continuity conditions for finite element analysis of solids in conventional finite element formulations the concept of node a point where one of the shape functions is unitary and all others are nil is used to advantage as it simplifies the definition of interelement continuity conditions this constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and in particular of equilibrium elements in the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes interelement continuity conditions are imposed a posteriori as in hybrid elements the derivation of the element matrices is based upon the equations expressing equilibrium compatibility and the constitutive relations without explicitly using variational principles this results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and or to use conforming or non conforming elements as the approach used is independent of the choice of basic functions and of the shape of the elements it is perfectly general it allows the parallel analysis of kinematically and statically admissible formulations as proposed by fraeijs de veubeke 1 as the interelement continuity conditions are imposed a posteriori new variables are used to express this condition

the effects of hearing loss on the contribution of high and low frequency speech information to speech understanding ii sloping hearing loss the speech understanding of persons with sloping high frequency hf hearing impairment hi was compared to normal hearing nh controls and previous research on persons with flat losses hornsby and ricketts 2003 j acoust soc am 113 1706 1717 to examine how hearing loss configuration affects the contribution of speech information in various frequency regions speech understanding was assessed at multiple low and high pass filter cutoff frequencies crossover frequencies defined as the cutoff frequencies at which low and high pass filtering yielded equivalent performance were significantly lower for the sloping hi compared to nh group suggesting that hf hi limits the utility of hf speech information speech intelligibility index calculations suggest this limited utility was not due simply to reduced audibility but also to the negative effects of high presentation levels and a poorer than normal use of speech information in the frequency region with the greatest hearing loss the hf regio

patch recovery based on superconvergent derivatives and equilibrium in this paper a postprocessing technique is developed for determining first order derivatives fluxes stresses at nodal points based on derivatives in superconvergent points it is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu in contrast to that technique all flux or stress components are interpolated at the same time coupled by equilibrium equations at the superconvergent points the equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries

a basis for bounding the errors of proper generalised decomposition solutions in solid mechanics summary this paper presents an approach that extends the classical error bounding techniques to parametric models it departs from appropriate pairs of complementary solutions of a linear elastic problem obtained using a proper generalised decomposition methodology to determine approximations of selected local outputs and strict bounds of the error of these approximations the paper starts by presenting the procedures used to obtain the complementary solutions the properties the convergence characteristics of the global error and the determination of an indicator of the error distribution are illustrated for a very simple example the demonstration of the procedure used for determining local outputs and their bounds also accompanied by illustrative examples completes the paper copyright 2013 john wiley sons ltd

complementary energy principle for elastodynamics free of volumetric locking abstract this paper proposes a complementary energy principle for elastodynamic problems in doing so the stresses and the inertial forces that satisfy the equilibrium equations a priori are chosen as basic variables and then the complementary variational formulation is established by weakly enforcing the kinematic constraints the eventual formulation is posed to be an integral equation with respect to the time dimension and can be easily applied to free and forced vibration analysis in addition the volumetric locking free property inherent in the complementary energy principle is addressed numerical study on a rectangular plate is performed to validate the proposed complementary energy principle as well as to verify the featured locking free property moreover extensions of the dynamic complementary energy principle to tackle visco elastodynamics and stokes flows are also presented

recovery of equilibrium on star patches from conforming finite elements with a linear basis summary a previous technique for recovering equilibrated stresses from compatible finite element models of structural mechanics problems is extended to cover those cases where the partitioned loads applied to star patches are not initially balanced regarding rotational equilibrium the residual moments are removed by adding a suitable corrective stress field to the compatible one before deriving the fictitious body forces corrective stress fields are determined by solving another set of local problems based on subdomains that each contain elements forming a neighbourhood of a loaded kernel element the conditions for the existence of a solution of these problems are studied for simplicial elements the parameters that control the extended technique are assessed from numerical tests on a variety of two dimensional linear elastic problems based on constant strain elements for the compatible solutions these tests are presented in the context of computing bounds on quantities of interest such as total strain energy and local reactions and displacements copyright 2011 john wiley sons ltd

