multiple solutions of periodic boundary value problems for first order differential equations by applying the well known leggett williams multiple fixed point theorem and fixed point theorem of cone expansion and compression this paper investigates the existence of multiple positive solutions of periodic boundary value problems for first order differential equations meanwhile two examples are worked out to demonstrate the main results

computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation a mathematical formulation and some numerical approximation techniques are described for a system of coupled partial differential and algebraic equations describing multiphase flow transport and interactions of chemical species in the subsurface a parallel simulator parsim has been developed based on these approximation techniques and is being used to study contaminant remediation strategies numerical results for a highly complex geochemistry problem involving strontium disposal in a pit at oak ridge national laboratory are presented

solution of the helmholtz eigenvalue problem via the boundary element method the numerical solution of the helmholtz eigenvalue problem is considered the application of the boundary element method reduces it to that of a non linear eigenvalue problem through a polynomial approximation with respect to the wavenumber the non linear eigenvalue problem is reduced to a standard generalized eigenvalue problem the method is applied to the test problems of a three dimensional sphere with an axisymmetric boundary condition and a two dimensional square

two and three dimensional soil consolidation by bem via particular integral abstract particular integral formulations are presented for two and three dimensional soil consolidation poroelasticity analysis the steady state poroelasticity equation is used as the complementary solution and a set of global shape functions is considered to approximate the transient terms of the poroelasticity equation to obtain the required particular integrals some numerical results for four example problems are given and compared with their analytical solutions or the results from the convolution method developed earlier by dargush and banerjee int j numer meth engng 28 1989 2423 j appl mech 58 1991 28

the generalized finite element method for helmholtz equation theory computation and open problems in this paper we address the generalized finite element method for the helmholtz equation we obtain our method by employing the finite element method on cartesian meshes which may overlap the boundaries of the problem domain and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity method here we address the q convergence of the method where q is the number of plane waves added at each vertex for the class of smooth analytic solutions for which we get better than exponential convergence for sufficiently small h depending on p an important observation is that we can monitor the accuracy in any computed solution quantity of interest at negligible cost by using q extrapolation our results assume exact integration of all the employed integrals further studies are needed to analyze the effects of the numerical integrations and also the effect of the roundoff errors

a converse lyapunov theorem for nonlinear switched systems abstract in this paper we present a converse lyapunov theorem for uniform asymptotic stability of switched nonlinear systems its proof is a simple consequence of some results on converse lyapunov theorems for systems with bounded disturbances obtained by lin et al siam j control optim 34 1996 124 160 once an association of the switched system with a nonlinear system with disturbances is established

the iiss property for globally asymptotically stable and passive nonlinear systems this paper investigates the integral input to state stability iiss property for passive nonlinear systems we show that under mild technical assumptions a passive nonlinear system which is globally asymptotically stable is also iiss moreover the integral term from the definition of the iiss property has a very simple form like an l 1 norm we illustrate the result by proving that the drive train of a wind turbine with quadratic torque control is iiss

supernatural quad4 a template formulation abstract a universal template for a 4 node quadrilateral in plane stress is constructed using a combination of old and new techniques the use of natural quantities strongly advocated by j h argyris since his continua and discontinua 1965 exposition is further expanded the qualifier supernatural means that all governing equations kinematic constitutive and equilibrium are expressed in both cartesian and natural forms these two sets are used to build different components of the template with timely help from a computer algebra system a template that include all possible quadrilateral elements that pass the individual element test of bergan and hanssen emerges it yields an infinite number of hitherto undiscovered instances that may be customized to fit special needs a striking example is the construction of a two trapezoid macroelement that is bending exact about one direction for any amount of distortion this concludes a five decade search that begins with the formulation of the wing cover rectangular panel in argyris 1954 seminal serial on energy methods and structural analysis

