ratio and strong added mass effects in a uniform axial flow using a systematic series of fluid structure simulations a detailed analysis of the coupled response as a function of mass ratio for the case of very low bending rigidity has been presented

treatment of acoustic fluid structure interaction by localized lagrange multipliers formulation a new concept is presented for modeling the dynamic interaction between an acoustic fluid and an elastic structure the coupling of this multiphysics system is done by inserting a kinematic interface frame between the fluid and the structure and using node collocated lagrange multipliers to connect the frame to each subsystem the time domain response analysis is performed by a partitioned analysis procedure the main advantages of this localized lagrange multiplier llm primal dual coupling method are complete localization of the structure and fluid subsystems elimination of the conventional predictor in the partitioned time integration method and the ability to accommodate non matching meshes the standard newmark time integrator is used on both the fluid and structure models it is shown that if the integrator is a stable and second order accurate for a monolithic treatment it retains those properties for both mortar and llm partitioned solution procedures infinite and finite piston problems are used to explain and verify the methodology a sequel paper under preparation presents and discusses a set of benchmark and application examples that involve the response of existing dams to seismic excitation

stable inversion for nonlinear nonminimum phase time varying systems we extend stable inversion to nonlinear time varying systems and study computational issues the technique is applicable to minimum phase as well as nonminimum phase systems the inversion technique is new even in the linear time varying case and relies on partitioning the dichotomic split of the linearized system dynamics into time varying stable and unstable submanifolds this dichotomic split is used to build time varying filters which are in turn the basis of a contraction used to find a bounded inverse input state trajectory finding the inverse input state trajectory allows the development of exact output tracking controllers the method is local to the time varying trajectory and requires that the internal dynamics vary slowly however the method represents a significant advance relative to presently available tracking controllers present techniques are restricted to time invariant nonlinear systems and in the general case track only asymptotically

direct solution of two dimensional navier stokes equations for static aeroelasticity problems a new method has been developed to calculate the steady flow and structural deformations for fluid structure interaction problems the discretized fluid dynamic and structural equations are regarded as a single set of coupled nonlinear algebraic equations the equilibrium solution is directly obtained using newton s method the governing equations used for the fluid flow are the two dimensional navier stokes equations and a finite element model is used to represent the structure this paper describes the analytical method and presents sample calculations demonstrating the technique the results show rapid convergence and good agreement with experimental data nomenclature bw half bandwidth of tangent matrix d set of structural displacement variables e set of governing equations for the aeroelastic system f flux vector in x direction g flux vector in y direction h distance from nozzle throat to centerline number of fluid dynamic control volumes in streamwise direction j number of fluid dynamic control volumes in cross stream direction l reference length total length of nozzle n total number of variables in system p pressure pe exit static pressure pt total pressure r system residual r magnitude of residual r radius at nozzle throat t tangent matrix system jacobian t wall thickness u set of fluid dynamic variables x set of variables for the aeroelastic system ax change in system variables during a newton iteration x streamwise coordinate y cross stream coordinate

inversion of nonlinear time varying systems a procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or more generally to mechanical structures is given the procedure is presented in a general setting for nonlinear time varying systems an iterative algorithm that computes a smooth controlled invariant time varying manifold the mathematical properties of which are illustrated and exploited is also proposed an application to a flexible two link manipulator illustrates the algorithm and its computational advantages

stable inversion for nonlinear systems abstract there have been two recent major developments in output tracking for nonlinear systems and our first main contribution is to relate these under appropriate assumptions we show that the bounded solution of the partial differential equation of isidori and byrnes for each trajectory of an exosystem must be given by an integral representation formula of devasia chen and paden under restrictive hypotheses devasia chen and paden develop a picard process that converges to the solution of the integral equation this solution to the integral equation is also a bounded solution to a dynamical equation driven by the desired outputs in aircraft applications our nonlinear systems are perturbations of pure feedback systems with outputs and we find a solution to the stable inversion problem i e finding bounded controls and bounded state trajectories in response to bounded output signals in two steps the first step ignores the perturbation error and computes the major part of the desired control and corresponding state trajectory the second step computes the remaining control and states by finding a noncausal and stable solution to an error driven dynamical equation in other words the method of devasia chen and paden is applied to an error system and not to the full system this two step procedure is the second main contribution of this paper throughout this paper it is assumed that our nonlinear systems have vector relative degree

