scattering by a hybrid asymptotic finite element method abstract we describe a hybrid asymptotic finite element method with application to the solution of the helmholtz equation for large wavenumber thus this method is suitable to compute the acoustic field radiated or scattered by acoustically large objects the method is based on patching a short wavelength asymptotic expansion of the outer field to an fem interpolation of the inner field the patching takes place on an artificial boundary continuity of the field and its normal derivative across the artificial boundary is enforced weakly in a variational setting the variational principle is described as is an element like implementation strategy two example applications are included diffraction by a truncated wedge and radiation by a source on a wave bearing surface

algebras with separating almost cyclic coherent auslander reiten components we prove that the class of artin algebras whose auslander reiten quiver admits a separating family of almost cyclic coherent components coincides with the class of generalized multicoil enlargements of concealed canonical algebras moreover the module category homological properties and the representation type of artin algebras with separating families of almost cyclic coherent auslander reiten components are described

spectral super elements for wave propagation in structures with local non uniformities the spectral element method for the analysis of wave propagation in structures is extended by the introduction of a super element concept to handle local regions of non uniformity the region of interest is meshed with conventional finite elements and its stiffness and mass matrices dynamically condensed leaving only the connection degrees of freedom these are further condensed to just waveguide connectivities thus making the element suitable for assembly with other spectral elements the formulation is verified by comparison with 2 d finite element solutions examples of its use in waveguides with cracks holes and extended joints are demonstrated

an exact model reduction procedure for mechanical systems abstract this paper gives details of an exact model reduction procedure for the dynamic analysis of general mechanical systems in this procedure the system is first transformed into an equivalent one dimensional id lumped mass spring damping system by coordinate transformations the 1d lumped system is further reduced into a lower order model with arbitrarily selected degrees of freedom three numerical examples are given for a distributed lumped mass spring system a truss frame structure and a cantilever plate

fictitious domain approach with hp finite element approximation for incompressible fluid flow we consider the application of fictitious domain approach combined with least squares spectral elements for the numerical solution of fluid dynamic incompressible equations fictitious domain methods allow problems formulated on a complicated shaped domain to be solved on a simpler domain containing least squares spectral element method has been used to develop the discrete model as this scheme combines the generality of finite element methods with the accuracy of spectral methods moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation this paper presents the formulation and validation of the fictitious domain least squares spectral element approach for the steady incompressible navier stokes equations the convergence of the approximated solution is verified solving two dimensional benchmark problems demonstrating the predictive capability of the proposed formulation

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

the green function of an infinite fluid loaded membrane abstract in this paper the response of a fluid loaded plane structure a membrane to a concentrated line force excitation is considered in great detail the normalized velocity response here called the green function g depends upon a dimensionless range x0 km x where km is the free wavenumber on the membrane in a vacuum on the mach number m k 0 k m the ratio of wave phase speed km on the unloaded membrane to the sound speed k0 and on a parameter which can be regarded as a measure of fluid loading at the coincidence condition m 1 in the analogous problem involving a thin elastic plate the corresponding parameter is independent of frequency and plate thickness and may be regarded as an intrinsic measure of fluid loading moreover in cases of common interest steel in water aluminium in air that parameter is small in the present paper the asymptotic structure of g x0 m is therefore sought in the limit 0 naturally no single asymptotic expansion can be expected to be valid throughout the x0 m plane and the programme therefore involves the delineation of regions of that plane in which distinct asymptotic results apply the construction and discussion of those results and the asymptotic matching according to the procedures of the method of matched asymptotic expansions of results holding in adjoining regions the fourier integral for g is broken into surface wave and acoustic components and the asymptotic structure obtained for each previously obtained results for the behaviour at large distances are recovered with a demonstration that very large distances indeed x0 2 may be needed for their validity for some ranges of m and the drive point behaviour of g x0 0 m as 0 qua function of m is shown to correspond to that already discussed in the literature elsewhere in the covering of the whole x0 m plane by different asymptotic expressions a wide variety of analytical results is found reflecting the achievement in different regions of different balances among the five competing physical mechanisms represented in the model namely structural stiffness structural inertia fluid pressures fluid compressibility and fluid inertia these different balances give rise to a wide variety of expressions for the phase and amplitude of the surface wave and acoustic components which can now be used to isolate the dominant structural and acoustic mechanisms at any point in the x0 m plane

