finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

global attractors for the extensible thermoelastic beam system abstract this work is focused on the dissipative system t t u x x x x u x x x u l 2 0 1 2 x x u f t x x x x t u g describing the dynamics of an extensible thermoelastic beam where the dissipation is entirely contributed by the second equation ruling the evolution of under natural boundary conditions we prove the existence of bounded absorbing sets when the external sources f and g are time independent the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters r the same result holds true when the first equation is replaced by t t u x x t t u x x x x u x x x u l 2 0 1 2 x x u f with 0 in both cases the solutions on the attractor are strong solutions

the nsbeti method an extension of the feti method to non symmetrical bem fem coupled problems summary the finite element tearing and interconnecting feti method is recognized as an effective domain decomposition tool to achieve scalability in the solution of partitioned second order elasticity problems in the boundary element tearing and interconnecting beti method a direct extension of the feti algorithm to the bem the symmetric galerkin bem formulation is used to obtain symmetric system matrices making possible to apply the same feti conjugate gradient solver in this work we propose a new beti variant labeled nsbeti that allows to couple substructures modeled with the fem and or non symmetrical bem formulations the method connects non matching bem and fem subdomains using localized lagrange multipliers and solves the associated non symmetrical flexibility equations with a bi cgstab iterative algorithm scalability issues of nsbeti in bem bem and combined bem fem coupled problems are also investigated copyright 2012 john wiley sons ltd

reduction of substructural interface degrees of freedom in flexibility based component mode synthesis a flexibility based component mode synthesis cms is proposed for reduced order modelling of dynamic behaviour of large structures the approach employs partitioning via the localized lagrange multiplier method the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes the flexibility based cms method has shown significant advantages over the classical craig bampton method a key feature of the method is its substructural mode selection criterion that is independent of loading conditions unlike the majority of available cms approaches where one retains the full dimension of partition boundary degrees of freedom dofs the flexibility based method allows to reduce significantly the interface dofs the reduction of interface dofs represents the major contribution of the present communication the efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3d structure both partitioned into several substructures copyright 2006 john wiley sons ltd

non matching mesh gluing by meshless interpolation an alternative to lagrange multipliers rewards of using non matching meshes are great in many aspects sub meshing a complex structure in a sub structure wise manner separately and or in parallel selective local refinement unlimited scalability guarantee for generating meshes in increasingly large scale finite element simulation etc however when meshes do not match a gluing algorithm is required to enforce inter domain continuity non matching terminologically originates from mesh discretization in nature and the non matching mesh issue is therefore avoidable or does not exist in a node based or meshless discretization in meshless methods motivated by this a gluing algorithm is developed based on meshless interpolation the gluing is accomplished by continuous trial and test functions across non matching meshes constructed using nodes only the developed gluing algorithm is tested in static and wave propagation problems in two and three dimensions it is demonstrated that the gluing algorithm does not deteriorate convergence and accuracy compared with the one piece conforming mesh compared with lagrange multiplier gluing one of the most common approaches the current algorithm has two significant benefits 1 easier implementation in any dimension and 2 positive definite banded system matrices not acting against equation solvers and hence better suited for large scale finite element analysis

interface element method iem for a partitioned system with non matching interfaces abstract a novel method for non matching interfaces on the boundaries of finite elements in partitioned domains is presented by introducing interface elements in this paper the interface element method iem satisfies the continuity conditions exactly through interface element domains without recourse to lagrange multiplier technique the interface elements take an interpolation scheme used in meshless methods to join partitioned domains the moving least square mls approximations in the present study are implemented to construct the shape functions of the interface elements the compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method and the completeness of the shape functions of the interface elements transfers rigid body motions and strain fields correctly moreover alignment of the boundaries of sub domains in the mls approximations and integration domains provides a consistent numerical integration the numerical examples show that the iem is a useful tool for the analysis of a partitioned system and for a global local analysis

an algebraically partitioned feti method for parallel structural analysis algorithm description an algebraically partitioned feti method for the solution of structural engineering problems on parallel computers is presented the present algorithm consists of three attributes an explicit generation of the orthogonal null space matrix associated with the interface nodal forces the floating subdomain rigid body modes computed from the subdomain static equilibrium equation of the classical force method and the identification of redundant interface force constraint operator that emanates when the interface force computations are localized comparisons of the present method with the previously developed differentially partitioned feti method are offered in terms of the saddle point formulations at the end of the paper a companion paper reports implementation details and numerical performance of the proposed algorithm 1997 john wiley sons ltd

a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

containment problem for points on a reducible conic in p2 abstract given an ideal i in a noetherian ring one can ask the containment question for which m and r is the symbolic power i m contained in the ordinary power i r c bocci and b harbourne study the containment question in a geometric setting where the ideal i is in a polynomial ring over a field like them we will consider special geometric constructs in particular we obtain a complete solution in two extreme cases of ideals of points on a pair of lines in p 2 in one case the number of points on each line is the same while in the other all the points but one are on one of the lines