the sobolev orthogonality and spectral analysis of the laguerre polynomials l n k for positive integers k for k n we consider the analysis of the classical laguerre differential expression l k y x 1 x ke x x k 1e xy x rx ke xy x x 0 where r 0 is fixed in several nonisomorphic hilbert and hilbert sobolev spaces in one of these spaces specifically the hilbert space l2 0 x ke x it is well known that the glazman krein naimark theory produces a self adjoint operator a k generated by l k that is bounded below by rl where i is the identity operator on l2 0 x ke x consequently as a result of a general theory developed by littlejohn and wellman there is a continuum of left definite hilbert spaces h s k v s k s k s 0 and left definite self adjoint operators b s k s 0 associated with the pair l2 0 x ke x a k for a k and each of the operators b s k it is the case that the tail end sequence l n k n k of laguerre polynomials form a complete set of eigenfunctions in the corresponding hilbert spaces in 1995 kwon and littlejohn introduced a hilbert sobolev space w k 0 in which the entire sequence of laguerre polynomials is orthonormal in this paper we construct a self adjoint operator in this space generated by the second order laguerre differential expression l k having l n k n 0 as a complete set of eigenfunctions the key to this construction is in identifying a certain closed subspace of w k 0 with the kth left definite vector space v k k

the spectral method for high order problems with proper simulations of asymptotic behaviors at infinity in this paper we investigate new spectral and multidomain spectral methods for high order problems we introduce a family of new generalized laguerre functions which are mutually orthogonal with the weight function x a d x c d 0 a and c being arbitrary real numbers the corresponding quasi orthogonal approximation and laguerre gauss radau type interpolation are proposed the spectral and multidomain spectral schemes are provided for several model problems which not only fit the mixed inhomogeneous boundary conditions on the fixed boundary exactly but also match the asymptotic behaviors at infinity reasonably numerical results demonstrate the efficiency of suggested algorithms and confirm the analysis well

the stability of stars of simplicial hybrid equilibrium finite elements for solid mechanics summary in this paper we define the spurious kinematic modes of hybrid equilibrium 2d and 3d simplicial elements of general degree and present the results of studies on the stability of star patches of such elements the approach used in these studies is based on first establishing the kinematic properties of a pair of elements that share an interface this approach is introduced by its application to star patches of hybrid equilibrium triangular plate elements for modelling membrane and plate bending problems and then generalised to 3d continua it is then shown how the existence of spurious kinematic modes depends on the topological and geometrical properties of a patch as well as on the degree of the polynomial approximation functions of stress and displacement copyright 2015 john wiley sons ltd

the effects of high presentation levels on consonant feature transmission the effect of high speech presentation levels on consonant recognition and feature transmission was assessed in eight participants with normal hearing consonant recognition in noise 0 db signal to noise ratio was measured at five overall speech levels ranging from 65 to 100 db spl consistent with the work of others overall percent correct performance decreased as the presentation level of speech increased e g g a studebaker r l sherbecoe d m mcdaniel and c a gwaltney j acoust soc am 105 4 2431 2444 1999 confusion matrices were analyzed in terms of relative percent information transmitted at each speech presentation level as a function of feature six feature sets voicing place nasality duration frication and sonorance were analyzed results showed the feature duration long consonant duration fricatives to be most affected by increases in level while the voicing feature was relatively unaffected by increases in level in addition alveolar consonants were substantia

dual adaptive finite element refinement for multiple local quantities in linear elastostatics in this paper we summarize how dual analysis techniques can be used to determine upper bounds of the discretization error both in terms of global and local outputs we present formulas for the bounds of the error in local outputs based on the approach proposed by greenberg in 1948 and we show that the resulting intervals are the same as those previously presented based on the approach proposed by washizu in 1953 we then explain how the elemental contributions to these bounds can be used to define an adaptive strategy that considers multiple quantities and we present its application to a simple plane stress problem copyright 2010 john wiley sons ltd

the superconvergent patch recovery spr and adaptive finite element refinement abstract the error estimation processes which have been developed by the authors depend on the accuracy with which stresses gradients can be recovered the recovery methods available currently such as the l 2 projection and averaging are inaccurate and an improved process is needed this paper presents a very much improved recovery process yielding superconvergent values throughout the domain details of this method named the superconvergent patch recovery are presented with test results showing its efficiency examples of adaptive h based refinement are given showing high local and overall efficiency indices for error estimation

jacobi and laguerre quasi orthogonal approximations and related interpolations in this paper we investigate jacobi quasi orthogonal approximation and generalized jacobi gauss lobatto interpolation we also propose laguerre quasi orthogonal approximation and generalized laguerre gauss radau interpolation a series of sharp results on these approximations are established which are applicable to spectral and pseudospectral methods for mixed nonhomogeneous boundary value problems of high order

on self adjoint boundary conditions for singular sturm liouville operators bounded from below abstract we extend the classical boundary values 0 1 g a w u a 0 g a lim x a g x u a 0 x g 1 a p g a w u a 0 g a lim x a g x g a u a 0 x u a 0 x for regular sturm liouville operators associated with differential expressions of the type r x 1 d d x p x d d x q x for a e x a b r to the case where is singular on a b r and the associated minimal operator t m i n is bounded from below here u a 0 and u a 0 denote suitably normalized principal and nonprincipal solutions of u 0 u for appropriate 0 r respectively our approach to deriving the analog of 0 1 in the singular context employing principal and nonprincipal solutions of u 0 u is closely related to a seminal 1992 paper by niessen and zettl 58 we also recall the well known fact that the analog of the boundary values in 0 1 characterizes all self adjoint extensions of t m i n in the singular case in a manner familiar from the regular case we briefly discuss the singular weyl titchmarsh kodaira m function and finally illustrate the theory in some detail with the examples of the bessel legendre and kummer resp laguerre operators

a spectral study of the second order exceptional x1 jacobi differential expression and a related non classical jacobi differential expression abstract the exceptional x 1 jacobi differential expression is a second order ordinary differential expression with rational coefficients it was discovered by gomez ullate kamran and milson in 2009 in their work they showed that there is a sequence of polynomial eigenfunctions p n n 1 called the exceptional x 1 jacobi polynomials there is no exceptional x 1 jacobi polynomial of degree zero these polynomials form a complete orthogonal set in the weighted hilbert space l 2 1 1 w where w is a positive rational weight function related to the classical jacobi weight among other conditions placed on the parameters and it is required that 0 in this paper we develop the spectral theory of this expression in l 2 1 1 w we also consider the spectral analysis of the extreme non exceptional case namely when 0 in this case the polynomial solutions are the non classical jacobi polynomials p n 2 n 2 we study the corresponding jacobi differential expression in several hilbert spaces including their natural l 2 setting and a certain sobolev space s where the full sequence p n 2 n 0 is studied and a careful spectral analysis of the jacobi expression is carried out

a general formulation of equilibrium macro elements with control of spurious kinematic modes the exorcism of an old curse this paper illustrates a method whereby a family of robust equilibrium elements can be formulated in a general manner the effects of spurious kinematic modes present to some extent in all primitive equilibrium elements are eliminated by judicious assembly into macro equilibrium elements these macroelements are formulated with sufficient generality so as to retain the polynomial degree of the stress field as a variable such a family of macro elements is a new development and results for polynomials of degree greater than two have not been seen before the quality of results for macro equilibrium elements with varying degrees of polynomial is demonstrated by numerical examples

monosyllabic word recognition at higher than normal speech and noise levels the effects of intensity on monosyllabic word recognition were studied in adults with normal hearing and mild to moderate sensorineural hearing loss the stimuli were bandlimited nu 6 word lists presented in quiet and talker spectrum matched noise speech levels ranged from 64 to 99 db spl and s n ratios from 28 to 4 db in quiet the performance of normal hearing subjects remained essentially constant in noise at a fixed s n ratio it decreased as a linear function of speech level hearing impaired subjects performed like normal hearing subjects tested in noise when the data were corrected for the effects of audibility loss from these and other results it was concluded that 1 speech intelligibility in noise decreases when speech levels exceed 69 db spl and the s n ratio remains constant 2 the effects of speech and noise level are synergistic 3 the deterioration in intelligibility can be modeled as a relative increase in the effective masking level 4 normal hearing and hearing impaired subjects are affected similarly by increased signal level when differences in speech audibility are considered 5 the negative effects of increasing speech and noise levels on speech recognition are similar for all adult subjects at least up to 80 years and 6 the effective dynamic range of speech may be larger than the commonly assumed value of 30 db

a general left definite theory for certain self adjoint operators with applications to differential equations we show that any self adjoint operator a bounded or unbounded in a hilbert space h v that is bounded below generates a continuum of hilbert spaces hr r 0 and a continuum of self adjoint operators ar r 0 for reasons originating in the theory of differential operators we call each hr the rth left definite space and each ar the rth left definite operator associated with h a each space hr can be seen as the closure of the domain d ar of the self adjoint operator ar in the topology generated from the inner product arx y x y d ar furthermore each ar is a unique self adjoint restriction of a in hr we show that the spectrum of each ar agrees with the spectrum of a and the domain of each ar is characterized in terms of another left definite space the hilbert space spectral theorem plays a fundamental role in these constructions we apply these results to two examples including the classical laguerre differential expression l in which we explicitly find the left definite spaces and left definite operators associated with a the self adjoint operator generated by l in l2 0 t e t having the laguerre polynomials as eigenfunctions

frequency selectivity and consonant recognition for hearing impaired and normal hearing listeners with equivalent masked thresholds thresholds in notched noise maskers nn and narrow band maskers nb were measured for normal hearing and hearing impaired subject pairs who were listening in a background of spectrally shaped broadband noise ssbb consonant recognition was also measured in ssbb ssbb was adjusted so that thresholds in that noise for each normal hearing hearing impaired subject pair were equal threshold and signal level differences between subject pairs were minimized with the addition of threshold elevating ssbb and the presence of a noise background for both groups provided a comparable listening environment for all subjects at signal frequencies outside masker passbands thresholds in nn and nb for hearing impaired subjects were higher than for normal hearing subjects although threshold differences were much smaller than observed between normal hearing and hearing impaired subjects without ssbb no consistent differences in consonant recognition measured in ssbb were observed between groups the pattern of results is comparable to that observed in a previous experiment dubno and schaefer j acoust soc am 91 2110 2121 1992 in which thresholds in nn and nb and consonant recognition for hearing impaired listeners were compared to results obtained for normal hearing subjects but only normal hearing subjects listened in ssbb using a modified power law model of masking additivity thresholds in combined masker conditions were estimated masking effects for spectrally overlapping maskers were similar for normal hearing and hearing impaired listeners and suggest that residual differences between subject groups are not due to the presence of an additional background noise

intelligibility of speech in noise at high presentation levels effects of hearing loss and frequency region these experiments examined how high presentation levels influence speech recognition for high and low frequency stimuli in noise normally hearing nh and hearing impaired hi listeners were tested in experiment 1 high and low frequency bandwidths yielding 70 correct word recognition in quiet were determined at levels associated with broadband speech at 75db spl in experiment 2 broadband and band limited sentences based on passbands measured in experiment 1 were presented at this level in speech shaped noise filtered to the same frequency bandwidths as targets noise levels were adjusted to produce 30 correct word recognition frequency bandwidths and signal to noise ratios supporting criterion performance in experiment 2 were tested at 75 87 5 and 100db spl in experiment 3 performance tended to decrease as levels increased for nh listeners this rollover effect was greater for high frequency and broadband materials than for low frequency stimuli for hi listeners the 75 to87 5 db incr

the computation of bounds for linear functional outputs of weak solutions to the two dimensional elasticity equations we present a method for the computation of upper and lower bounds for linear functional outputs of the exact solutions to the two dimensional elasticity equations the method can be regarded as a generalization of the well known complementary energy principle the desired output is cast as the supremum of a quadratic linear convex functional over an infinite dimensional domain using duality the computation of an upper bound for the output of interest is reduced to a feasibility problem for the complementary or dual problem in order to make the problem tractable from a computational perspective two additional relaxations that preserve the bounding properties are introduced first the domain is triangulated and a domain decomposition strategy is used to generate a sequence of independent problems to be solved over each triangle the lagrange multipliers enforcing continuity are approximated using piecewise linear functions over the edges of the triangulation second the solution of the adjoint problem is approximated over the triangulation using a standard galerkin finite element approach a lower bound for the output of interest is computed by repeating the process for the negative of the output reversing the sign of the computed upper bound for the negative of the output yields a lower bound for the actual output the method can be easily generalized to three dimensions however a constructive proof for the existence of feasible solutions for the outputs of interest is only given in two dimensions the computed bound gaps are found to converge optimally that is at the same rate as the finite element approximation an attractive feature of the proposed approach is that it allows for a data set to be generated that can be used to certify and document the computed bounds using this data set and a simple algorithm the correctness of the computed bounds can be established without recourse to the original code used to compute them in the present paper only computational domains whose boundary is made up of straight sided segments and polynomially varying loads are considered two examples are given to illustrate the proposed methodology

the stability of stars of triangular equilibrium plate elements equilibrium models for finite element analyses are becoming increasingly important in complementary roles to those from conventional conforming models but when formulating equilibrium models questions of stability or admissibility of loads are of major concern this paper addresses these questions in the context of flat plates modelled with triangular hybrid elements involving membrane and or flexural actions patches of elements that share a common vertex are considered and such patches are termed stars stars may be used in global analyses as assemblies of elements forming macro elements or in local analyses the conditions for stability or the existence and number of spurious kinematic modes are determined in a general algebraic procedure for any degree of the interpolation polynomials and for any geometric configuration the procedure involves the determination of the rank of a compatibility matrix by its transformation to row echelon form examples are presented to illustrate some of the characteristics of spurious kinematic modes when they exist in stars with open or closed links copyright 2008 john wiley sons ltd

a set of hybrid equilibrium finite element models for the analysis of three dimensional solids in this paper an approach to the formulation of equilibrium elements for the analysis of three dimensional elasticity problems is presented this formulation is an extension of the approach previously proposed for the analysis of two dimensional elasticity problems the general aspects of the formulation remain unchanged when applied to the new problem but new points are considered namely the way to perform volume integrations for general elements and the techniques used to obtain the self equilibrated three dimensional stress approximation functions the numerical behaviour of such elements is presented and discussed

local problems on stars a posteriori error estimators convergence and performance a new computable a posteriori error estimator is introduced which relies on the solution of small discrete problems on stars it exhibits built in flux equilibration and is equivalent to the energy error up to data oscillation without any saturation assumption a simple adaptive strategy is designed which simultaneously reduces error and data oscillation and is shown to converge without mesh pre adaptation nor explicit knowledge of constants numerical experiments reveal a competitive performance show extremely good effectivity indices and yield quasi optimal meshes

comparison of frequency selectivity and consonant recognition among hearing impaired and masked normal hearing listeners frequency selectivity and consonant recognition were determined for normal hearing and hearing impaired listeners using techniques that facilitate comparisons of performance among listeners whose absolute thresholds vary in magnitude and configuration first for each of six subjects with cochlear hearing loss masked thresholds in notched noise and narrow band noise maskers were obtained and compared to results for three normal hearing listeners whose thresholds were precisely matched to the impaired listeners by masking with spectrally shaped broadband noise second for hearing impaired listeners and their masked normal hearing controls measurements of consonant recognition were obtained at several speech presentation levels selected on the basis of articulation index predictions to assure equal speech spectrum audibility across listeners the results suggest that frequency selectivity is poorer for hearing impaired listeners than for masked normal hearing listeners even when thresholds among subjects are equated but the deviation from normal frequency selectivity is smaller than estimated from comparisons with normal hearing listeners in quiet critical ratios for hearing impaired listeners are equivalent to normal although frequency selectivity is reduced there is no consistent difference in consonant recognition between hearing impaired subjects and masked normal hearing subjects when performance is assessed under conditions that assure equal speech spectrum audibility across subjects

upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems abstract when local quantities are computed using the principle of virtual work dual analysis which provides an upper bound of the global error may also be applied to the virtual problem greenberg and washizu proposed alternative approaches to combine the global error bounds of the real and virtual problems providing upper bounds of the local error it is shown in this paper that optimising greenberg s approach corresponds to using washizu s approach which in turn may be further improved these approaches are used to provide finite element error indicators for adaptive refinement

subdomain based flux free a posteriori error estimators a new residual type flux free error estimator is presented it estimates upper and lower bounds of the error in energy norm the proposed approach precludes the main drawbacks of standard residual type estimators circumvents the need of flux equilibration and results in a simple implementation that uses standard resources available in finite element codes this is specially interesting for 3d applications where the implementation of this technique is as simple as in 2d recall that on the contrary the complexity of the flux equilibration techniques increases drastically in the 3d case the bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs representing quantities of engineering interest the presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest

left definite theory with applications to orthogonal polynomials in the past several years there has been considerable progress made on a general left definite theory associated with a self adjoint operator a that is bounded below in a hilbert space h the term left definite has its origins in differential equations but littlejohn and wellman l l littlejohn r wellman a general left definite theory for certain self adjoint operators with applications to differential equations j differential equations 181 2 2002 280 339 generalized the main ideas to a general abstract setting in particular it is known that such an operator a generates a continuum h r r 0 of hilbert spaces and a continuum of a r r 0 of self adjoint operators in this paper we review the main theoretical results in l l littlejohn r wellman a general left definite theory for certain self adjoint operators with applications to differential equations j differential equations 181 2 2002 280 339 moreover we apply these results to several specific examples including the classical orthogonal polynomials of laguerre hermite and jacobi

some remarks on a paper by l carlitz we study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by l carlitz we show that they are a special case of the sheffer polynomials and point out some interesting connections with certain sobolev orthogonal polynomials

recovery of equilibrium on star patches using a partition of unity technique a technique for recovering equilibrated element stresses is developed for finite element models of structural mechanics problems the data for the method consist of the prescribed loading and the stress and displacement fields resulting from a conventional compatible finite element model local problems are defined for each star of elements via the introduction of fictitious body forces and strains these problems can be solved independently for equilibrium in a process that can be easily parallelized the quality of the solutions is assessed for two dimensional linear elastic problems by using them to compute bounds of the error of the finite element solutions in terms of both global and local quantities of interest copyright 2009 john wiley sons ltd

an extended class of orthogonal polynomials defined by a sturm liouville problem abstract we present two infinite sequences of polynomial eigenfunctions of a sturm liouville problem as opposed to the classical orthogonal polynomial systems these sequences start with a polynomial of degree one we denote these polynomials as x 1 jacobi and x 1 laguerre and we prove that they are orthogonal with respect to a positive definite inner product defined over the compact interval 1 1 or the half line 0 respectively and they are a basis of the corresponding l 2 hilbert spaces moreover we prove a converse statement similar to bochner s theorem for the classical orthogonal polynomial systems if a self adjoint second order operator has a complete set of polynomial eigenfunctions p i i 1 then it must be either the x 1 jacobi or the x 1 laguerre sturm liouville problem a rodrigues type formula can be derived for both of the x 1 polynomial sequences