diffraction from simple shapes by a hybrid asymptotic finite element method the application of a hybrid asymptotic finite element method to the problem of scattering from two dimensional submerged objects is considered the hybrid method is based on patching a short wavelength asymptotic expansion of the scattered field to a finite element interpolation of the near field in patching the diffracted field shape functions with unknown amplitude are forced to agree smoothly with the solution in the near field along a curve at a prescribed distance from the diffraction points a new hybrid finite element on this artificial boundary represents the effect of the outer domain on the solution within this new boundary this allows the replacement of the original boundary value problem with an asymptotically equivalent boundary value problem the domain of which is small and efficiently discretized the method is applied to diffraction by a blunted wedge which in this context represents a degenerate prism the hybrid scattering solution shall be compared to an analytic field representat

inverse aeroacoustic problem for a rectangular wing an investigation is made of the feasibility of aeroacoustic inversion where the pressure on a thin flat rigid rectangular wing undergoing rigid oscillations or interacting with unsteady subsonic flow is to be predicted from the far field acoustic signal this problem is ill posed because small pressure fluctuations in the far field are larger in the near field by a factor equal to the reciprocal of the distance from the wing in the inverse model this ill posedness manifests itself in the kernel of a two dimensional fredholm integral equation of the first kind discretization of this integral equation using a physically meaningful collocation series results in an ill conditioned system of equations which is solved using the singular value decomposition svd the svd generally requires regularization techniques to discard redundant or unphysical information an algorithm is developed for optimally determining the near field pressure without relying on a user specified regularization parameter tests using numerically generated input data show the inversion is feasible and accurate for accurate input data the inversion remains feasible when errors are introduced in the far field measurements and the measurable parameters of the flow

dtn based mixed dimensional coupling using a boundary stress recovery technique abstract a new computational approach for the mixed dimensional modeling of time harmonic waves in elastic structures is proposed a two dimensional 2d structure is considered which includes a part that is assumed to behave in a one dimensional 1d way the 2d and 1d structural regions are discretized by using 2d and 1d finite element fe formulations the hybrid model if designed properly is much more efficient than the standard 2d model taken for the entire problem one important issue related to such hybrid 2d 1d models is the way the 2d 1d coupling is done and the coupling error generated here three closely related coupling methods are considered they are all based on the dirichlet to neumann dtn map associated with the 1d problem on the interface the first coupling method is the dtn method in its usual form where the dtn map is calculated numerically and where the 1d and 2d problems are solved separately the second coupling method is the one devised by carka mear and landis cml which is equivalent to the former one but in which the 2d and 1d interface solutions are solved for simultaneously in the third coupling method the dtn map is enforced on the interface iteratively direct application of these three methods results in low accuracy as a recent study shows therefore these methods are used here in conjunction with a boundary stress recovery bsr technique originally proposed by hughes which provides the same order of accuracy for the stress as for the primary variable the performance of the three methods is demonstrated and they are compared via numerical examples conclusions are drawn on their relative merit

analytical numerical matching for fluid loaded structures with discontinuities the method of analytical numerical matching anm is applied to several example problems involving the radiation and vibration of a fluid loaded cylindrical shell with structural discontinuities these problems are used to verify the accuracy of the method compared to a purely numerical approach and to demonstrate the usefulness of anm for solving problems involving nonaxisymmetric forcing and constraints on structures that are otherwise axisymmetric the principal advantage of the anm method for this application is its ability to employ a spectral method modal decomposition in azimuth in the solution of a problem that is nonaxisymmetric anm divides the original problem into local and global subproblems that are solved separately the discontinuity is handled using a high resolution local finite element model smooth forces are derived from solving an analytical matching problem on the local domain and these smooth forces are then applied to a low resolution numerical global problem the superposition of solutions to the subproblems is equivalent to the solution of the original problem for fluid loading the local high resolution model is solved in vacuo and the effects of fluid loading are included completely by the low resolution global problem