finite element approximation of transmission conditions in fluids and solids introducing boundary subgrid scales terms involving jumps of stresses on boundaries are proposed for the finite element approximation of the stokes problem and the linear elasticity equations these terms are designed to improve the transmission conditions between subdomains at three different levels namely between the element domains between the interfaces in homogeneous domain interaction problems and at the interface between the fluid and the solid in fluid structure interaction problems the benefits in each case are respectively the possibility of using discontinuous pressure interpolations in a stabilized finite element approximation of the stokes problem a stronger enforcement of the stress continuity in homogeneous domain decomposition problems and a considerable improvement of the behavior of iterative schemes to couple the fluid and the solid in fluid structure integration algorithms the motivation to introduce these terms stems from a decomposition of the unknown into a conforming and a non conforming part a hybrid formulation for the latter and a simple approximation for the unknowns involved in the hybrid problem copyright 2011 john wiley sons ltd

iterative strong coupling of dimensionally heterogeneous models in this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone the novel methodology takes full advantage of the small number of interface unknowns in this kind of problems existing algorithms can be viewed as variants of the natural staggered algorithm in which each domain transfers function values to the other and receives fluxes or forces and vice versa this natural algorithm is known as dirichlet to neumann in the domain decomposition literature essentially we propose a framework in which this algorithm is equivalent to applying gauss seidel iterations to a suitably defined linear or nonlinear system of equations it is then immediate to switch to other iterative solvers such as gmres or other krylov based method which we assess through numerical experiments showing the significant gain that can be achieved indeed the benefit is that an extremely flexible automatic coupling strategy can be developed which in addition leads to iterative procedures that are parameter free and rapidly converging further in linear problems they have the finite termination property copyright 2009 john wiley sons ltd

applying the method of normal forms to second order nonlinear vibration problems vibration problems are naturally formulated with second order equations of motion when the vibration problem is nonlinear in nature using normal form analysis currently requires that the second order equations of motion be put into first order form in this paper we demonstrate that normal form analysis can be carried out on the second order equations of motion in addition for forced damped nonlinear vibration problems we show that the invariance properties of the first and second order transforms differ as a result using the second order approach leads to a simplified formulation for forced damped nonlinear vibration problems

mls based variable node elements compatible with quadratic interpolation part i formulation and application for non matching meshes two dimensional variable node elements compatible with quadratic interpolation are developed using the moving least square mls approximation the mapping from the parental domain to the physical element domain is implicitly obtained from mls approximation with the shape functions and their derivatives calculated and saved only at the numerical integration points it is shown that the present mls based variable node elements meet the patch test if a sufficiently large number of integration points are employed for numerical integration the cantilever problem with non matching meshes is chosen to check the feasibility of the present mls based variable node elements and the result is compared with that from the lower order case compatible with linear interpolation copyright 2005 john wiley sons ltd

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

numerical simulation of fluid structure interaction with the volume penalization method we present a novel scheme for the numerical simulation of fluid structure interaction problems it extends the volume penalization method a member of the family of immersed boundary methods to take into account flexible obstacles we show how the introduction of a smoothing layer physically interpreted as surface roughness allows for arbitrary motion of the deformable obstacle the approach is carefully validated and good agreement with various results in the literature is found a simple one dimensional solid model is derived capable of modeling arbitrarily large deformations and imposed motion at the leading edge as it is required for the simulation of simplified models for insect flight the model error is shown to be small while the one dimensional character of the model features a reasonably easy implementation the coupled fluid solid interaction solver is shown not to introduce artificial energy in the numerical coupling and validated using a widely used benchmark we conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

polyhedral elements with strain smoothing for coupling hexahedral meshes at arbitrary nonmatching interfaces abstract managing nonmatching interfaces between dissimilar hexahedral meshes is complicated because the interfaces which are arbitrarily formed by the intersection of element edges are composed of various types of polygons in this paper a simple and efficient scheme is proposed for dealing with nonmatching interfaces using polyhedral elements because polyhedral elements can have arbitrary numbers of polygonal faces and nodes they can be used as transition elements for coupling nonmatching meshes a strain smoothing technique in the cell based smoothed finite element method is introduced to resolve critical difficulties in defining shape functions and in conducting numerical integration for the polyhedral elements as well as to further enhance the accuracy and efficiency of finite element analyses the effectiveness of the proposed scheme is demonstrated through several numerical examples involving nonmatching interfaces the effects of decomposition types of smoothing cells in the strain smoothing technique are also discussed in terms of numerical stability and accuracy

numerically generated tangent stiffness matrices for nonlinear structural analysis accurate tangent stiffness matrices are essential for the solution of nonlinear structural problems via newton like methods the present paper presents an accurate numerical procedure for the generation of tangent stiffness matrices from the internal force generation modules the present procedure is attractive for problems that require complex constitutive relations and or kinematic nonlinearities whose models are difficult to linearize and for incorporating newton like solution strategies into vectorial based nonlinear structural analysis codes

a survey of parametrized variational principles and applications to computational mechanics abstract this survey paper describes recent developments in the area of parametrized variational principles pvps and selected applications to finite element computational mechanics a pvp is a variational principle containing free parameters that have no effect on the euler lagrange equations the theory of single field pvps based on gauge functions also known as null lagrangians is a subset of the inverse problem of variational calculus that has limited value on the other hand multifield pvps are more interesting from theoretical and practical standpoints following a tutorial introduction the paper describes the recent construction of multifield pvps in several areas of elasticity and electromagnetics it then discusses three applications to finite element computational mechanics the derivation of high performance finite elements the development of element level error indicators and the construction of finite element templates the paper concludes with an overview of open research areas