wavelet based ilu preconditioners for the numerical solution by pufem of high frequency elastic wave scattering daubechies family of wavelets combined to the incomplete lower upper ilu factorization are considered as preconditioners for a block sparse linear system arising from the approximation of the time harmonic elastic wave equations by the partition of unity finite element method pufem after applying the discrete wavelet transform dwt to each dense block in the final matrix and the known right hand side due to the local enrichment by pressure p and shear s plane waves the resulting linear system is solved by the restarted generalized minimum residual method gmres with ilu preconditioners allowing fill in elements in the l and u matrix factors a reordering algorithm of the vertices based on gibbs method is also introduced it leads to a significant reduction of the bandwidth of the wave based finite element fe matrix and enables the ilu preconditioners to be more effective to study the performance of the proposed preconditioners a problem of a horizontal s plane wave scattered by a rigid circular body in an infinite elastic medium is considered the numerical tests show the good performance of the dwt based ilu preconditioners in improving the rate of convergence of gmres for high numbers of approximating p and s plane waves on coarse mesh grids containing multi wavelength sized elements moreover the haar dwt enhances the scalability with respect to the problem size when the number of the nodal points increases of the ilu preconditioner which uses the threshold strategy in the control of the fill in elements despite the high level of the conditioning a good accuracy may be achieved for a discretization level of around 1 9 degrees of freedom per s wavelength which is far below the rule of thumb of 10 nodal points per wavelength adopted for the conventional fe

a comparison of nrbcs for pufem in 2d helmholtz problems at high wave numbers in this work exact and approximate non reflecting boundary conditions nrbcs are implemented with the partition of unity finite element method pufem to solve short wave scattering problems governed by the helmholtz equation in two dimensions by short wave problems we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer various nrbcs are implemented and a comparison of their performance is carried out based on the accuracy of the results ease of implementation and computational cost the aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number

derivative superconvergence of rectangular finite elements for the reissner mindlin plate abstract the finite element method with rectangular meshes for the reissner mindlin plate is analyzed for a plate with thickness bounded below by a positive constant moderately thick plate derivative superconvergence of the finite element solution at the gaussian points is justified and optimal error estimates for both rotation and displacement are established

a note on the design of hp adaptive finite element methods for elliptic partial differential equations we introduce an hp adaptive finite element algorithm based on a combination of reliable and efficient residual error indicators and a new hp extension control technique which assesses the local regularity of the underlying analytical solution on the basis of its local legendre series expansion numerical experiments confirm the robustness and reliability of the proposed algorithm

finite dimensional approximation of bifurcation problems in presence of symmetries we give here a brief summary of the results of 4 14 the aim of our work was not only the finite dimensional approximation of the specific problem studied in 3 but we also wanted to show how to adapt to discrete problems and how to use in this case some classical mathematical tools e g the splitting lemma of gromoll meyer magnus the singularity theory etc such considerations are developed in 5 in particular we prove in 5 that in most cases e g in the examples given in 6 7 9 10 the discrete bifurcation problem behaves as an imperfect bifurcation problem and we improve the methods of 12 another way to use universal unfoldings in the approxima tion of bifurcation problems is suggested by 2

an asymptotic ratio characterization of input to state stability for continuous time nonlinear systems with inputs we introduce the notion of an asymptotic ratio input to state stability iss lyapunov function the derivative of such a function along solutions is upper bounded by the difference of two terms whose ratio is asymptotically smaller than 1 for large states this asymptotic ratio condition is sometimes more convenient to check than standard iss lyapunov function conditions we show that the existence of an asymptotic ratio iss lyapunov function is equivalent to iss a related notion of iss with nonuniform convergence rate is also explored

boundary value problems for second order integro differential equations of fredholm type in this paper we study a two point boundary value problem for a nonlinear second order integro differential equation of fredholm type by using upper and lower solutions then we apply our results to investigate some higher order boundary value problems