a stable second order partitioned iterative scheme for freely vibrating low mass bluff bodies in a uniform flow abstract we present a stable partitioned iterative scheme for solving fluid body interaction problems at low structure to fluid mass ratio the scheme relies on the so called nonlinear interface force correction based on aitken s extrapolation process to stabilize the coupled partitioned system employing an arbitrary lagrangian eulerian finite element framework approximate interface force correction is constructed through subiterations to account for the missing effects of off diagonal jacobian terms in the partitioned staggered scheme through the generalized aitken s geometric extrapolation process with a dynamic stabilization parameter the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid structure interaction with strong added mass effects to assess the proposed iterative scheme against the standard strong coupling effects of mass ratio are investigated for a freely vibrating circular cylinder we show that our second order scheme is stable for low mass density ratio and hence is able to handle strong added mass effects the numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake induced vibration and galloping

stress based topology optimization method for steady state fluid structure interaction problems abstract this research developed a new stress based topology optimization method stom for a steady state fluid structure interaction fsi problem that minimizes the volume subject to the local stress constraints despite numerous studies on stom challenging optimization issues related to stress based topology optimization to procedures for fluid structure multiphysics systems still exist critical issues involved in creating a successful to for an fsi structure include the interpolation approach between the fluid equation and the structure equation with respect to locally defined design variables the mutual multiphysics coupling boundary conditions at dramatically evolving interfacing boundaries and a clear interpretation of the governing equations and the interaction boundary conditions for spatially varying intermediate design variables in addition to these three issues which are related to multiphysics equations there are three important considerations related to the stom the stress singularity issue the issues of multiple constraints and the highly nonlinear behavior of the stress constraints to resolve all of the aforementioned issues we applied a monolithic analysis integrating the qp relaxation method and the global p norm approach using the present method we created optimal layouts that minimize the volume constraining local stress values for a steady state fluid and structural interaction system

a tightly coupled domain decomposition approach for highly nonlinear stochastic multiphysics systems multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations when used with a domain decomposition dd algorithm such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost effective temporal integration we develop a conservative dd approach in which tight coupling is obtained by using a jacobian free newton krylov jfnk method with a generalized minimum residual iterative linear solver this strategy is tested on a coupled nonlinear diffusion system forced by a truncated gaussian noise at the boundary enforcement of path wise continuity of the state variable and its flux as opposed to continuity in the mean at interfaces between subdomains enables the dd algorithm to correctly propagate boundary fluctuations throughout the computational domain reliance on a single newton iteration explicit coupling rather than on the fully converged jfnk implicit coupling may increase the solution error by an order of magnitude increase in communication frequency between the dd components reduces the explicit coupling s error but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered finally the dd algorithm with the implicit jfnk coupling resolves temporally correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

guaranteed performance in semi global trajectory tracking for matched disturbance nonlinear systems in this article we present a semi global trajectory tracking approach that guarantees a priori computable l 2 and l performance bounds for matched disturbance control affine systems the proposed controller is derived by combining a standard inverse control technique with an extended nonlinear robust state feedback the latter is based on a control lyapunov function used for stabilising one operating point inside the considered state space a difference gradient formulation of this lyapunov function is then applied to prove stabilisation along any trajectory in the considered state space results for l 2 and l bounded disturbances will be presented and further extended to the case of actuator uncertainties and disturbance offsets the theoretical contributions are verified applying them to a numerical example