high order boundary conditions and finite elements for infinite domains a finite element method for the solution of linear elliptic problems in infinite domains is proposed the two dimensional laplace helmholtz and modified helmholtz equations outside an obstacle and in a semi infinite strip are considered in detail in the proposed method an artificial boundary b is first introduced to make the computational domain finite then the exact nonlocal dirichlet to neumann dtn boundary condition is derived on b this condition is localized and a sequence of local boundary conditions on b of increasing order is obtained the problem in with a localized dtn boundary condition on b is then solved using the finite element method the numerical stability of the scheme is discussed a hierarchy of special conforming finite elements is developed and used in the layer adjacent to b in conjunction with the local high order boundary condition applied on b an error analysis is given for both nonlocal and local boundary conditions numerical experiments are presented to demonstrate the performance of the method

a characterization of selfinjective algebras of strictly canonical type abstract we prove that the class of selfinjective algebras of strictly canonical type investigated in kwiecien and skowronski 2009 27 kwiecien and skowronski 2009 28 coincides with the class of selfinjective algebras having triangular galois coverings with infinite cyclic group and the auslander reiten quiver with quasi tubes maximally saturated by simple and projective modules satisfying natural conditions

a matrix methodology for spectral analysis of wave propagation in multiple connected timoshenko beams the dynamics of the timoshenko beam is recast such that the description requires information only at the end points this is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements the analysis gives the exact frequency dependent response for the timoshenko beam irrespective of the length of the element the frequency domain response is converted to the time domain response using the fast fourier algorithm fft examples of its use in wave propagation studies are given

fictitious domain methods for the numerical solution of two dimensional scattering problems fictitious domain methods for the numerical solution of two dimensional scattering problems are considered the original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary first order second order and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries the finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes and the discrete equations are solved with fictitious domain methods a special finite element method using nonmatching meshes is considered this method uses the macro hybrid formulation based on domain decomposition to couple polar and cartesian coordinate systems a special preconditioner based on fictitious domains is introduced for the arising algebraic saddle point system such that the subspace of constraints becomes invariant with respect to the preconditioned iterative procedure the performance of the new method is compared to the fictitious domain methods both with respect to accuracy and computational cost

on the application of the gtd mm technique and its limitations in 1975 two techniques were published that combined the method of moments mm and the geometrical theory of diffraction gtd one technique extended the moment method through the use of the gtd while the second used the moment method to solve for unknown diffraction coefficients thereby extending the use of the gtd it is the latter method that is considered in this paper and is referred to as the gtd mm technique one problem area that existed with the original gtd mm work was associated with a field incident along or nearly along one wall of a wedge structure an improved series representation for the diffracted current that is sufficient at all incidence angles is shown the improved formulation is then applied to the problem of bistatic scattering by a three sided pyramid radar cross section rcs results that compare very well with experimental measurements are obtained this is believed to be the first use of the gtd mm technique in treating a three dimensional geometry

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

a domain decomposition method for discontinuous galerkin discretizations of helmholtz problems with plane waves and lagrange multipliers a nonoverlapping domain decomposition dd method is proposed for the iterative solution of systems of equations arising from the discretization of helmholtz problems by the discontinuous enrichment method this discretization method is a discontinuous galerkin finite element method with plane wave basis functions for approximating locally the solution and dual lagrange multipliers for weakly enforcing its continuity over the element interfaces the primal subdomain degrees of freedom are eliminated by local static condensations to obtain an algebraic system of equations formulated in terms of the interface lagrange multipliers only as in the feti h and feti dph dd methods for continuous galerkin discretizations this system of lagrange multipliers is iteratively solved by a krylov method equipped with both a local preconditioner based on subdomain data and a global one using a coarse space numerical experiments performed for two and three dimensional acoustic scattering problems suggest that the proposed dd based iterative solver is scalable with respect to both the size of the global problem and the number of subdomains copyright 2009 john wiley sons ltd