global stability results for switched systems based on weak lyapunov functions in this paper we study the stability of nonlinear and time varying switched systems under restricted switching we approach the problem by decomposing the system dynamics into a nominal like part and a perturbation like one most stability results for perturbed systems are based on the use of strong lyapunov functions i e functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state however switched systems under restricted switching may not admit strong lyapunov functions even when asymptotic stability is uniform over the set of switching signals considered the main contribution of the current paper consists in providing stability results that are based on the stability of the nominal like part of the system and require only a weak lyapunov function these results may have wider applicability than results based on strong lyapunov functions the results provided follow two lines first we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal like and the perturbation like parts of the system second we provide input to state stability iss results for the case when the nominal like part is switched linear time varying we provide two types of iss results standard iss that involves the essential supremum norm of the input and a modified iss that involves a power type norm

numerical methods for treating problems of viscoelastic isotropic solid deformation mathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are discussed and their discretization using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described the range of applicability of this type of formulation is reviewed in the context of geometric and constitutive linearity nonlinearity and the limitations imposed by the availability of physical data are discussed one of the above models is a volterra integral equation of the second kind in this when the kernel is separable an established technique due to goursat 1933 can be exploited to reformulate the problem as a system of ordinary differential equations this approach will be described for the special case of a linear viscoelastic isotropic homogeneous synchronous constant poisson s ratio solid this method results in a complete decoupling of the space and time dependence in this case the problem can be solved at each time level by solving first a problem of linear elasticity and then a system of ordinary differential equations for each point in the spatial mesh at which the viscoelastic displacements are required the advantages disadvantages and limitations offered by this and various other schemes for solving problems of viscoelasticity as outlined below are discussed

modeling of convection dominated thermoporomechanics problems using incomplete interior penalty galerkin method abstract in order to obtain converged and accurate numerical solutions in general small time steps are required for time dependent problems for popular continuous finite elements however the use of small time steps often results in oscillatory pressures and temperatures for thermoporomechanics problems with low conductivities moreover convection dominated thermal poromechanics problems often have very sharp temperature fronts that propagate over spatial domains when applied to these problems continuous elements present serious deficiencies in that large error induced in coarse mesh zones will propagate and pollute the solutions in fine mesh zones such oscillatory and polluted solutions are nonphysical and must be precluded we propose discontinuous galerkin methods to be alternatives to handle these challenges this paper focuses on the finite element formulation of the incomplete interior penalty galerkin method on thermoporoelasticity problems with heat convection in this formulation we propose discontinuous spaces for all three field variables to deal with the convection effect an upwinding scheme is simply and elegantly implemented through element interfaces which is favored by the discontinuous galerkin framework in addition the inner pressure boundary conditions important to many engineering problems are also taken into account in our discontinuous galerkin formulation excellent performance of this discontinuous galerkin method on precluding temperature oscillations and on blocking error propagation is demonstrated through solving a convection dominated oil well injection problem

a boundary element method for steady incompressible thermoviscous flow a boundary element formulation is presented for moderate reynolds number steady incompressible thermoviscous flows the governing integral equations are written exclusively in terms of velocities and temperatures thus eliminating the need for the computation of any gradients furthermore with the introduction of reference velocities and temperatures volume modelling can often be confined to only a small portion of the problem domain typically near obstacles or walls the numerical implementation includes higher order elements adaptive integration and multiregion capability both the integral formulation and implementation are discussed in detail several examples illustrate the high level of accuracy that is obtainable with the current method

bounded energy input convergent state property of dissipative nonlinear systems an i iss approach for a class of dissipative nonlinear systems it is shown that an iiss integral input to state stability gain can be computed directly from the corresponding supply function the result is used to prove the convergence to zero of the state whenever the input signal has bounded energy where the energy functional is determined by the supply function

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

an eulerian method for transient nonlinear free surface wave problems abstract an eulerian difference method is developed for the transient potential flow of an incompressible fluid with fully nonlinear free surface conditions the free surface coordinate y x t and the velocity potential x y t on the free surface are recognized as the primary unknowns to be solved as an initial value problem from the pair of nonlinear partial differential equations representing the dynamic and the kinematic conditions of the free surface the continuity relation 2 0 for the velocity potential x y t over the flow field below the free surface is recognized as a subsidiary condition to be enforced at all times the field of computation is transformed into a time invariant cartesian region with the free surface x t represented by a coordinate line or surface the iterative solution for x y t p x y t in this fixed field of computation is facilitated by the use of fast fourier transform fft the iterative process converges rapidly in terms of this converged x y t the free surface location x t and its potential x y t are advanced in time results from two planar examples are illustrated the method is equally applicable to problems in three space dimensions possibly involving interactive matching with neighboring flow fields if the initial free surface potential x y t 0 is unknown difficulties may be encountered in data specification for securing a well posed problem for solution

critical friction for wedged configurations abstract a wedged configuration with coulomb friction is a nontrivial equilibrium state of a linear elastic body in a frictional unilateral contact with a rigid body under vanishing external loads we analyze here the relation between the geometry of the elastic body and the friction coefficient for which wedged configurations exist in a 3 d context the critical friction coefficient w is defined as the infimum of a supremal functional defined on the set of admissible normal displacement and tangential stresses for friction coefficients with w the wedged problem has at least a solution and for the wedged problem is stated in a discrete framework using a mixed finite element approach and the discrete critical friction coefficient h w is introduced as the solution of a global minimization problem involving a non differentiable and non convex functional the existence of h the displacement field of a critical wedged state is proved and a specific numerical method based on a genetic algorithm was developed to compute the critical wedged configurations some techniques to handle the discontinuities of the normal vector on the contact surface are presented and the analysis is illustrated with three numerical simulations

a characterization of integral input to state stability the notion of input to state stability iss is now recognized as a central concept in nonlinear systems analysis it provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite l sup 2 gains it plays a central role in recursive design coprime factorizations controllers for nonminimum phase systems and many other areas in this paper a newer notion that of integral input to state stability iiss is studied the notion of iiss generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states in that sense generalizing the linear h sup 2 theory it allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance we obtain several necessary and sufficient characterizations of the iiss property expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations

on some recent adventures into improved finite element cfd methods for convective transport abstract the quest continues for computational fluid dynamics cfd algorithms that are accurate and efficient for convection dominated applications including shocks travelling fronts and wall layers the boundary value optimal galerkin weak statement invariably requires manipulation either in the test space or in an augmented form for the conservation law system to handle the disruptive character introduced by the discretized first order convection term an incredible variety of methodologies have been derived and examined to address this issue in particular seeking achievement of accurate and monotone discrete approximate solutions in an efficient implementation the utk cfd research group continues its search on examining the breadth of approaches leading to development of a consistent encompassing theoretical statement exhibiting quality performance included herein are adventures into generalized taylor series lax wendroff methods characteristic euler flux resolutions sub grid embedded high degree lagrange bases with static condensation and assembled stencil fourier analysis optimization for finite element weak statement implementations for appropriate model problems including steady convection diffusion and pure unsteady convection and benchmark navier stokes definitions recent advances have lead to candidate accurate monotone methods with linear basis efficiency this contribution highlights the theoretical developments and presents quantitative documentation of achievable high quality solutions

free vibration analysis of three dimensional solids by bem in practical applications it is often necessary to determine the natural frequencies and mode shapes of a solid in addition to the static response under a variety of loading conditions this paper discusses the calculation of natural frequencies and mode shapes of three dimensional solids using the boundary element method the method developed is based on the use of particular integrals of the elastic equilibrium equations and employs only real arithmetic it represents an extension to three dimensions of work previously carried out for two dimensional problems in references 1 and 15 the method has been incorporated for multiregion analysis in the best3d boundary element solution technology three dimensional computer program 11 results of the boundary element calculations are compared with analytical finite element and experimental results

on zero input stability inheritance for time varying systems with decaying to zero input power abstract stability results for time varying systems with inputs are relatively scarce as opposed to the abundant literature available for time invariant systems this paper extends to time varying systems existing results that ensure that if the input converges to zero in some specific sense then the state trajectory will inherit stability properties from the corresponding zero input system this extension is non trivial in the sense that the proof technique is completely novel and allows to recover the existing results under weaker assumptions in a unifying way

a characterization of integral iss for switched and time varying systems most of the existing characterizations of the integral input to state stability iiss property are not valid for time varying or switched systems in cases where converse lyapunov theorems for stability are not available this paper provides a characterization that is valid for switched and time varying systems and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions the results provided also pinpoint suitable iiss gains and relate these to supply functions and bounds on the function defining the system dynamics

remarks on the periodic boundary value problems for integrodifferential equations of volterra type this paper is concerned with the monotone method on the periodic boundary value problems for integrodifferential equations of volterra type this problem has been studied by several authors 1 6 the purpose of this paper is to relax the restrictions as much as possible on the coefficients m and n that appear in the one sided lipschitz condition

a priori and a posteriori error analysis for a large scale ocean circulation finite element model we consider the finite element solution of the stream function vorticity formulation for a large scale ocean circulation model first we study existence and uniqueness of solution for the continuous and discrete problems under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in h1 seminorm second we introduce and analyze an h adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant we propose an a posteriori anisotropic error indicator based on the recovery of the hessian from the finite element solution which allows us to obtain well adapted meshes the numerical experiments show an optimal order of convergence of the adaptive scheme furthermore this strategy is efficient to eliminate the oscillations around the boundary layer

periodic boundary value problem for a second order integrodifferential equation of hammerstein type a comparison result dealing with second order integrodifferential inequality of hammerstein type with periodic boundary conditions is proved and the extremal solutions of a corresponding second order integrodifferential equation without increasingness assumption on the integral operator are obtained as limits of monotone iterates an application is given to a fourth order mixed boundary value problem

equilibrium subsets for multi parametric structural analysis the paper discusses multi parametric formulations for structural equilibrium problems by seeking subsets of equilibrium states which also fulfil extra conditions more detailed information on structural behaviour can be obtained these conditions can be related to analyses of e g critical behaviour imperfections or optimisation the paper shows a general problem setting and some interesting augmentations a solution method for the special case of one dimensional equilibrium subsets is described the algorithm is a generalisation of a path following algorithm where new methods are developed for the evaluation of the path tangent and for the isolation of special solution points examples are used to show the properties and the possibilities of the ideas

modal decomposition of exterior acoustic structure interaction a modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented the fluid loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem the eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented the modal sound power contributions using both fluid loaded structural modes and acoustic radiation modes are presented the results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem

fem bem coupling for the large body limit in micromagnetics we present and analyze a coupled finite element boundary element method for a model in stationary micromagnetics the finite element part is based on mixed conforming elements for two and three dimensional settings we show well posedness of the discrete problem and present an a priori error analysis for the case of lowest order elements

parallel domain decomposition procedures of improved d d type for parabolic problems two parallel domain decomposition procedures for solving initial boundary value problems of parabolic partial differential equations are proposed one is the extended d d type algorithm which extends the explicit implicit conservative galerkin domain decomposition procedures given in 5 from a rectangle domain and its decomposition that consisted of a stripe of sub rectangles into a general domain and its general decomposition with a net like structure an almost optimal error estimate without the factor h 1 2 given in dawson dupont s error estimate is proved another is the parallel domain decomposition algorithm of improved d d type in which an additional term is introduced to produce an approximation of an optimal error accuracy in l 2 norm