development of three dimensional interface elements for coupling of non matching hexahedral meshes gluing of a non matching interface between dissimilar meshes is one of challenging tasks in computational mechanics the interface element method iem has been developed using an appropriate interpolation scheme between partitioned finite element meshes the continuity of displacements across the interface is satisfied exactly and the completeness of interface element shape functions provides a reasonable transfer of strain fields between dissimilar finite element meshes research related to the iem has been mainly accomplished in two dimensions because the construction of interface elements in three dimensions is not as simple as the case of two dimensions in this paper a new scheme is presented to construct the interface elements for connecting dissimilar hexahedral finite element meshes with an arbitrarily curved non matching interface element edges crossing any other edges in an interface region are modified into continuous intersection polygons to eliminate overlays and gaps between dissimilar meshes and these polygons are divided into triangles to create prism shaped interface elements numerical experiments on a linear elasticity problem with non matching meshes illustrate the effectiveness of the method

comparison of symbolic and ordinary powers of ideals all given rings in this paper are commutative associative with identity and noetherian recently l ein r lazarsfeld and k smith els discovered a remarkable and surprising fact about the behavior of symbolic powers of ideals in affine regular rings of equal characteristic 0 if h is the largest height of an associated prime of i then i hn i n for all n 0 here if w is the complement of the union of the associated primes of i i t denotes the contraction of i t rw to r where rw is the localization of r at the multiplicative system w their proof depends on the theory of multiplier ideals including an asymptotic version and in particular requires resolution of singularities as well as vanishing theorems we want to acknowledge that without their generosity and quickness in sharing their research this manuscript would not exist our objective here is to give stronger results that can be proved by methods that are in some ways more elementary our results are valid in both equal characteristic 0 and in positive prime characteristic p but depend on reduction to characteristic p we use tight closure methods and in consequence we need neither resolution of singularities nor vanishing theorems that may fail in positive characteristic for the most basic form of the result all that we need from tight closure theory is the definition of tight closure and the fact that in a regular ring every ideal is tightly closed we note that the main argument here is closely related to a proof given in hu 5 14 16 p 45 that regular local rings in characteristic p are ufds

a monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure poisson equation this paper describes a new monolithic approach based on the fluid pressure poisson equation ppe to solve an interaction problem of incompressible viscous fluid and an elastic body the ppe is derived so as to be consistent with the coupled equation system for the fluid structure interaction fsi based on this approach we develop two kinds of efficient monolithic methods in both methods the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all other unknown variables are derived fully explicitly or partially explicitly the coefficient matrix of the ppe for the fsi becomes symmetric and positive definite and its condition is insensitive to inhomogeneity of material properties the arbitrary lagrangian eulerian ale method is employed for the fluid part in order to take into account the deformable fluid structure interface to demonstrate fundamental performances of the proposed approach the developed two monolithic methods are applied to evaluate the added mass and the added damping of a circular cylinder as well as to simulate the vibration of a rectangular cylinder induced by vortex shedding copyright 2005 john wiley sons ltd

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

a direct flexibility method we present a direct flexibility method dfm for the solution of finite element equations this method is based on a decomposition of the finite element model into substructures which may reduce to individual elements substructures are preprocessed by the direct stiffness method dsm to generate free free flexibility matrices for floating substructures the interface problem is solved for the interface forces and the solution recovered over substructure interiors the dfm shares with the dsm the advantages of being automatic maintaining locality and sparseness efficiently handling continuum elements and requiring only the availability of element stiffness libraries the new method appears to be advantageous for specific applications these include massively parallel processing inverse problems treatment of rigid members and inclusions and use of underintegrated elements without spurious mode stabilization

analysis of non linear dynamical systems by the normal form theory abstract a method is proposed for calculating the periodic solutions of non linear mechanical systems with analytical non linearities the jordan normalization procedure for the case of non linear autonomous systems is described and generalized to dampened harmonically excited oscillators non linear modes for hamiltonian systems are introduced normal forms simplify the analysis of bifurcation it is shown how to extend the modal synthesis procedure the proposed non linear modes obtained from free vibrations are used to construct a superposition technique to describe the forced response of harmonically excited systems these results are tested for one and two degrees of freedom systems with cubic non linearities the results are compared with expressions obtained by classical analytical methods averaging or multiple scales methods or runge kutta numerical methods

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

the two level feti method part ii extension to shell problems parallel implementation and performance results the two level feti method presented in part i of this work is a mathematically optimal and scalable substructuring algorithm for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems in this paper we extend the two level feti method to shell problems describe a variant approach revisit the preconditioning problem address the efficient implementation of the corresponding iterative solvers on massively parallel processors highlight the computational price of mathematical optimality and discuss its consequences and report some impressive performance results on two paragon xp s and ibm sp2 massively parallel processors for several realistic plate and shell problems

a formulation based on localized lagrange multipliers for bem fem coupling in contact problems this paper presents a unified formulation for the combination of the finite element method fem and the boundary element method bem in 3d frictional contact problems that is based on the use of localized lagrange multipliers llms resolution methods for the contact problem between non matching meshes have traditionally been based on a direct coupling of the contacting solids using classical lagrange multipliers these methods tend to generate strongly coupled systems that require a deep knowledge of the discretization characteristics on each side of the contact zone complicating the process of mixing different numerical techniques in this work a displacement contact frame is inserted between the fe and be interface meshes discretized and finally connected to the contacting substructures using llms collocated at the mesh interface nodes this methodology will provide a partitioned formulation which preserves software modularity and facilitates the connection of non matching fe and be meshes