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

the application of analytical numerical matching to structural discontinuities in structural acoustic problems analytical numerical matching anm is introduced to more efficiently model structural discontinuities in structural acoustic problems the general method is explained in detail for the simple example problem of normal incidence acoustic scattering from a periodically line supported elastic membrane a modal series solution exists for this problem the most slowly convergent part of this solution the dominant high resolution large wave number content is removed from the series representation and summed in closed form in what is called the anm local solution this local solution is represented by a piecewise polynomial that is zero outside of a small region the remaining part of the solution containing the overall low resolution content is called the anm global solution and converges very rapidly in the present example the series representing the global solution falls by three powers of the index faster than the classical modal solution the result is an anm composite local plus global solution that requires far less computational effort to resolve in addition to providing a clear abstraction of the method the example problem allows the equivalence of the anm solution to be verified and indicates the importance of resolving the fine scale effects of discontinuities in constrained scattering problems

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

edge based finite element techniques for non linear solid mechanics problems edge based data structures are used to improve computational efficiency of inexact newton methods for solving finite element non linear solid mechanics problems on unstructured meshes edge based data structures are employed to store the stiffness matrix coefficients and to compute sparse matrix vector products needed in the inner iterative driver of the inexact newton method numerical experiments on three dimensional plasticity problems have shown that memory and computer time are reduced respectively by factors of 4 and 6 compared with solutions using element by element storage and matrix vector products copyright 2001 john wiley sons ltd

free vortex calculations using analytical numerical matching with solution pyramiding the motion of a free vortex system is predicted using a novel method called analytical numerical matching anm analytical numerical matching is a hybrid mathematical and numerical technique that results in a new problem formulation with high accuracy and increased computational efficiency the approach capitalizer on the disparity of characteristic length scaler that occur in many fluid dynamics problems accordingly many problems can be decomposed into two distinct problems involving a local high resolution near field often solvable analytically end a global low resolution far field solved numerically the anm technique breaks the free vortex problem into these local and global problems each of which are easier end more efficient to solve than the traditional problem formulation in addition the anm decomposition can be repeated to form a hierarchy of nested problems of increasing resolution using a method called pyramiding the anm method with pyramiding called anm p is studied to assess its accuracy and computational efficiency for two dimensional and three dimensional vortex dynamics problems in calculations of vortex sheet rollup end vortex ring motion and interactions this method war found to be relatively easy to implement end exhibited reductions in computational time from a factor of three to more than an order of magnitude

positive galois coverings of self injective algebras abstract in the article we study the structure of galois coverings of self injective artin algebras with infinite cyclic galois groups in particular we characterize all basic connected self injective artin algebras having galois coverings by the repetitive algebras of basic connected artin algebras and with the galois groups generated by positive automorphisms of the repetitive algebras

a fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems part 2 neumann boundary conditions we present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound hard scatterer we apply this method to the solution of a mock up submarine problem and highlight its computational advantages and intrinsic parallelism a key component of our method is an original idea for addressing a neumann boundary condition in the general framework of a fictitious domain method this idea is applicable to many other linear partial differential equations besides the helmholtz equation copyright 2003 john wiley sons ltd