enhanced allman quadrilateral for finite drilling rotations the paper concerns a four node quadrilateral element based on allman shape functions undergoing finite unrestricted drilling rotations and aims at improving its accuracy and facilitating its implementation firstly the classical allman shape functions are valid only for small in plane rotations and must be used with a co rotational frame which embeds finite rotations we derive a new form of allman shape functions which is valid for finite drilling rotations and allows to avoid the use of such a frame secondly the classical allman quadrilateral shows locking in the in plane shear test we study this problem identify its source and remove it by enhancing the element with two additional modes via the enhanced assumed displacement gradient eadg method to accomplish this we extend the original version of the method to mixed functionals including rotations two variational formulations including the drilling rotation via the rotation constraint rc equation are considered one based on the green strain and the other on the relaxed non symmetric right stretch strain numerical tests of the corresponding finite elements show that the improved allman elements are as exact in linear tests as the eadg4 element and perform very well in a severe in plane shear test for one layer of elements undergoing large rotations

nonuniform in time input to state stability and the small gain theorem for time varying control systems various equivalent characterizations of the nonuniform in time input to state stability iss property are established these characterizations enable us to derive sufficient conditions for nonuniform in time iss concerning composite time varying systems our main result generalizes the well known small gain theorem due to jiang teel praly for autonomous systems under the presence of uniform in time iss

bubble functions prompt unusual stabilized finite element methods a second order linear scalar differential equation including a zero th order term is approximated using first the standard galerkin method enriched with bubble functions static condensation of the bubbles suggest an unusual stabilized finite element method for which we establish a convergence study and obtain successful numerical simulations the method is generalized to allow for a convection operator in the equation this work may be employed as a starting point for simulation of nonlinear equations governing turbulence phenomena flows with chemical reactions and other important problems

2d and 3d transient heat conduction analysis by bem via particular integrals abstract particular integral formulations are presented for 2d and 3d transient potential flow heat conduction analysis the results of the analysis are compared with an alternative formulation developed using the volume integral conversion approach although the mathematical foundation of the two methods are different both formulations are shown to produce almost identical results for the particular integral formulation the steady state heat conduction equation is used as the complementary solution and two global shape functions gsfs are considered to approximate the transient term of the heat conduction equation the numerical results for three example problems are given and compared with their analytical solutions

domain decomposition based mathcal h lu preconditioning hierarchical matrices provide a data sparse way to approximate fully populated matrices the two basic steps in the construction of an mathcal h matrix are a the hierarchical construction of a matrix block partition and b the blockwise approximation of matrix data by low rank matrices in this paper we develop a new approach to construct the necessary partition based on domain decomposition compared to standard geometric bisection based mathcal h matrices this new approach yields mathcal h lu factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements these rigorously proven and numerically verified improvements result from an mathcal h matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an lu factorization we provide numerical results in which a domain decomposition based mathcal h lu factorization is used as a preconditioner in the iterative solution of the discrete three dimensional convection diffusion equation

existence of solutions for nth order integro differential equations in banach spaces abstract this paper discusses the existence of solutions of initial value problems for n th order nonlinear integro differential equations of mixed type on an infinite interval in a banach space

a new bem formulation for tow and three dimensional elastoplasticity using particular integras new two and three dimensional bem formulations are developed for elastoplastic stress analysis these new procedures differ from previous work in that volume integration is not required to incorporate the nonlinear effects in the analysis instead initial stress rates are introduced in the bem system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

on the formulation of the acoustic boundary element eigenvalue problems acoustic algebraic eigenvalue analysis by the boundary element method bem can be formulated by the dual reciprocity method drm of nardini and brebbia or by the complementary function particular integral method pim proposed by ahmad and banerjee but both drm and pim require inversion of a matrix of size at least as large as the system matrices before the equations can be cast in the form of generalized eigensystem this makes these methods inefficient for large problems of practical interest in this paper a rather simple technique is proposed which eliminates the need to invert any matrix in the process of setting up the algebraic eigenvalue problem especially for the most important case where all the boundary walls are acoustically hard p n 0 a few example problems having known analytical and experimental results are solved in order to demonstrate the validity of the new technique it is also demonstrated that unlike in elasticity here the boundary element domain must be adequately zoned or an adequate number of internal points must be incorporated in order to solve truly 2 d or 3 d problems

transient analysis of three dimensional wave propagation using the boundary element method in the past the time domain solution of the wave equation has been limited to simplified problems this was due to the limitations of analytical methods and the capacity of computers to manipulate and store large blocks of spatial information with the advent of super computers the ability to solve such problems has significantly increased this paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method the technique presented will allow the definition of a domain the input of impedance conditions on the domain s surface the specification of inputs on the surface and the specification of initial conditions within the domain it will produce a complete solution of the wave equation inside the domain the techniques are demonstrated using a program with a boundary element formulation of kirchhoff s equation the elements used are triangular and compatible

a new boundary element formulation for two and three dimensional thermoelasticity using particular integrals new two and three dimensional boundary element formulations are developed for steady state and transient uncoupled thermoelasticity these new procedures differ from previous work in that additional surface or volume integration is not required to incorporate thermal loads in the analysis instead thermal body forces are introduced in the boundary element system via particular integrals the present formulation is implemented in a general purpose multi region system and examples are presented to demonstrate the accuracy and versatility of the method

nonrobustness of asymptotic stability of impulsive systems with inputs abstract suitable continuity and boundedness assumptions on the function f defining the dynamics of a time varying nonimpulsive system with inputs are known to make the system inherit stability properties from the zero input system whether this type of robustness holds or not for impulsive systems was still an open question by means of suitable counter examples we show that such stability robustness with respect to the inclusion of inputs cannot hold in general not even for impulsive systems with time invariant flow and jump maps in particular we show that zero input global uniform asymptotic stability 0 guas does not imply converging input converging state cics and that 0 guas and uniform bounded energy input bounded state ubebs do not imply integral input to state stability iiss we also comment on available existing results that however show that suitable constraints on the allowed impulse time sequences indeed make some of these robustness properties possible

uniform asymptotic stability of nonlinear switched systems with an application to mobile robots this paper is concerned with the study of both local and global uniform asymptotic stability for general nonlinear and time varying switched systems two concepts of lyapunov functions are introduced and used to establish uniform lyapunov stability and uniform global stability with the help of output functions an almost bounded output energy condition and an output persistent excitation condition are then proposed and employed to guarantee uniform local and global asymptotic stability based on this result a generalized version of krasovskii lasalle theorem in time varying switched systems is proposed for switched systems with persistent dwell time the output persistent excitation condition is guaranteed to hold under a zero state observability condition it is shown that several existing results in past literature can be covered as special cases using the proposed criteria interestingly as opposed to previous work the main results of this paper are applicable to the situation where some switching systems are not asymptotically stable at the origin the robust practical regulation problem of nonholonomic mobile robots is studied as a way of demonstrating the power of the proposed new criteria a novel switching controller is proposed with guaranteed robustness to orientation error and unknown parameters in mobile robots

on converse lyapunov theorems for iss and iiss switched nonlinear systems abstract in this paper we present converse lyapunov theorems for iss and integral input to state stable iiss switched nonlinear systems their proofs are based on existing converse lyapunov theorems for input output to state stable and iiss nonlinear systems and on the association of the switched system with a nonlinear system with inputs and disturbances that take values in a compact set

a boundary integral equation method for radiation and scattering of elastic waves in three dimensions etude du rayonnement et de la diffusion d ondes elastiques par des obstacles de forme arbitraire

an accurate and efficient acoustic eigensolver based on a fast multipole bem and a contour integral method an accurate numerical solver is developed in this paper for eigenproblems governed by the helmholtz equation and formulated through the boundary element method a contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations in order to accelerate the solution procedure the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared moreover a wideband fast multipole method is implemented with a block idr s solver to reduce the overall solution cost of the boundary element systems of equations with multiple right hand sides the burton miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains the actual effect of the burton miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as i k is confirmed through exterior sphere examples furthermore the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method

stability and persistent excitation in signal sets persistent excitation pe conditions have been widely used to analyze stability properties of various parameter identification algorithms and to establish uniform global asymptotic stability ugas for a large class of nonlinear time varying systems in order to generalize such conditions to a more general setting a new pe condition is proposed with three basic ingredients a signal set to represent a family of time functions e g trajectories a pseudo distance measure to describe the convergence and some binary relations e g state to output relations closely related to detectability this pe condition is a necessary condition to guarantee ugas under uniform global stability and an integral inequality it becomes a sufficient condition of ugas a novel concept m pair which aims at simplifying the checking of the pe condition is introduced by using m pair it is possible to simplify the structure of the referred signal set in the spirit of the classic krasovskii lasalle theorem and to extend the dimension of the reference signal set similar to the matrosov theorem thus the framework of m pair not only unifies these well known results but also generates more flexibility in checking the pe conditions when applied to nonlinear switched systems three new tools to verify the pe condition are obtained finally an example illustrates that a nonlinear time varying switched system with arbitrary switching can be shown to be ugas without using a common lyapunov function

strong iss implies strong iiss for time varying impulsive systems abstract for time invariant nonimpulsive systems it is already well known that the input to state stability iss property is strictly stronger than integral input to state stability iiss very recently we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics iss implies iiss also for time varying systems in this paper we show that this implication remains true for impulsive systems provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

the lanczos algorithm applied to unsymmetric generalized eigenvalue problem application of the two sided lanczos recursion to the unsymmetric generalized eigenvalue problem is presented the system matrices are real and unsymmetric therefore the recursions are performed in real arithmetic and complex arithmetic is employed in the qr algorithm used to extract the eigenvalues of the transformed tridiagonal matrix the biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in appendices issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed the example problems solved demonstrate the working of the algorithm in extracting the complex and or real eignevalues of an unsymmetric system of matrices also the algorithm is applied to extract a few of the eigenvalues of a large fluid structure interaction problem and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature

periodic boundary value problems for integro differential equations of volterra type on etudie l existence des solutions pour un probleme aux valeurs limites periodique pour l equation integrodifferentielle u f t u tu u 0 u 2 f c 0 2 r r r tu t 0 t k t s u s ds et k c 0 2 0 2 r

boundary element finite element coupled eigenanalysis of fluid structure systems the eigenanalysis of acoustical cavities with flexible structure boundaries such as a fluid filled container or an automobile cabin enclosure is considered an algebraic eigenvalue problem formulation for the fluid structure problem is presented by combining the acoustic fluid boundary element eigenvalue analysis method and the structural finite elements for many practical eigenproblems use of finite elements to discretize the fluid domain leads to large stiffness and mass matrices since the acoustic boundary element discretization requires putting nodes only on the wetted surface of the structure the size of the eigenproblem is reduced considerably thus reducing the eigenvalue extraction effort futhermore unlike in ordinary cases the finite element discretization of pressure displacement based fluid structure problem gives rise to unsymmetric matrices therefore the fact that the boundary element formulation produces unsymmetric matrices does not introduce additional difficulties here compared to the finite element case in the choice of an eigenvalue extraction procedure examples are included to demonstrate the fluid structure eigenanalysis using boundary elements for the fluid domain and finite elements for the structure

boundary element analysis in thermoelasticity with and without internal cells in this paper a set of internal stress integral equations is derived for solving thermoelastic problems a jump term and a strongly singular domain integral associated with the temperature of the material are produced in these equations the strongly singular domain integral is then regularized using a semi analytical technique to avoid the requirement of discretizing the domain into internal cells domain integrals included in both displacement and internal stress integral equations are transformed into equivalent boundary integrals using the radial integration method rim two numerical examples for 2d and 3d respectively are presented to verify the derived formulations copyright 2003 john wiley sons ltd

solution of parabolic and hyperbolic time dependent problems using boundary elements abstract the present paper reviews some recent advances in the solution of time dependent problems by using boundary elements