partitioned formulation of internal fluid structure interaction problems by localized lagrange multipliers abstract a partitioned formulation of compressible internal fluid structure interaction problems is presented by employing a displacement model for both the fluid and structure partitioning is effected by a localized version of the method of lagrange multipliers which assigns two independent sets of lagrange multipliers to the structural and fluid interfaces two major features of the present formulation include an interface compliance normalization that helps capture the predominant physics of interaction phenomena when the interfaces are characterized by two radically different rigidities and a novel transformation of the displacement model into a fluid pressure model that is suitable for both transient and vibration analyses the present formulation first solves for the interface lagrange multipliers which are subsequently used to solve for the structural displacements and the fluid displacement or pressure by employing two independent analysis modules

uniform bounds and symbolic powers on smooth varieties the purpose of this note is to show how one can use multiplier ideals toestablish effective uniform bounds on the multiplicative behavior of certainfamilies of ideal sheaves on a smooth algebraic variety in particular weprove a quick but rather surprising result concerning the symbolic powersof radical ideals on such a variety let

an approach to the connection between subdomains with non matching meshes for transient mechanical analysis this paper describes a general method for coupling non matching linear finite element meshes in transient dynamic analysis we propose a method based on schur s dual formulation whose main advantage is to provide equilibrium as well as kinematic continuity throughout the interface the essence of our work lies in the particular discretization of the space of lagrange multipliers and in the validation of the method through two and three dimensional static calculations as well as two dimensional dynamic calculations an example is also presented and the results are compared to those of the mortar method copyright 2002 john wiley sons ltd

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

analysis of the block gauss seidel solution procedure for a strongly coupled model problem with reference to fluid structure interaction the block gauss seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid structure interaction based on a simple model problem this work presents a detailed analysis of the convergence behaviour of the method in particular the model problem is used to highlight some aspects that arise in the context of the application of the block gauss seidel method to fsi problems thus the effects of the time integration schemes chosen of relaxation techniques of physical constraints and non linearities on the convergence of the iterations are investigated

partitioned component mode synthesis via a flexibility approach a new flexibility based component mode synthesis method is presented which is derived by approximating the partitioned equations of motion that employ a localized method of lagrange multipliers the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes hence the resulting interface flexibility matrices are uniquely determined and well suited for the present method development an attractive feature of the present method is its substructural mode selection criterion that is independent of loading conditions numerical experiments show that the present modal selection criterion is reliable and that the proposed flexibility based component mode synthesis method performs well relative to the classical craig bampton method in terms of accuracy and of its ability to include dominant substructural modes for simple plates and a relatively complex solid ring

an improved interface element with variable nodes for non matching finite element meshes extensive improvements of the interface element method iem are proposed for the efficient treatment of non matching finite element meshes our approach enables us to establish the master element via the moving least square mls approximation and so to remove the cumbersome process of constructing interface elements the values of shape functions and their derivatives are therefore mapped from the master element as in the conventional finite element method for the assurance of convergence and compatibility condition a patch test is demonstrated through several examples of 2d linear elasticity the convergence rate is compared between the present interface element and the previous version

fat lines in p3 powers versus symbolic powers abstract we study the symbolic and regular powers of ideals i for a family of special configurations of lines in p 3 for this family we show that i m i m for all integers m if and only if i 3 i 3 we use these configurations to answer a question of huneke that asks whether i m i m for all m if equality holds when m equals the big height of the ideal i

the two level feti method for static and dynamic plate problems part i an optimal iterative solver for biharmonic systems abstract we present a lagrange multiplier based substructuring method for solving iteratively large scale systems of equations arising from the finite element discretization of static and dynamic plate bending problems the proposed method is essentially an extension of the feti domain decomposition algorithm to fourth order problems the main idea is to enforce exactly the continuity of the transverse displacement field at the substructure corners throughout the preconditioned conjugate projected gradient iterations this results in a two level feti substructuring method where the condition number of the preconditioned interface problem does not grow with the number of substructures and grows at most polylogarithmically with the number of elements per substructure these theoretically proven optimal convergence properties of the new feti method are numerically demonstrated for several finite element plate bending static and transient problems the two level iterative solver presented in this paper is applicable to a large family of biharmonic time independent as well as time dependent systems it is also extendible to shell problems

a simple explicit implicit finite element tearing and interconnecting transient analysis algorithm summary a simple explicit implicit finite element tearing and interconnecting feti algorithm afeti ei algorithm is presented for partitioned transient analysis of linear structural systems the present algorithm employs two decompositions first the total system is partitioned via spatial or domain decomposition to obtain the governing equations of motions for each partitioned domain second for each partitioned subsystem the governing equations are modally decomposed into the rigid body and deformational equations the resulting rigid body equations are integrated by an explicit integrator for its stability is not affected by step size restriction on account of zero frequency contents 0 the modally decomposed partitioned deformation equations of motion are integrated by an unconditionally stable implicit integration algorithm it is shown that the present afeti ei algorithm exhibits unconditional stability and that the resulting interface problem possesses the same solution matrix profile as the basic feti static problems the present simple dynamic algorithm as expected falls short of the performance of the feti dp but offers a similar performance of implicit two level feti d algorithm with a much cheaper coarse solver hence its simplicity may offer relatively easy means for conducting parallel analysis of both static and dynamic problems by employing the same basic scalable feti solver especially for research mode numerical experiments copyright 2011 john wiley sons ltd