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

incorporation of linear multipoint constraints in substructure based iterative solvers part 1 a numerically scalable algorithm we consider the iterative solution by a class of substructuring methods of the large scale systems of equations arising from the nite element discretization of structural models with an arbitrary set of linear multipoint constraints we present a methodology for generalizing to such problems numerically scalable substructure based iterative solvers without interfering with their formulations and their well established local and global preconditioners we apply this methodology to the feti method and show that the resulting algorithm is numerically scalable with respect to both the substructure and problem sizes 1998 john wiley sons ltd

high order dynamic modeling and parameter identification of structural discontinuities in timoshenko beams by using reflection coefficients abstract properties of discontinuities such as bolt joints and cracks in the waveguide structures are difficult to evaluate by either analytical or numerical methods due to the complexity and uncertainty of the discontinuities in this paper the discontinuity in a timoshenko beam is modeled with high order parameters and then these parameters are identified by using reflection coefficients at the discontinuity the high order model is composed of several one order sub models in series and each sub model consists of inertia stiffness and damping components in parallel the order of the discontinuity model is determined based on the characteristics of the reflection coefficient curve and the accuracy requirement of the dynamic modeling the model parameters are identified through the least square fitting iteration method of which the undetermined model parameters are updated in iteration to fit the dynamic reflection coefficient curve with the wave based one by using the spectral super element method ssem simulation cases including one order discontinuities on infinite and finite beams and a two order discontinuity on an infinite beam were employed to evaluate both the accuracy of the discontinuity model and the effectiveness of the identification method for practical considerations effects of measurement noise on the discontinuity parameter identification are investigated by adding different levels of noise to the simulated data the simulation results were then validated by the corresponding experiments both the simulation and experimental results show that 1 the one order discontinuities can be identified accurately with the maximum errors of 6 8 and 8 7 respectively 2 and the high order discontinuities can be identified with the maximum errors of 15 8 and 16 2 respectively and 3 the high order model can predict the complex discontinuity much more accurately than the one order discontinuity model

an evaluation of substepping and implicit stress point algorithms abstract elasto plastic finite element analyses of geotechnical boundary value problems involve the use of a non linear solution strategy a popular and efficient strategy is the modified newton raphson approach of which a key element is the integration of the constitutive laws over a finite strain step two algorithms for performing such an integration are the substepping and return methods in this paper the basic assumptions behind these methods are described and the associated errors compared this comparative study is undertaken both at a fundamental level and when applied to a typical boundary value problem the errors associated with both methods are increment size dependent it is shown in the problems considered that for a particular increment size the substepping method is the more accurate

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

a novel boundary infinite element a new improved infinite element based on mapping is proposed for modelling unbounded domain problems mapping has previously been used in such problems not only for the entire domain but also for the infinite element itself the novelty of the present approach is the simplicity of the mapping and the retention of standard integration abscissae and weights the implementation of these elements is very straightforward and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions

automorphisms of repetitive algebras abstract let b be the repetitive algebra of a finite dimensional algebra b over a field k by the b bimodule db hom b k and let be the nakayama automorphism of b we determine the positive automorphisms of b such that the orbit algebra b is isomorphic to a splittable extension algebra of b by the b bimodule db for an automorphism of b and we characterize weakly symmetric algebras and symmetric algebras of the form b with a positive automorphism of b as an application we characterize some class of weakly symmetric algebras with non periodic generalized standard auslander reiten components

solution of large nonlinear systems in elastoplastic incremental analysis the paper concerns the solution of three dimensional problems of elastoplasticity by the incremental finite element method attention is devoted to the inexact newton like methods for solving large nonlinear systems arising in load steps and to the preconditioned conjugate gradient method for solving large linear systems within newton like iterations numerical experiments illustrate the performance of the described numerical technique