brittle and ductile failure constraints of stress based topology optimization method for fluid structure interactions abstract this study considers failure theories for brittle and ductile materials in the stress based topology optimization method stom for steady state fluid structure interactions fsi in some relevant studies the subject of the stress based topology optimization to minimize volumes with local von mises stress constraints has been researched however the various failure theories for ductile and brittle materials such as the maximum shear stress theory the brittle and ductile mohr coulomb theory and the drucker prager theory have not been considered for successful stom for fsi in addition to alleviating physics interpolation issues between structure and fluid and some numerical issues related to stom the mathematical characteristics of the various failure theories should be properly formulated and constrained to resolve all the involved computational issues the present study applies the monolithic analysis method the qp relaxation method and the p norm approach to the failure constraints the present topology optimization method can create optimal layouts while minimizing volume constraining local failure constraints for ductile and brittle materials for steady state fluid and structural interaction system

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

a behavioral approach to inversion based control abstract a new simplified behavior theory is proposed to address inversion based control for linear nonminimum phase siso systems the chosen space of signals is the set of piecewise c functions and input output pairs as weak solutions satisfy a differential integral equation with additional smoothness requirements a related key result is the output input or inverse representation of the behavior set that leads to the solution of a general stable inversion problem where polynomially unbounded noncausal desired outputs are allowed it is shown that this problem has a solution if and only if the smoothness degree of the desired output is greater than or equal to the system relative degree minus one when this straightforward condition is satisfied a closed form expression provides the inverse input then an analysis on preaction and postaction control follows two examples are included showing the relevance of output signal design in control applications

optimal output transitions for linear systems this article addresses the optimal minimum input energy output transition problem for linear systems the goal is to transfer the output from an initial value y t email protected for all time t t f previous methods solve this output transition problem by transforming it into a state transition problem the initial and final states x t i x t f respectively are chosen and a minimum energy state to state transition problem is solved however the choice of the initial and final states can be ad hoc and the resulting output transition cost input energy may not be minimal the contribution of this article is the solution of the optimal output transition problem an example system with elastic dynamics is studied to illustrate the proposed method simulation results are presented that show substantial reduction of transition costs with the use of the proposed method when compared to the use of minimum energy state to state transitions

optimal inversion based control for the set point regulation of nonminimum phase uncertain scalar systems we propose an optimal inversion based control for the set point constrained regulation of nonminimum phase uncertain scalar systems this approach is based on a new control architecture where the main purpose of the feedback is to reduce the sensitivity to parametric plant uncertainties permitting in such a way the effective use of a feedforward action determined via a stable dynamic inversion essential constituents of the architecture are a parameterized family of transition polynomials to shape ideal output transfers and a parameterized controller ensuring the internal model principle the methodology is then centered on the optimal combined design of the feedback controller and of the inversion based command signal in order to minimize the worst case settling time subject to an amplitude constraint on the control variable and to arbitrarily assigned overshoot and undershoot bounds finally an approximate or suboptimal solution to the resulting nonlinear optimization problem can be obtained by genetic algorithms a worked example highlights the effectiveness of the overall methodology

topology optimization for stationary fluid structure interaction problems using a new monolithic formulation this paper outlines a new procedure for topology optimization in the steady state fluid structure interaction fsi problem a review of current topology optimization methods highlights the difficulties in alternating between the two distinct sets of governing equations for fluid and structure dynamics hereafter the fluid and structural equations respectively and in imposing coupling boundary conditions between the separated fluid and solid domains to overcome these difficulties we propose an alternative monolithic procedure employing a unified domain rather than separated domains which is not computationally efficient in the proposed analysis procedure the spatial differential operator of the fluid and structural equations for a deformed configuration is transformed into that for an undeformed configuration with the help of the deformation gradient tensor for the coupling boundary conditions the divergence of the pressure and the darcy damping force are inserted into the solid and fluid equations respectively the proposed method is validated in several benchmark analysis problems topology optimization in the fsi problem is then made possible by interpolating young s modulus the fluid pressure of the modified solid equation and the inverse permeability from the damping force with respect to the design variables

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

brief optimal noncausal set point regulation of scalar systems this paper presents a novel system inversion approach to the set point regulation of linear scalar minimum phase systems this approach uses closed form expressions of cause effect pairs that make possible an arbitrarily smooth transition between two given output set points the cause effect pairs are based on the introduced concept of transition polynomials simple optimization procedures are then proposed to solve the relevant optimal output synthesis and optimal input synthesis the potentiality of the method is highlighted by the examples presented namely a synthesis of elevator velocity profiles and the performance improving of a pid controller

using stable input output inversion for minimum time feedforward constrained regulation of scalar systems the paper approaches the feedforward minimum time smooth control of non minimum phase linear scalar systems for set point regulation the aim is to synthesize a bounded input subject to non saturating constraints on the input and its derivatives till a prespecified arbitrary order the provided solution relies on a stable input output dynamic inversion technique and an ad hoc parameterized family of output transition functions the synthesized minimum time input that exhibits pre and post actuation is determined by means of easily implementable closed form expressions examples are given to illustrate the methodology

energy conservation under incompatibility for fluid structure interaction problems concurrent numerical methods for fluid structure interaction problems are typically based on partitioned solution procedures however such partitioned methods are inherently non conservative in the present work we investigate the conservation properties of monolithic discretisations for fluid structure interaction problems we consider a prototypical fluid structure interaction problem viz the piston problem a variational formulation allows us to establish precisely the conservation properties of the continuum problem and its discretisation by the finite element method we show that the conservation of energy by monolithic discretisations is only trivially maintained under restrictive compatibility conditions on the approximation spaces in the fluid and the structure moreover we introduce a new discretisation based on coincidence conditions which ensures energy conservation under incompatibility numerical results which illustrate the effectiveness of the new discretisation are presented

a canonical expansion for nonlinear systems the importance of differential geometry in particular lie brackets of vector fields in the study of nonlinear systems is well established under very mild assumptions we show that a real analytic nonlinear system has an expansion in which the coefficients are computed in terms of lie brackets this expansion occurs in a special coordinate system we also explain the concept of a pure feedback system for control design involving a nonlinear system one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths

the relevance of conservation for stability and accuracy of numerical methods for fluid structure interaction numerical simulation of fluid structure interactions has typically been done using partitioned solution methods however partitioned methods are inherently non conservative and generally numerically unstable the deficiencies of partitioned methods have motivated the investigation of monolithic solution methods conservation is possible for monolithic methods the conditions have recently been presented e h van brummelen s j hulshoff r de borst energy conservation under incompatibility for fluid structure interaction problems comput methods appl mech engrg 192 2003 2727 2748 in the present paper we investigate the relevance of maintaining conservation for a model fluid structure interaction problem viz the piston problem to distinguish the effect of the error induced by the interface coupling from the fluid and structure discretization errors we use fluid subcycling and an exact time integration method for the structure a comparison between conservative and non conservative monolithic methods as well as partitioned methods is made we show that maintaining conservation has considerable impact on the stability and accuracy of the numerical method these results also indicate that only for a conservative monolithic scheme the improvement in accuracy over partitioned methods warrants the computational cost associated with a monolithic solution moreover we illustrate the implications that particular combinations of fluid and structure discretizations can have on the conservation properties of the fluid structure interaction problem

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

the immersed structural potential method for haemodynamic applications in this paper a new fluid structure interaction immersed computational methodology based upon the original immersed boundary method ibm 1 is outlined with the final aim of modelling cardiovascular phenomena specifically heart valve related problems the principal characteristic of such immersed techniques is the representation of any deformable or rigid body immersed within an incompressible viscous flow field as a momentum forcing source in the navier stokes equations a number of shortcomings within the immersed formulation still require further investigation and improvement including the excessive numerical diffusion caused by the interpolation spreading process the need to include realistic viscoelastic composite constitutive models describing more accurately the nature of cardiovascular tissues and also the need to capture more effectively stresses developed at the fluid structure interface by following the same philosophy as the original ibm a more sophisticated formulation is derived in this paper the immersed structural potential method ispm the method introduced presents an alternative approach to compute the equivalent fluid structure interaction forces at the fluid mesh accounts for a sophisticated viscoelastic fibre reinforced constitutive model to better describe the mechanics of cardiovascular tissues and utilises a novel time integration methodology for the computation of the deformation gradient tensor which ensures compliance with the incompressibility constraint a series of numerical examples will be presented in order to demonstrate the robustness and applicability of this new methodology

long time behavior of a coupled heat wave system arising in fluid structure interaction this paper is devoted to the analysis of the long time behavior of a coupled wave heat system in which a wave and a heat equation evolve in two bounded domains with natural transmission conditions at a common interface these conditions couple in particular the heat unknown with the velocity of the wave solution this model may be viewed as a simplified version of linearized models which arise in fluid structure interaction first we show the strong asymptotic stability of solutions to this system then based on the construction of ray like solutions by means of geometric optics expansions and a careful analysis of the transfer of energy at the interface we show the lack of uniform decay in general domains further we obtain a polynomial decay result for smooth solutions of the system under a suitable geometric assumption which guarantees that the heat domain envelopes the wave domain finally in the absence of geometric conditions we show a logarithmic decay result for the same system but with simplified transmission conditions at the interface we also analyze the difficulty there is to extend this result to the more natural transmission conditions

a monolithical fluid structure interaction algorithm applied to the piston problem abstract an investigation of time marching computational fluid structure interaction algorithms is presented the analysis is applied to the piston problem attention is focussed on the time integration properties of the coupling algorithms the staggered scheme is first investigated where fluid and structure are alternately integrated by separate solvers in a predictor corrector fashion this algorithm suffers from a time lag between the integration of the fluid and structure the influence of the time lag is investigated by the comparison of different predictions for the structure a novel monolithical algorithm is then introduced in order to annihilate the time lag this algorithm integrates fluid structure and interaction as a single system by an implicit algorithm linear acoustic as well as nonlinear euler equations for gas dynamics are investigated the numerical results of the staggered scheme reveal a non physical deviation of the mean position of the piston at higher cfl numbers the deviation of the mean position is not present in the calculation with the monolithical scheme stability analysis shows the unconditional stability of the monolithical scheme for the acoustic equations whereas the staggered scheme has a limited domain of stability this domain can be enlarged by an improvement of the structural prediction analysis of the damping shows an energy production in the staggered scheme while the monolithical scheme has no energy production term the analyses lead to the formulation of the interaction consistency law which prescribes the relation for the time discretisation between fluid and structure solvers and their boundary conditions

a b spline based pseudo inversion approach for constrained optimal output transition the contribution of this paper is to propose a new method for the continuous time optimal output transition problem under constraints on the control effort the new method situates in the recently

two level algorithms for partitioned fluid structure interaction computations abstract in this paper we use the multigrid algorithm commonly used to improve the efficiency of the flow solver to improve the efficiency of partitioned fluid structure interaction iterations coupling not only the structure with the fine flow mesh but also with the coarse flow mesh often present due to the multigrid scheme leads to a significant efficiency improvement as solution of the flow equations typically takes much longer than the structure solve and as multigrid is not standard in structure solvers we do not coarsen the structure or the interface as a result the two level method can be easily implemented into existing solvers two types of two level algorithms were implemented 1 coarse grid correction of the partitioning error and 2 coarse grid prediction or full multigrid to generate a better initial guess the resulting schemes are combined with a fourth order runge kutta implicit time integration scheme for the linear one dimensional piston problem with compressible flow the superior stability accuracy and efficiency of the two level algorithms is shown the parameters of the piston problem were chosen such that both a weak and a strong interaction case were obtained even the strong interaction case with a flexible structure could be solved with our new two level partitioned scheme with just one iteration on the fine grid this is a major accomplishment as most weakly coupled methods fail in this case of the two algorithms the coarse grid prediction or full multigrid method was found to perform best the resulting efficiency gain for our one dimensional problem is around a factor of ten for the coarse to intermediate time steps at which the high order time integration methods should be run for two and three dimensional problems the efficiency gain is expected to be even larger

generalized lattice boltzmann algorithm for the flow of a nematic liquid crystal with variable order parameter a lattice boltzmann lb scheme is described which recovers the equations developed by qian sheng for the hydrodynamics of a nematic liquid crystal with a tensor order parameter the standard mesoscopic lb scalar density is generalized to a tensor quantity and the macroscopic momentum density and tensor order parameter are recovered from appropriate moments of this mesoscopic density a single lattice boltzmann equation is used with a direction dependent bhatnagar gross and krook bgk collision term with additional forcing terms to recover the antisymmetric terms in the stress tensor a chapman enskog analysis is presented which demonstrates that the qian sheng scheme is recovered provided a lattice with sixth order isotropy is used the method is validated against analytical results for a number of cases including flow alignment of the order tensor and the miesowicz viscosities in the presence of an aligning magnetic field the algorithm accurately recovers the predicted changes in the order parameter in the presence of aligning flow and magnetic fields preliminary results are given for an extension of the method to model the interface between isotropic and nematic fluids

stable inversion for nonlinear discrete time systems we solve the exact output tracking problem for square nonlinear discrete time systems through stable inversion this stable inversion problem involves finding a bounded solution of a dynamical system driven by a bounded signal such a solution is given by a difference representation formula whose existence under the proper assumptions can be proven using a picard process

lattice boltzmann algorithm for surface tension with greatly reduced microcurrents we present an algorithm for inserting an interface between the immiscible phases of a multicomponent lattice boltzmann fluid which is based solely upon the appropriate continuum physics stress boundary conditions and continuity of velocity results are presented for the algorithm when applied to static neutrally buoyant drops it is shown that the present algorithm gives a significant reduction in the spurious velocities which are reported for previous schemes and a concomitant improvement in the isotropy of the interface

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

adaptive neural control of high order uncertain nonaffine systems a transformation to affine systems approach abstract this brief investigates the adaptive neural network nn control of a class of high order nonaffine nonlinear systems with completely unknown dynamics since the control terms appear within the unknown nonlinearity traditional control schemes and stability analysis are usually rendered extremely complicated our main contribution includes a novel system transformation that converts the nonaffine system into an affine system through a combination of a low pass filter and state transformation as a result the state feedback control of the nonaffine system can be viewed as the output feedback control of an affine system in normal form the transformed system becomes linear with respect to the new input while the traditional backstepping approach is not needed thus allowing the synthesis to be extremely simplified it is theoretically proven that all the signals in the closed loop system are uniformly ultimately bounded uub simulation results are provided to demonstrate the performance of the developed controller

adaptive control for a class of uncertain strict feedback nonlinear systems based on a generalized fuzzy hyperbolic model in this study we propose an effective method for designing an adaptive controller for a class of uncertain strict feedback nonlinear systems with unknown bounded disturbances during the controller design process all of the unknown functions are accumulated at the intermediate steps to approximate the last step in addition only one generalized fuzzy hyperbolic model is used to approximate the total unknown functions for the system thus only the actual control law needs to be implemented and one adaptive law is proposed for the overall controller design process as a result the controller design is much simpler and the computational burden is reduced greatly using lyapunov techniques we obtain the uniformly ultimately bounded stability of all the signals for the closed loop system our simulation results verified the theoretical analysis and they illustrated the superior performance of the method proposed in this study

an arbitrary lagrangian eulerian finite element approach for fluid structure interaction phenomena the present contribution is concerned with the design of a family of consistent fluid structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations the characterization of the moving fluid structure interface is realized by means of the arbitrary lagrangian eulerian technique the spatial discretization is performed with the finite element method whereby either a first order upwind scheme or the classical second order upwind petrov galerkin technique are used to discretize the linearized fluid equations while the standard bubnov galerkin method is applied to the structural equations in order to streamline coupling the structure is discretized in a velocity based fashion the temporal discretization of both the fluid and the structural equations is embedded in the generalized framework by making use of classical newmark approximations in time to quantify the sources of error of the proposed algorithms systematic studies in terms of the one dimensional piston model problem are presented copyright 2003 john wiley sons ltd