strong coupling strategy for fluid structure interaction problems in supersonic regime via fixed point iteration abstract in this paper some results on the convergence of the gauss seidel iteration when solving fluid structure interaction problems with strong coupling via fixed point iteration are presented the flow induced vibration of a flat plate aligned with the flow direction at supersonic mach number is studied the precision of different predictor schemes and the influence of the partitioned strong coupling on stability is discussed

normal form analysis of a forced aeroelastic plate abstract a nonlinear elastic plate in a supersonic unsteady flow forced by a dynamic excitation and a biaxial compressive load is studied the physical behavior of the plate is modelized by the von karman equations and the aerodynamic loads are modeled by using the piston theory including nonlinearities up to the third order the space continuum model is space discretized by a galerkin projection and then studied by a perturbation approach based on the normal form method in order to reduce the system to a simpler and essential form defined by its resonance conditions a physical interpretation of the involved small divisors is given by analyzing how different equation parameters influence the reduced normal form model in the neighborhood of both static and dynamic bifurcation points

a contact formulation based on localized lagrange multipliers formulation and application to two dimensional problems the non penetration condition in contact problems is traditionally based on the classical lagrange multiplier method this method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non matching to deal with this problem we introduce a novel element in the lagrange multiplier approach of contact modelling namely a contact frame placed in between contacting bodies it acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic the contact frame has its own independent freedoms which allows the formulation to pass contact patch tests by design copyright 2002 john wiley sons ltd

acceleration of uncertainty propagation through lagrange multipliers in partitioned stochastic method abstract a partitioned stochastic method psm is proposed for the solution of static structural mechanics problems with uncertainties whose solution vectors are the displacements for each partition and lagrange multipliers along with the partition interfaces the proposed partitioned stochastic method employs three stochastic basis selection steps an arbitrary initial choice of displacement random bases a set of conjugate bases for the lagrange multipliers and finally modification of the displacement bases affected by those of the lagrange multipliers the present psm thus propagates the uncertainties instantly across partitioned substructures resulting in an improved rate of convergence numerical experiments illustrate the proposed psm outperforms a conventional partitioned solution method for structural mechanics problems

star configurations in pn abstract star configurations are certain unions of linear subspaces of projective space they have appeared in several different contexts the study of extremal hilbert functions for fat point schemes in the plane the study of secant varieties of some classical algebraic varieties the study of the resurgence of projective schemes in this paper we study some algebraic properties of the ideals defining star configurations including getting partial results about hilbert functions generators and minimal free resolutions of the ideals and their symbolic powers we also show that their symbolic powers define arithmetically cohen macaulay subschemes and we obtain results about the primary decompositions of the powers of the ideals as an application we compute the resurgence for the ideal of the codimension n 1 star configuration in p n in the monomial case i e when the number of hyperplanes is n 1

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

partitioned formulation of internal and gravity waves interacting with flexible structures abstract this paper presents a partitioned modeling of internal and gravity fluid waves that interact with flexible structures the governing interaction model consists of three completely partitioned entities fluid model structural model and interface model that acts as an internal constraint on the fluid structure interface boundary thus the proposed partitioned multi physics modeling can employ two completely modular fluid and structure software modules plus an interface solver hence amenable to partitioned solution algorithms the interface discretization can exploit the nonmatching interface algorithm previously developed via the method of localized lagrange multipliers also noted is that the present fluid model can make use of widely available finite element software for standard poisson type problems

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

hardening softening behaviour in non linear oscillations of structural systems using non linear normal modes the definition of a non linear normal mode nnm as an invariant manifold in phase space is used in conservative cases it is shown that normal form theory allows one to compute all nnms as well as the attendant dynamics onto the manifolds in a single operation then a single mode motion is studied the aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results using single non linear mode motion predicts the correct behaviour hence the nonlinear change of co ordinates allowing one to pass from the linear modal variables to the normal ones linked to the nnms defines a framework to properly truncate non linear vibration pdes two examples are studied a discrete system a mass connected to two springs and a continuous one a linear euler bernoulli beam resting on a non linear elastic foundation for the latter a comparison is given between the developed method and previously published results

on a mixed and multiscale domain decomposition method this paper presents a reexamination of a multiscale computational strategy with homogenization in space and time for the resolution of highly heterogeneous structural problems focusing on its suitability for parallel computing spatially this strategy can be viewed as a mixed multilevel domain decomposition method or more accurately as a structure decomposition method regarding time a parallel property is also described we also draw bridges between this and other current approaches

a partial differential equation with infinitely many periodic orbits chaotic oscillations of a forced beam this paper delineates a class of time periodically perturved evolution equations in a banach space whose associated poincar e map contains a smale horseshoe this implies that such systems possess periodic orbits with arbitrarily high period the method uses techniques originally due to melnikov and applies to systems of the form x f0 x f1 x t where x f0 x is hamiltonian and has a homoclinic orbit we give an example from structural mechanics sinusoidally forced vibrations of a buckled beam

explicit synchronous partitioned algorithms for interface problems based on lagrange multipliers abstract traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem as a result these schemes may require multiple subdomain solves acceleration techniques or optimized transmission conditions to achieve sufficient accuracy and or stability we present a new synchronous partitioned method derived from a well posed mixed finite element formulation of the coupled problem we transform the resulting differential algebraic equation dae to a hessenberg index 1 form in which the algebraic equation defines the lagrange multiplier as an implicit function of the states using this fact we eliminate the multiplier and reduce the dae to a system of explicit odes for the states explicit time integration both discretizes this system in time and decouples its equations as a result the temporal accuracy and stability of our formulation are governed solely by the accuracy and stability of the explicit scheme employed and are not subject to additional stability considerations as in traditional partitioned schemes we establish sufficient conditions for the formulation to be well posed and prove that classical mortar finite elements on the interface are a stable choice for the lagrange multiplier we show that in this case the condition number of the schur complement involved in the elimination of the multiplier is bounded by a constant the paper concludes with numerical examples illustrating the approach for two different interface problems

post buckling longterm dynamics of a forced nonlinear beam a perturbation approach abstract the aim of this paper is to determine by a singular perturbation approach the dynamic response of a harmonically forced system experiencing a pitchfork bifurcation the model of an extensible beam forced by a harmonic excitation and subject to an axial static buckling is space discretized by a galerkin approach and studied by the normal form method for different values of equation parameters influencing the nonlinear dynamic behavior like damping coefficient load amplitude and frequency a relevant issue in the perturbation methods is the concept of small and zero divisors which are related to the possibility to build a transformation that simplifies the original studied problem i e to obtain the normal form by eliminating as much as possible nonlinearities in the equations for nonconservative systems like structural damped systems there are no conditions in the prior literature that define what small means relatively to a divisor in the present paper some conditions about the order of magnitude of the divisors with respect to the perturbation entity are given and related to some physical parameters in the governing equations in order to estimate the relevance of some nonlinear effects

on the l2 and the h1 couplings for an overlapping domain decomposition method using lagrange multipliers in this paper a comparison of the l 2 and the h couplings is made for an overlapping domain decomposition method using lagrange multipliers the analysis of the local equations arising from the formulation of the coupling of two mechanical models shows that continuous weight functions are required for the l 2 coupling term whereas both discontinuous and continuous weight functions can be used for the h 1 coupling the choice of the lagrange multiplier space is discussed and numerically studied the paper ends with some numerical examples of an end loaded cantilever beam and a cracked plate under tension and shear it is shown that the continuity enforced with the h 1 coupling leads to a link with a flexibility that can be beneficial for coupling a very coarse mesh with a very fine one to limit the effect of the volume coupling on the global response a narrow coupling zone is recommended in this case volume coupling tends to a surface coupling especially with a l 2 coupling

a variational approach for coupling kinematically incompatible structural models abstract in this work an extended variational framework aimed at properly addressing the coupling of kinematically incompatible structural models is presented the main goal is to variationally state the theoretical bases to deal with the coupling of structural models with different dimensionality in this approach the coupling conditions are naturally derived from the governing variational principle formulated at the continuous level furthermore by means of a real parameter we manage to build different continuous mechanical models that have different mechanical and mathematical features in particular the coupling of 3d solid models and 2d shell models under naghdi hypothesis is treated by introducing the corresponding kinematical assumptions into the proposed extended variational principle also the coupling between 3d solid and 1d beam models under bernoulli hypothesis is presented moreover for the continuous 3d 2d coupled problem a numerical approximation is addressed via the finite element method and some numerical results are given comparing the responses of the system when the discrete model varies by changing the value of the parameter finally a discussion comprising the main conclusions of the work is given

cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure the direct methods for the solution of systems of linear equations with a symmetric positive semidefinite sps matrix a usually comprise the cholesky decomposition of a nonsingular diagonal block a of a and effective evaluation of the action of a generalized inverse of the corresponding schur complement in this note we deal with both problems paying special attention to the stiffness matrices of floating structures without mechanisms we present a procedure which first identifies a well conditioned positive definite diagonal block a of a then decomposes a by the cholesky decomposition and finally evaluates a generalized inverse of the schur complement s of a the schur complement s is typically very small so the generalized inverse can be effectively evaluated by the singular value decomposition svd if the rank of a or a lower bound on the nonzero eigenvalues of a are known then the svd can be implemented without any epsilon moreover if the kernel of a is known then the svd can be replaced by effective regularization the results of numerical experiments show that the proposed method is useful for effective implementation of the feti based domain decomposition methods copyright 2011 john wiley sons ltd

a variational approach for estimating the compliance of the cardiovascular tissue an inverse fluid structure interaction problem estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest an inverse elasticity problem is then solved for young s modulus estimation in the case of arteries no forced deformation is required since vessels naturally move under the action of blood young s modulus can therefore be estimated by solving a coupled inverse fluid structure interaction problem in this paper we focus on the mathematical properties of this problem and its numerical solution we give some well posedness analysis and some preliminary results based on a synthetic data set i e test cases where the exact young s modulus is known and the displacement dataset is numerically generated by solving a forward fluid structure interaction problem we address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates

locality constraints within multiscale model for non linear material behaviour this paper presents a two scale approach for the mechanical and numerical modelling of materials with microstructure like concrete or fibre reinforced concrete in the non linear regime it addresses applications where the assumption of scale separation as the basis for classical homogenization methods does not hold this occurs when the resolution of micro and macro scale does not differ ab initio or when evolving fluctuations in the macro fields are in the order of the micro scale during the loading progress typical examples are localization phenomena the objective of the present study is to develop an efficient solution method exploiting the physically existing multiscale character of the problem the proposed method belongs to the superposition based methods with local enrichment of the large scale solution by a small scale part u the main focus of the present formulation is to allow for locality of the small scale solution within the large scale elements to achieve an efficient solution strategy at the same time the small scale information exchange over the large scale element boundaries is facilitated while maintaining the accuracy of a refined complete solution thus the emphasis lies on finding appropriate locality constraints for u to illustrate the method the formulation is applied to a damage mechanics based material model for concrete like materials copyright 2006 john wiley sons ltd

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

use of substructural transmission zeros for structural health monitoring a method of localized structural health monitoring is presented that utilizes an invariance property of transmission zeros of substructural frequency response functions these functions are obtained by partitioning the global dynamic flexibility into a substructural form it is shown that the transmission zeros of the frequency response functions of a damaged substructure are invariant whereas those of healthy substructures are affected the present method exploits this invariance property for the detection of damage in a structure numerical examples are presented to demonstrate the utility of the proposed method

a semi implicit level set method for multiphase flows and fluid structure interaction problems in this paper we present a novel semi implicit time discretization of the level set method introduced in 8 for fluid structure interaction problems the idea stems from a linear stability analysis derived on a simplified one dimensional problem the semi implicit scheme relies on a simple filter operating as a pre processing on the level set function it applies to multiphase flows driven by surface tension as well as to fluid structure interaction problems the semi implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost it is validated through comparisons with the original explicit scheme and refinement studies on two dimensional benchmarks

a minimal element distortion strategy for computational mesh dynamics mesh motion strategy is one of the key points in many fluid structure interaction fsi problems due to the increasing application of fsi to solve the current challenging engineering problems this topic has become of great interest there are several different strategies to solve this problem some of them use a discrete and lumped spring mass system to propagate the boundary motion into the volume mesh and many others use an elastostatic problem to deform the mesh in all these strategies there is always risk of producing an invalid mesh i e a mesh with some elements inverted normally this condition is irreversible and once an invalid mesh is obtained it is difficult to continue in this paper the mesh motion strategy is defined as an optimization problem by its definition this strategy can be classified as a particular case of an elastostatic problem where the material constitutive law is defined in terms of the minimization of certain energy functional that takes into account the degree of element distortion some advantages of this strategy are its natural tendency to high quality meshes its robustness and its straightforward extension to 3d problems several examples included in this paper show these capabilities even though this strategy seems to be very robust it is not able to recover a valid mesh starting from an invalid one this improvement is left for future work copyright 2006 john wiley sons ltd

inverse mass matrix via the method of localized lagrange multipliers summary an efficient method for generating the mass matrix inverse of structural dynamic problems is presented which can be tailored to improve the accuracy of target frequency ranges and or wave contents the present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces and constructs the free free inverse mass matrix employing the standard fem procedure the various boundary conditions are realized by the the method of localized lagrange multipliers in particular the present paper constructs the kernel inverse matrix by employing the standard fem elemental mass matrices it is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices numerical experiments with the proposed inverse mass matrix are carried out to validate its effectiveness when applied to vibration analysis of bars beams and plain stress problems this article is protected by copyright all rights reserved

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

a time and space mortar method for coupling linear modal subdomains and non linear subdomains in explicit structural dynamics this paper deals with an extension of dynamic subdomain methods it relies on time multi scale algorithms in the particular case of explicit dynamics it introduces new opportunities in terms of proper modeling on each subdomain adapted to its effective loading in order to reduce the calculation time of the simulations treatment of non matching meshes and local modal projection methods are thus especially discussed the efficiency of the method is then illustrated with two large scale examples

a variational framework for fluid solid interaction problems based on immersed domains theoretical bases abstract in this work the theoretical bases to handle the fluid solid interaction problem based on the conception of immersed domains are developed starting from a well known governing variational principle from the continuum mechanics the purpose of the present work is twofold firstly a variational principle to model the interaction between a fluid and a thin structure characterized as a shell for which its volume is geometrically neglected is devised by incorporating suitable kinematical assumptions into the original problem this leads to a rather general formulation for the fluid shell interaction problem that embraces methodologies such as the immersed boundary method secondly no longer is the volume of the solid disregarded and the variational principle is manipulated in order to attain a formulation that comprises the problem of an augmented fluid which is extended as a fictitious fluid to the whole domain of analysis interacting with an immersed solid in some parts the formulation resembles the immersed finite element method as well as the recently presented immersed continuous method due to the appearance of a volume force defined over the fictitious fluid domain one of the main differences lies in the fact that in the present approach the volume force is the lagrange multiplier that imposes the continuity of the velocity field along the whole overlapped domain the other noteworthy difference dwells in the handling of the mass conservation for the artificial fluid three aspects of this setting must be pointed out as original contributions of the work i a consistent generalization of the theoretical continuous setting of immersed boundary methods is carried out ii the variational basis for the finite element approximations is clearly posed written and easy to understand and iii when dealing with an immersed solid a more general formulation valid for all classes of combinations fluid solid is developed eliminating the restriction to compressible fluid compressible solid of the immersed continuous method and the incompressible fluid incompressible solid of the immersed finite element method

robin based semi implicit coupling in fluid structure interaction stability analysis and numerics in this paper we propose a semi implicit coupling scheme for the numerical simulation of fluid structure interaction systems involving a viscous incompressible fluid the scheme is stable irrespective of the so called added mass effect and allows for conservative time stepping within the structure the efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical convective nonlinearities through the use of the chorin temam projection scheme within the fluid stability comes from the implicit pressure solid coupling and a specific robin treatment of the explicit viscous solid coupling derived from nitsche s method

a three dimensional computational analysis of fluid structure interaction in the aortic valve numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle moreover the fluid structure interaction in the aortic valve system is most frequently ignored in numerical modelling the effect of this interaction on the valve s behaviour during systolic functioning is investigated the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood valve interaction modelling this has impeded numerical analyses of valves operating under physiological conditions a numerical method known as the lagrange multiplier based fictitious domain method is used to describe the large leaflet motion within the computational fluid domain this method is applied to a three dimensional finite element model of a stented aortic valve the model provides both the mechanical behaviour of the valve and the blood flow through it results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion

the d alembert lagrange principal equations and applications to floating flexible systems this paper addresses the dynamics and quasi statics of floating flexible structures as well as extensions to unconstrained substructures and partitions of coupled mechanical systems the principal solution is defined as the state of self equilibrated forces obtained as the particular solution of the rigid motion and interface equilibrium equations this solution is independent of the stress strain constitutive properties as well as of the compatibility equations for statically determinate systems the principal solution is the final force solution for statically indeterminate systems the correction due to flexibility and compatibility is orthogonal to the principal solution the formulation is done in the context of d alembert s principle which supplies the d alembert lagrange principal equations for floating bodies these are obtained by summation of virtually working forces and moments acting on the floating systems applications of this approach are demonstrated on a set of dynamic and quasi static example problems of increasing generality linkage to variational principles with an interface potential is eventually discussed as providing the theoretical foundation for handling interacting semi discrete subsystems linked by node collocated lagrange multipliers copyright 2008 john wiley sons ltd

nonlinear normal modes for damped geometrically nonlinear systems application to reduced order modelling of harmonically forced structures in order to build efficient reduced order models roms for geometrically nonlinear vibrations of thin structures a normal form procedure is computed for a general class of nonlinear oscillators with quadratic and cubic nonlinearities the linear perturbation brought by considering a modal viscous damping term is especially addressed in the formulation a special attention is focused on how all the linear modal damping terms are gathered together in order to define a precise decay of energy onto the invariant manifolds also defined as nonlinear normal modes nnms then this time independent formulation is used to reduce the dynamics governing the oscillations of a structure excited by an external harmonic force the validity of the proposed roms is systematically discussed and compared with other available methods in particular it is shown that large values of the modal damping of the slave modes may change the type of nonlinearity hardening softening behaviour of the directly excited master mode two examples are used to illustrate the main features of the method a two degrees of freedom dof system allows presentation of the main results through a simple example then a water filled circular cylindrical shell with external resonant forcing is considered in order to show the ability of the method to substantially reduce the dynamics of a continuous structure 2006 elsevier ltd all rights reserved

high fidelity flexibility based component mode synthesis method with interface degrees of freedom reduction the partitioned structural equations of motion via the method of localized lagrange multipliers palm consist of internal and interface variables the model reduction achieved based on palm is called flexibility based component mode synthesis f cms and it thus far has concentrated on reducing the internal degrees of freedom dofs or reducing the internal and interface dofs at once in this work well defined three level reduction formulations of the f cms method are proposed for better precision internal dofs the localized lagrange multipliers and the interface boundary displacement the proposed formulations include three different reduction techniques for the interface boundary displacement for better computational efficiency numerical experiments indicate that the proposed formulations can substantially reduce the overall reduced order models further without compromising the accuracy thus achieving a substantial additional reduction of computational cost compared with the previous works in a

partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes summary this work presents a partitioned finite element formulation for flexible multibody systems based on the floating frame ff approach under the assumption of small deformations but arbitrarily large rotations of the bodies in classical ff of reference methods deformational modes are normally computed by modal analysis in this approach free floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non linear finite rotations in this way all deformational modes are retained and no modal selection is needed the main difference between this work and a classical ff of reference formulation is an algebraic separation of pure deformational modes from rigid body motions the proposed methodology presents the following advantages first the position and orientation of the ff has no restriction and can be freely located in the body with identical results second the formulation uses only the linear finite element matrices of a classical vibration problem hence they can be easily obtained from linear fem packages third no selection of modes is needed all deformational modes are retained through the filtering process and finally thanks to the use of localized lagrangian multipliers llm a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers copyright 2014 john wiley sons ltd

fem and bem coupling in elastostatics using localized lagrange multipliers the equations produced by the finite and boundary element methods in structural mechanics are expressed in different variables and cannot be linked without modifications conventional coupling methods of these numerical techniques have traditionally been based on the use of classical lagrange multipliers making a direct connection of the two solids through their common interfaces using matching meshes and altering the formulation of one of the methods to make it compatible with the other in this work a discrete surface called frame is interposed between the connected subdomains to approximate their common interface displacements it is treated using a finite element discretization and connected to each substructure using localized lagrange multipliers collocated at the interface nodes this methodology facilitates the connection of non matching finite and boundary element meshes avoiding modifications to the numerical methods used and providing a partitioned formulation which preserves software modularity

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems