multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

variational projection methods for gradient crystal plasticity using lie algebras summary a computational method is developed for evaluating the plastic strain gradient hardening term within a crystal plasticity formulation while such gradient terms reproduce the size effects exhibited in experiments incorporating derivatives of the plastic strain yields a nonlocal constitutive model rather than applying mixed methods we propose an alternative method whereby the plastic deformation gradient is variationally projected from the elemental integration points onto a smoothed nodal field crucially the projection utilizes the mapping between lie groups and algebras in order to preserve essential physical properties such as orthogonality of the plastic rotation tensor following the projection the plastic strain field is directly differentiated to yield the nye tensor additionally an augmentation scheme is introduced within the global newton iteration loop such that the computed nye tensor field is fed back into the stress update procedure effectively this method results in a fully implicit evolution of the constitutive model within a traditional displacement based formulation an elemental projection method with explicit time integration of the plastic rotation tensor is compared as a reference a series of numerical tests are performed for several element types in order to assess the robustness of the method with emphasis placed upon polycrystalline domains and multi axis loading this article is protected by copyright all rights reserved

a variational multiscale discontinuous galerkin formulation for both implicit and explicit dynamic modeling of interfacial fracture abstract a stabilized discontinuous galerkin method is presented for modeling interfacial debonding under dynamic conditions the method s distinctive feature is its treatment of the inelastic gap at the interface as an internal variable that is evolved through a traction separation constitutive model enabling initially perfect adhesion to be captured numerical stability is derived using variational multiscale ideas and comparisons are drawn with both the intrinsic cohesive zone method and hybrid discontinuous galerkin cohesive zone method to expose subtle differences the proposed formulation is applied to model the nonlinear response of a composite unit cell under impact loading both explicit and implicit time integration schemes provide similar accuracy and stability and the critical time step for explicit analyses is only slightly reduced below the value for the continuous galerkin mesh without an interface further studies of mesh refinement and adjustments to the initial elastic interface stiffness in the reference cohesive zone model reveal the improved accuracy of the variational multiscale discontinuous galerkin method on coarser grids

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

a primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes abstract a variational multiscale discontinuous galerkin vmdg method is developed for microscale modeling of domains containing conforming and non conforming meshes essentially the product of the applied volume average strain or macro strain and the domain diameter acts as an imposed displacement jump within the vmdg terms hence the method is suitable for modeling deformation of both block and truly self periodic representative volume elements rves the primal displacement field and macro strain are the only unknowns because the method eliminates the lagrange multiplier lm enforcement of the kinematic constraint rigorous derivation of the method provides a framework to accommodate either the macro stress or macro strain as the driver of the microscale boundary value problem the method is developed first for finite deformations and then specialized to small deformation kinematics algorithmic modifications to the method are also studied for their effects on tangent symmetry and convergence rate the results from numerical studies for isotropic and anisotropic materials show that the proposed method is robust accurate stable and variationally consistent for modeling complicated conforming and nonconforming rves

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

a stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

f bar based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids part i formulation and benchmarking this paper proposes a new technique which allows the use of simplex finite elements linear triangles in 2d and linear tetrahedra in 3d in the large strain analysis of nearly incompressible solids the new technique extends the f bar method proposed by de souza neto et al int j solids and struct 1996 33 3277 3296 and is conceptually very simple it relies on the enforcement of near incompressibility over a patch of simplex elements rather than the point wise enforcement of conventional displacement based finite elements within the framework of the f bar method this is achieved by assuming for each element of a mesh a modified f bar deformation gradient whose volumetric component is defined as the volume change ratio of a pre defined patch of elements the resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near incompressibility as the original f bar procedure the present methodology preserves the displacement based structure of the finite element equations as well as the strain driven format of standard algorithms for numerical integration of path dependent constitutive equations and can be used regardless of the constitutive model adopted the new elements are implemented within an implicit quasi static environment in this context a closed form expression for the exact tangent stiffness of the new elements is derived this allows the use of the full newton raphson scheme for equilibrium iterations the performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two and three dimensional numerical examples

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

a framework for residual based stabilization of incompressible finite elasticity stabilized formulations and f methods for linear triangles and tetrahedra abstract a new variational multiscale framework for finite strain incompressible elasticity is presented significant contributions in this work are i a systematic derivation of multiscale formulations that include the classical f method as a particular subclass ii an error estimation procedure for nonlinear elasticity that emanates naturally from within the present multiscale framework and iii robust performance of linear triangular and tetrahedral elements for modeling nearly incompressible materials in the finite strain range when viewed from the variational multiscale perspective the classical f method is shown to include only a volumetric or diagonal fine scale deformation gradient while the proposed formulation includes the full spectrum of inter scale coupling effects also the error estimation procedure readily carries over from developments conducted for small strain linear problems the formulation is presented first in the context of displacement based methods and then extended to more general mixed methods accommodating arbitrary combinations of displacement pressure interpolations an extensive set of benchmark problems is investigated to show the performance of the method for a variety of hyperelastic materials exhibiting incompressible response

chirp transforms and chirp series abstract motivated by the recent work on the non harmonic fourier atoms initiated by t qian and the non harmonic fourier series which originated from the celebrated work of paley and wiener we introduce an integral version of the non harmonic fourier series called chirp transform as an integral transform with kernel e i t the chirp transform is an unitary isometry from l 2 r d onto l 2 r d and it can be explicitly defined in terms of generalized hermite polynomials the corresponding chirp series take e i n t as a basis which in some sense is dual to the theory of non harmonic fourier series which take e i n t as a basis the chirp version of the shannon sampling theorem and the poisson summation formula are also considered by dealing with sampling points which may non equally distributed since the chirp transform interchanges weighted derivatives into multiplications it plays a role in solving certain differential equations with variable coefficients in addition we extend t qian s theorem on the characterization of a measure to be a linear combination of a number of harmonic measures on the unit disc with positive integer coefficients to that with positive rational coefficients

higher order stabilized finite element method for hyperelastic finite deformation abstract this paper presents a higher order stabilized finite element formulation for hyperelastic large deformation problems involving incompressible or nearly incompressible materials a lagrangian finite element formulation is presented where mesh dependent terms are added element wise to enhance the stability of the mixed finite element formulation a reconstruction method based on local projections is used to compute the higher order derivatives that arise in the stabilization terms specifically derivatives of the stress tensor linearization of the weak form is derived to enable a newton raphson solution procedure of the resulting non linear equations numerical experiments using the stabilization method with equal order shape functions for the displacement and pressure fields in hyperelastic problems show that the stabilized method is effective for some non linear finite deformation problems finally conclusions are inferred and extensions of this work are discussed

weighted hardy modular inequalities in variable lp spaces for decreasing functions abstract we study weighted modular inequalities with variable exponents for the hardy operator restricted to non increasing functions we show that the exponents p for which these modular inequalities hold must have a constant oscillation at zero which implies that these exponents are either constant or extremely oscillating near the origin similarly to the constant case we introduce the class of weights b p and prove some of the classical properties in this context

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

output based error estimation and mesh adaptation for variational multiscale methods abstract duality based approaches to estimate errors for functional output quantities require the solution of an auxiliary dual problem this dual solution must be approximated in a richer function space than the one used for the original problem of interest a novel strategy for dual enrichment is proposed based on variational multiscale vms methods and an error representation for output quantities for vms methods is derived an implicit error estimate based on the derived error representation is compared to a recently developed explicit error estimate for vms methods it is shown that while both estimates are identical with respect to calculating the total output error the newly derived estimate provides superior local indicators for use in driving mesh adaptivity

on the orthogonal subgrid scale pressure stabilization of finite deformation j2 plasticity the use of stabilization methods is becoming an increasingly well accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics in this paper a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at finite deformations is presented a j2 flow theory plasticity model at finite deformations is considered a mixed formulation involving pressure and displacement fields is used as starting point within the finite element discretization setting continuous linear interpolation for both fields is considered to overcome the babuska brezzi stability condition a multiscale stabilization method based on the orthogonal subgrid scale osgs technique is introduced a suitable nonlinear expression of the stabilization parameter is proposed the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate and therefore very convenient for practical industrial applications numerical results obtained using the osgs stabilization technique are compared with results provided by the p1 standard galerkin displacements linear triangular tetrahedral element p1 p1 standard mixed linear displacements linear pressure triangular tetrahedral element and q1 p0 mixed bilinear trilinear displacements constant pressure quadrilateral hexahedral element for 2d 3d nearly incompressible problems in the context of a nonlinear finite deformation j2 plasticity model

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

a mixed enhanced formulation tetrahedral finite elements this paper considers the solution of problems in three dimensional solid mechanics using tetrahedral finite elements a formulation based on a mixed enhanced treatment involving displacement pressure and volume effects is presented the displacement and pressure are used as nodal quantities while volume effects and enhanced modes belong to individual elements both small and finite deformation problems are addressed and sample solutions are given to illustrate the performance of the formulation copyright 2000 john wiley sons ltd

a mixed finite element method for non linear and nearly incompressible elasticity based on biorthogonal systems we present a finite element method for non linear and nearly incompressible elasticity the formulation is based on petrov galerkin discretization for the pressure and is closely related to the average nodal pressure formulation presented earlier in the context of incompressible and nearly incompressible dynamic explicit applications commun numer meth engng 1998 14 437 449 some numerical examples are presented to show the efficiency of the approach copyright 2009 john wiley sons ltd

on a weighted inequality of hardy type in spaces lp abstract the boundedness of hardy type operator h f x t r n t x f t d t is studied in weighted variable exponent lebesgue spaces l p the necessary and sufficient criterion established on the weight functions v x x and exponents p x q x for the hardy operator to be bounded from l p to l q v the exponents satisfy a modified logarithmic condition near zero and at infinity 0 f f 0 r sup x b 0 f x f 0 ln 1 w x n 1 sup x r n b 0 n f x f ln w x where w x t r n t x 1 p t 1 t d t

mean strain eight node hexahedron with optimized energy sampling stabilization for large strain deformation summary a method for stabilizing the mean strain hexahedron for applications to anisotropic elasticity was described by krysl 2015 the technique relied on a sampling of the stabilization energy using the mean strain quadrature and the full gaussian integration rule this combination was shown to guarantee consistency and stability the stabilization energy was expressed in terms of input parameters of the real material and the value of the stabilization parameter was fixed in a quasi optimal manner by linking the stabilization to the bending behavior of the hexahedral element krysl submitted here the formulation is extended to large strain hyperelasticity as an example the formulation allows for inelastic behavior to be modeled the stabilization energy is expressed through a stored energy function and contact with input parameters in the small strain regime is made as for small strain elasticity the stabilization parameter is determined to optimize bending performance the accuracy and convergence characteristics of the present formulations for both solid and thin walled structures shells compare favorably with the capabilities of mean strain and other high performance hexahedral elements described in the open literature and also with a number of successful shell elements copyright 2015 john wiley sons ltd

a sampling theorem for non bandlimited signals using generalized sinc functions a ladder shaped filter of two real parameters a 1 a 2 1 1 is introduced in this note the impulse response of the corresponding linear time invariant lti system is a generalized sinc function of two parameters consequently a generalized shannon type sampling theorem is established for a class of non bandlimited signals with special spectrum properties associated with a ladder shaped filter of two parameters finally a mathematical characterization for the class of non bandlimited signals satisfying the generalized sampling theorem is offered these signals are restrictions to the real line of certain analytic functions in stripped domains symmetric about the real axis in the complex plane for these signals their spectra in higher frequency bands are measured by the spectrum of their base bands

hardy s inequality in power type weighted lp 0 spaces abstract in this article our aim is to prove hardy s inequality in power type weighted l p 0 spaces by obtaining regularity condition on the exponents p q and defined at every point of the domain of test function with u 0 0 or vanishing at infinity under the log holder continuity conditions at the origin and infinity

on the algorithmic and implementational aspects of a discontinuous galerkin method at finite strains in this work algorithmic modifications are proposed and analyzed for a recently developed stabilized finite strain discontinuous galerkin dg method the distinguishing feature of the original method referred to as vmdg is a consistently derived expression for the numerical flux and stability tensor that account for evolving material and geometric nonlinearity in the vicinity of the interface herein the proposed modifications involve simplifications to the residual force vector and tangent stiffness matrix of the vmdg method that lead to formulations similar to other existing dg methods but retain the enhanced definition for the stability parameters the primary objective is to reduce the costs associated with implementing the method as well as executing simulations while retaining accuracy and flexibility thereby making the formulation amenable to boarder material classes such as inelasticity each simplification has associated implications on the mathematical and algorithmic properties of the method such as l 2 convergence rate solution accuracy continuity enforcement and stability of the nonlinear equation solver these implications are carefully quantified and assessed through a comprehensive numerical performance study the range of two and three dimensional problems under consideration involves both isotropic and anisotropic materials both triangular and quadrilateral element types are employed along with h and p refinement the ability of the proposed methods to produce stable and accurate results for such a broad class of problems is highlighted

maximal functions on classical lorentz spaces and hardy s inequality with weights for nonincreasing functions a characterization is given of a class of classical lorentz spaces on which the hardy littlewood maximal operator is bounded this is done by determining the weights for which hardy s inequality holds for nonincreasing functions an alternate characterization valid for nondecreasing weights is also derived

a variational multiscale method for inelasticity application to superelasticity in shape memory alloys this paper presents a variational multiscale method for developing stabilized finite element formulations for small strain inelasticity the multiscale method arises from a decomposition of the displacement field into coarse resolved and fine unresolved scales the resulting finite element formulation allows arbitrary combinations of interpolation functions for the displacement and the pressure fields and thus yields a family of stable and convergent elements specifically equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition become stable and convergent an important feature of the present method is that it does not lock in the incompressible limit a nonlinear constitutive model for the superelastic behavior of shape memory alloys is integrated in the multiscale formulation numerical tests of the performance of the elements are presented and representative simulations of the superelastic behavior of shape memory alloys are shown 2005 elsevier b v all rights reserved

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

residual based variational multiscale turbulence models for unstructured tetrahedral meshes abstract this paper presents three level residual based turbulence models for the incompressible navier stokes equations employing the variational multiscale vms framework the velocity and pressure fields are decomposed into two overlapping hierarchical scales thereby leading to a system of coupled mixed field problems the mixed problem at the fine scales is stabilized via a subsequent vms application that results in a further decomposition of the fine scale velocity field into level i and level ii scales the level ii scales are modeled using higher order bubble functions that are then variationally embedded in the level i formulation to stabilize it the level i problem is modeled via a second set of bubble functions that are linearly independent of the bubbles employed at level ii finally the resulting level i fine scales are variationally embedded in the coarse scale formulation this yields a residual based turbulence model for the larger or coarser scales a significant feature of the proposed method is that it results in a concurrent top down and bottom up two way nesting of the scales in addition the resulting turbulence model does not possess any embedded tunable parameters another attribute of the formulation is that the fine scales at every level are driven by the residuals of the euler lagrange equations of the coarser scales at the preceding levels thereby resulting in a method that is variationally consistent various algorithmic generalizations of the method are presented that lead to computationally economic residual based turbulence models the proposed telescopic depth in scales approach helps make these models accurate for low order tetrahedral and hexahedral elements a feature that is facilitated by the higher order bubble functions over element interiors and it results in an enhanced representation of the fine scale terms modeling the fine viscous effects from a computational perspective this method results in easy to implement equal order pressure velocity elements and possesses the desirable p refinement feature numerical performance of the method is assessed on turbulent channel flow problems at re 395 and re 590 also presented are the results for turbulent sd 7003 airfoil at re 60 000 and comparison is made with the published experimental data and numerical results

analytic unit quadrature signals with nonlinear phase abstract the notion of intrinsic mode functions imfs in the algorithm of hilbert huang transform hht n e huang z shen s r long m c wu h h shih q zheng n c yen c c tung h h liu the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis proc r soc london a 454 1998 903 995 is essentially an engineering description in relation to mono components of nonlinear and non stationary signals in this note we prove a version of bedrosian s theorem on the unit circle we give a sufficient condition together with an example for nonlinear phases t that make the unit quadrature signals e i t to be analytic we also establish a corresponding relationship between the periodic and non periodic signals on the whole time range

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

a variational multiscale a posteriori error estimation method for mixed form of nearly incompressible elasticity this paper presents an error estimation framework for a mixed displacement pressure finite element method for nearly incompressible elasticity the proposed method is based on variational multiscale vms concepts wherein the displacement field is decomposed into coarse scales that can be resolved by a given finite element mesh and fine scales that are beyond the resolution capacity of the mesh variational projection of fine scales onto the coarse scale space via variational embedding of the fine scale solution into the coarse scale formulation leads to the stabilized method with two major attributes first it is free of volumetric locking and second it accommodates arbitrary combinations of interpolation functions for the displacement and pressure fields this vms based stabilized method is equipped with naturally derived error estimators and offers various options for numerical computation of the error specifically two error estimators are explored the first method employs an element based strategy and a representation of error via a fine scale error equation defined over element interiors which is evaluated by a direct post solution evaluation this quantity when combined with the global pollution error results in a simple explicit error estimator the second method involves solving the fine scale error equation through localization to overlapping patches spread across the domain thereby leading to an implicit calculation of the local error this implicit calculation when combined with the global pollution error results in an implicit error estimator the performance of the stabilized method and the error estimators is investigated through numerical convergence tests conducted for two model problems on uniform and distorted meshes the sharpness and robustness of the estimators is shown to be consistent across the test cases employed