discontinuity location on a timoshenko beam by using a novel wave reflection technique abstract based on the physical phenomenon that some propagating waves are partially reflected by discontinuities in waveguide structures this paper proposes a novel discontinuity locating method which is potentially able to detect both the added and embedded discontinuities such as supports and cracks in this method the reflection coefficients of a discontinuity can be obtained experimentally by using a generalized discontinuity approach without the information of the discontinuity position on the other hand these reflection coefficients can be derived from a reflection coefficient prediction model in terms of the discontinuity position by minimizing the error between the reflection coefficients from measurements and those from the prediction model in the frequency bands in which the guided waves are sensitive to the discontinuity and can propagate with low decay rate the discontinuity position parameter in the prediction model can then be identified two numerical cases of locating an added discontinuity and an embedded discontinuity on a beam are proposed to introduce the effectiveness of the method simulation results show that these two discontinuities can be located accurately with zero error in practice the accuracy of discontinuity locating may be influenced by some factors 1 boundary conditions of the beam 2 sizes and locations of the discontinuity and 3 measurement noise the investigation of these factors in simulation shows that this locating method is insensitive to the boundary conditions of the beam effective to small size of the discontinuity and robust to the measurement noise finally three experiments were developed to locate an added discontinuity on a finite beam a crack in an infinite beam with depth ratio of 1 2 and a crack in an infinite beam with depth ratio of 1 6 respectively the corresponding locating errors of these three experiments are 0 percent 0 077 percet and 0 154 percent

model reduction and perturbation analysis of wave finite element formulations for computing the forced response of coupled elastic systems involving junctions with uncertain eigenfrequencies abstract the wave finite element method is investigated for computing the low and mid frequency forced response of coupled elastic systems involving straight structures with junctions the relevance of the method is discussed when a component mode synthesis procedure is used for modeling the junctions a norm wise selection criterion is proposed so as to reduce efficiently the number of junction modes retained in the wave based formulations component wise perturbation bounds of the wave based displacement force solutions are also derived to address slight uncertainties for the junction eigenfrequencies numerical comparisons with standard finite element solutions as well as monte carlo simulations highlight the relevance of the formulation

an illustration of analytical numerical matching with finite element analysis for structural vibration problems analytical numerical matching anm is an accurate and efficient method for solving many types of problems with discontinuities the method separates local and global effects and solves separate subproblems using high resolution around the discontinuity and low resolution away from the discontinuity the work presented in this manuscript demonstrates a methodology for applying anm to a dynamic structure using finite element analysis fea for the solution of the high resolution local and the low resolution global subproblems the anm method is illustrated on a thick two dimensional beam having several displacement constraints attached to its lower surface ordinarily and here for verification purposes this problem would be solved using two dimensional plane elements due to the local discontinuities around the constraints and the thickness of the beam using anm these discontinuities and through thickness effects are modeled in the geometrically compact local problem using a high resolution mesh

selfinjective algebras having a generalized standard family of quasi tubes maximally saturated by simple and projective modules abstract we give a complete description of finite dimensional selfinjective algebras over an algebraically closed field whose auslander reiten quiver admits a generalized standard family of quasi tubes maximally saturated by simple and projective modules in particular we show that these algebras are selfinjective algebras of strictly canonical type

analytical numerical matching for efficient calculation of scattering from cylindrical shells with lengthwise constraints structural discontinuities in highly coupled fluid structure systems are modeled by an approach called analytical numerical matching anm this method separates the low resolution global influence of a discontinuity from the relatively high resolution local effects a continuous smoothed replacement for a fundamental structural discontinuity is constructed so that the system is identically unchanged beyond a small smoothing region simultaneously the precise local effect of smoothing the discontinuity is retained in analytical form the smoothed problem is solved by numerical techniques with rapid convergence and reduced computational cost the original discontinuous character is restored using the analytical expression for the local difference between the smoothed and the original problems anm has been successfully applied to two dimensional cases of acoustic scattering from a thin infinitely long cylindrical shell with multiple structural discontinuities local solutions for longitudinal line discontinuities with radial tangential and rotational constraints have been formulated using anm line constrained scattering problems as well as line driven problems are investigated the ability of analytical numerical matching to replace a discontinuous physical problem by a well behaved continuous one for numerical evaluation while ultimately retaining the original geometry and physical behavior is illustrated

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

wave propagation in multiply connected deep waveguides the longitudinal dynamics of a deep waveguide segment is recast such that the description requires information only at its end points this is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements the analysis gives the exact frequency dependent response for the waveguide segment irrespective of its length by combining these results with a previously presented spectral formulation for the flexural dynamics of a deep timoshenko beam a spectral formulation for the dynamics of multiply connected waveguides forming frames is obtained examples of its use in analyzing wave propagation in connected structures are given and compared with results from a two dimensional finite element analysis

convergence of newton type methods in incremental return mapping analysis of elasto plastic problems abstract the incremental finite element algorithm with return mapping stress computation is considered for the solution of problems of elasto plasticity this algorithm performed in load steps leads to the necessity of solving large scale nonlinear systems the properties of these systems are investigated in the presented paper together with two iterative techniques for their solution the main results of the paper are rigorous proofs of the convergence of the inexact initial stiffness method and the local quadratic convergence of the inexact newton method with the consistent tangent operator

analysis of wave motion in one dimensional structures through fast fourier transform based wavelet finite element method abstract this paper presents a hybrid method that combines the b spline wavelet on the interval bswi finite element method and spectral analysis based on fast fourier transform fft to study wave propagation in one dimensional 1d structures bswi scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high accuracy dynamic stiffness matrix dynamic reduction on element level is applied to eliminate the interior degrees of freedom of bswi elements and substantially reduce the size of the system matrix the dynamic equations of the system are then transformed and solved in the frequency domain through fft based spectral analysis which is especially suitable for parallel computation a comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high frequency wave problems other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1d rods and beams finally the errors caused by fft and their corresponding solutions are presented

convergence of inexact newton like iterations in incremental finite element analysis of elasto plastic problems abstract convergence of two inexact newton like methods suitable for application in incremental finite element analysis of problems of elasto plasticity is investigated by a new technique based on a certain approximation condition it is shown that the convergence can be controlled by the size of load increments a numerical example illustrates the developed theoretical results

mapped wave envelope elements for acoustical radiation and scattering wave envelope elements provide an alternative to boundary element methods for the solution of exterior wave problems applications to date have been to axisymmetric geometries and have involved the use of large but finite wave envelope meshes compatibly matched to denser near field meshes of conventional elements in the present paper the wave envelope idea is extended by the inclusion of an element mapping taken directly from infinite element methodology and by modifications to the residual formulation taken in conjunction these two measures permit the outer boundary of the wave envelope region to be moved to infinity while preserving the boundedness of the acoustic mass and stiffness integrals the present formulation is developed initially with reference to a simple one dimensional model and is then applied in two and three dimensions comparisons between computed results and those obtained from analytic solutions where applicable and from boundary element codes demonstrate the effectiveness of the method

on finite element domain imbedding methods finite element domain imbedding methods for the helmholtz equation with neumann and dirichlet boundary conditions on nonrectangular domains in two space dimensions are considered a survey and comparison of known methods are given and a number of improvements suggested results of numerical experiments are also presented

boundary infinite elements for the helmholtz equation in exterior domains a novel approach to the development of infinite element formulations for exterior problems of time harmonic acoustics is presented this approach is based on a functional which provides a general framework for domain based computation of exterior problems special cases include non reflecting boundary conditions such as the dtn method a prominent feature of this formulation is the lack of integration over the unbounded domain simplifying the task of discretization the original formulation is generalized to account for derivative discontinuities across infinite element boundaries typical of standard infinite element approximations continuity between finite elements and infinite elements is enforced weakly precluding compatibility requirements various infinite element approximations for two dimensional configurations with circular interfaces are presented implementation requirements are relatively simple numerical results demonstrate the good performance of this scheme 1998 john wiley sons ltd

numerical accuracy of a pade type non reflecting boundary condition for the finite element solution of acoustic scattering problems at high frequency the present text deals with the numerical solution of two dimensional high frequency acoustic scattering problems using a new high order and asymptotic pade type artificial boundary condition the pade type condition is easy to implement in a galerkin least squares iterative finite element solver for arbitrarily convex shaped boundaries the method accuracy is investigated for different model problems and for the scattering problem by a submarine shaped scatterer as a result relatively small computational domains optimized according to the shape of the scatterer can be considered while yielding accurate computations for high frequencies copyright 2005 john wiley sons ltd

bayliss turkel like radiation conditions on surfaces of arbitrary shape this paper addresses the extension of the bayliss turkel second order radiation condition to an arbitrarily shaped surface the derivation is based mainly on the pseudo differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition the radiation condition then ranges among the most accurate of those of order two as a by product of the derivation almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared

a two level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems summary we present a lagrange multiplier based two level domain decomposition method for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed method is essentially an extension of the regularized feti finite element tearing and interconnecting method to indefinite problems its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves we show numerically that the proposed method is scalable with respect to the mesh size the subdomain size and the wavenumber we report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements

resonant beam vibration a wave evolution analysis abstract in an attempt to verify the concept of wave mode duality and to understand the wave train closure principle in resonant beam vibration an elastically supported beam subjected to a swept sinusoidal force is investigated through a simulation of wave evolution from initial to final steady state response wave evolution is simulated in the superposition and the degenerate states according to the nature of wave reflection at the boundaries of the beam from the results resonance condition is established and the natural frequencies and mode shapes are calculated using a simply supported beam and a cantilever beam as examples the concept of wave mode duality at resonance is verified an examination of the wave train closure principle shows that although the frequency equations obtained by using the principle are identical to those derived from the wave evolution results the principle does not describe the realistic process of the formulation of vibration modes in general the waves described in the wave train closure principle are not physical but virtual waves that represent final steady state waves which can only be asymptotically approached in reality the principle can be used as a convenient technique to obtain vibration modes from the point of view of wave propagation

aeroacoustic boundary element method using analytical numerical matching a unified aeroacoustic boundary element theory has been formulated using analytica numerical matching anm anm is a hybrid scheme combining a low resolution global numerical solution with high resolution local solutions to form a composite solution anm is applied to problems in unsteady aerodynamics and aeroacoustics this includes both two and three dimensions for lifting surfaces in unsteady compressible irrotational flow to calculate the unsteady aerodynamic loading and the associated acoustic field the solution procedure utilizes overlapping smoothed doublets and local corrections to calculate the doublet strength distribution on the surface of the boundary in question in anm a smoothing length scale is introduced that is larger than the length scale of numerical discretization and smaller than the largest physical scale the global low resolution solution is calculated numerically using smoothed doublet solutions to the convective wave equation and it converges quickly local corrections are done with high resolution analytical solutions the global numerical solution is asymptotically matched to the local analytical solutions via a matching solution the matching solution cancels the global solution in the near field and cancels the local solution in the far field the anm composite solution gives both the surface pressure distribution and the radiated acoustic field the method is very robust offering insensitivity to control point location no explicit wake geometry is assumed therefore a fixed or free wake model can be used anm provides high resolution calculations from low resolution numerics with analytical corrections while avoiding the subtlety involving singular integral equations and their numerical implementation

controllability method for the helmholtz equation with higher order discretizations we consider a controllability technique for the numerical solution of the helmholtz equation the original time harmonic equation is represented as an exact controllability problem for the time dependent wave equation this problem is then formulated as a least squares optimization problem which is solved by the conjugate gradient method such an approach was first suggested and developed in the 1990s by french researchers and we introduce some improvements to its practical realization we use higher order spectral elements for spatial discretization which leads to high accuracy and lumped mass matrices higher order approximation reduces the pollution effect associated with finite element approximation of time harmonic wave equations and mass lumping makes explicit time stepping schemes for the wave equation very efficient we also derive a new way to compute the gradient of the least squares functional and use algebraic multigrid method for preconditioning the conjugate gradient algorithm numerical results demonstrate the significant improvements in efficiency due to the higher order spectral elements for a given accuracy spectral element method requires fewer computational operations than conventional finite element method in addition by using higher order polynomial basis the influence of the pollution effect is reduced

a combined surface integral and finite element solution for a three dimensional contact problem a method is described to determine contact stresses and deformation using a combination of the finite element method and a surface integral form of the bousinesq solution numerical examples of contacting hypoid gears are presented

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation