sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors we assessed and compared sensitivities of dynamic simulations to musculotendon mt parameters for gait and dynamometer experiments our aim with this comparison was to investigate whether dynamometer experiments could provide information about mt parameters that are important to reliably study mt function during gait this would mean that dynamometer experiments could be used to estimate these parameters muscle contribution to the joint torque mt torque rather than relative mt force primarily affects the resulting gait pattern and torque measured by the dynamometer in contrast to recent studies therefore we assessed the sensitivity of the mt torque rather than the sensitivity of the relative mt force based on sensitivity of the mt torque to a parameter perturbation mt parameters of the knee flexors and extensors were classified in three categories low medium and high for gait classification was based on the average sensitivity during a gait cycle for isometric and isokinetic dynamometer experiments classification was based on the highest sensitivity found in the experiments the calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of mt parameters of the knee flexors and extensors suggesting that not all mt parameters need to be estimated in general the highest sensitivity was found for tendon slack length however for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium the classification of the individual mt parameters for gait and dynamometer experiments was largely similar we therefore conclude that dynamometer experiments provide information about mt parameters important to reliably study mt function during gait so that subject specific estimates of mt parameters could be made based on dynamometer experiments

variationally consistent extended fe model for 3d planar and curved imperfect interfaces abstract we propose an extended finite element method convergent to the asymptotic solution of a thin interface problem for both planar and curved imperfect interfaces in three dimensions the main advantage over standard cohesive zone models is the bulk mesh size independence with respect to standard extended finite element method in the proposed procedure blending and quadrature sub domains are not required the focus is on the evaluation of the accuracy of the proposed approach in solving three dimensional benchmark tests the numerical results are compared with those available from analytical solutions and spring like interface models

sensitivity of a hill based muscle model to perturbations in model parameters abstract musculoskeletal simulations of human movement commonly use hill muscle models to predict muscle forces but their sensitivity to model parameter values is not well understood the purpose of this study was to evaluate muscle model sensitivity to perturbations in 14 hill muscle model parameters in forward dynamic simulations of running and walking by varying each by 50 three evaluations of the muscle model were performed based on 1 calculating the sensitivity of the muscle model only 2 determining the continuous partial derivatives of the muscle equations with respect to each parameter and 3 evaluating the effects on the running and walking simulations model evaluations were found to be very sensitive percent change in outputs greater than parameter perturbation to parameters defining the series elastic component tendon force length curve of the contractile element and maximum isometric force for some parameters the range of literature values was larger than the model sensitivity model evaluations were insensitive to parameters defining the parallel elastic element force velocity curve of the contractile element and muscle activation time constants the derivative method provided similar results but also provided a generic continuous equation that can easily be applied to other motions the sensitivities of the running and walking simulations were reduced compared to the sensitivity of the muscle model alone results demonstrate the importance of evaluating sensitivity of a musculoskeletal simulation in a controlled manner and provide an indication of which parameters must be selected most carefully based on the sensitivity of a given movement

the xfem for high gradient solutions in convection dominated problems convection dominated problems typically involve solutions with high gradients near the domain boundaries boundary layers or inside the domain shocks the approximation of such solutions by means of the standard finite element method requires stabilization in order to avoid spurious oscillations however accurate results may still require a mesh refinement near the high gradients herein we investigate the extended finite element method xfem with a new enrichment scheme that enables highly accurate results without stabilization or mesh refinement a set of regularized heaviside functions is used for the enrichment in the vicinity of the high gradients different linear and non linear problems in one and two dimensions are considered and show the ability of the proposed enrichment to capture arbitrary high gradients in the solutions copyright c 2009 john wiley sons ltd

a new approach to wall modeling in les of incompressible flow via function enrichment a novel approach to wall modeling for the incompressible navier stokes equations including flows of moderate and large reynolds numbers is presented the basic idea is that a problem tailored function space allows prediction of turbulent boundary layer gradients with very coarse meshes the proposed function space consists of a standard polynomial function space plus an enrichment which is constructed using spalding s law of the wall the enrichment function is not enforced but allowed in a consistent way and the overall methodology is much more general and also enables other enrichment functions the proposed method is closely related to detached eddy simulation as near wall turbulence is modeled statistically and large eddies are resolved in the bulk flow interpreted in terms of a three scale separation within the variational multiscale method the standard scale resolves large eddies and the enrichment scale represents boundary layer turbulence in an averaged sense the potential of the scheme is shown applying it to turbulent channel flow of friction reynolds numbers from re 590 and up to 5 000 flow over periodic constrictions at the reynolds numbers re h 10 595 and 19 000 as well as backward facing step flow at re h 5 000 all with extremely coarse meshes excellent agreement with experimental and dns data is observed with the first grid point located at up to y 1 500 and especially under adverse pressure gradients as well as in separated flows

efficient adaptive integration of functions with sharp gradients and cusps in n dimensional parallelepipeds summary in this paper we study the efficient numerical integration of functions with sharp gradients and cusps an adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions the algorithm is based on a divide and conquer strategy and is independent of the location of the sharp gradient or cusp the error analysis reveals that for a c0 function derivative discontinuity at a point a rate of convergence of n 1 is obtained in rn two applications of the adaptive integration scheme are studied first we use the adaptive quadratures for the integration of the regularized heaviside function a strongly localized function that is used for modeling sharp gradients then the adaptive quadratures are employed in the enriched finite element solution of the all electron coulomb problem in crystalline diamond the source term and enrichment functions of this problem have sharp gradients and cusps at the nuclei we show that the optimal rate of convergence is obtained with only a marginal increase in the number of integration points with respect to the pure finite element solution with the same number of elements the adaptive integration scheme is simple robust and directly applicable to any generalized finite element method employing enrichments with sharp local variations or cusps in n dimensional parallelepiped elements copyright 2012 john wiley sons ltd

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

propagation algorithms for lexicographic ordering constraints finite domain constraint programming has been used with great success to tackle a wide variety of combinatorial problems in industry and academia to apply finite domain constraint programming to a problem it is modelled by a set of constraints on a set of decision variables a common modelling pattern is the use of matrices of decision variables the rows and or columns of these matrices are often symmetric leading to redundancy in a systematic search for solutions an effective method of breaking this symmetry is to constrain the assignments of the affected rows and columns to be ordered lexicographically this paper develops an incremental propagation algorithm gaclexleq that establishes generalised arc consistency on this constraint in o n operations where n is the length of the vectors furthermore this paper shows that decomposing gaclexleq into primitive constraints available in current finite domain constraint toolkits reduces the strength or increases the cost of constraint propagation also presented are extensions and modifications to the algorithm to handle strict lexicographic ordering detection of entailment and vectors of unequal length experimental results on a number of domains demonstrate the value of gaclexleq

localized axial green s function method for the convection diffusion equations in arbitrary domains a localized axial green s function method lagm is proposed for the convection diffusion equation the axial green s function method agm enables us to calculate the numerical solution of a multi dimensional problem using only one dimensional green s functions for the axially split differential operators this agm has been developed not only for the elliptic boundary value problems but also for the steady stokes flows however this paper is concerned with the localization of the agm this localization of the method is needed for practical purpose when computing the axial green s function specifically for the convection diffusion equation on a line segment that we call the local axial line although our focus is mainly on the convection dominated cases in arbitrary domains this method can solve other cases in a unified way numerical results show that despite irregular types of discretization on an arbitrary domain we can calculate the numerical solutions using the lagm without loss of accuracy even in cases of large convection in particular it is also shown that randomly distributed axial lines are available in our lagm and complicated domains are not a burden

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

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

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

a spline based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations summary a novel enrichment function which can model arbitrarily shaped inclusions within the framework of the extended finite element method is proposed the internal boundary of an arbitrary shaped inclusion is first discretized and a numerical enrichment function is constructed on the fly using spline interpolation we consider a piecewise cubic spline which is constructed from seven localized discrete boundary points the enrichment function is then determined by solving numerically a nonlinear equation which determines the distance from any point to the spline curve parametric convergence studies are carried out to show the accuracy of this approach compared with pointwise and linear segmentation of points for the construction of the enrichment function in the case of simple inclusions and arbitrarily shaped inclusions in linear elasticity moreover the viability of this approach is illustrated on a neo hookean hyperelastic material with a hole undergoing large deformation in this case the enrichment is able to adapt to the deformation and effectively capture the correct response without remeshing copyright 2013 john wiley sons ltd

parametric enrichment adaptivity by the extended finite element method an adaptive method within the extended finite element method xfem framework which adapts the enrichment function locally to the physics of a problem as opposed to polynomial or mesh refinement is presented the method minimizes a local residual and determines the parameters of the enrichment function we consider an energy form and a strong form of the residual as error measures to drive the algorithm numerical examples for boundary layers and solid mechanics problems illustrate that the procedure converges moreover when only the character of the solution is known a good approximation is obtained in the area of interest it is also shown that the method can be used to determine the order of singularities in solutions copyright 2007 john wiley sons ltd

improving the accuracy of xfem crack tip fields using higher order quadrature and statically admissible stress recovery this study is concerned with improving the accuracy of crack tip fields obtained using the extended generalized finite element method xfem first the numerical integration of the element stiffness matrices which guarantees convergence with quadrature of not only the regular nodal displacements but also additional degrees of freedom corresponding to the enrichment functions is studied as the accuracy of the stresses obtained by direct differentiation of the converged with quadrature regular nodal displacements and of the coefficients corresponding to enrichment functions is still not satisfactory a statically admissible stress recovery sar scheme is introduced sar uses basis functions which meet the equilibrium equations within the domain and the local traction conditions on the boundary and moving least squares mls to fit the stresses at sampling points e g quadrature points obtained by the xfem important parameters controlling the accuracy of crack tip fields using the xfem and sar namely the order of quadrature the number of retained terms in the crack tip asymptotic field the number of enriched layers and use of arbitrary branch functions a proper choice of the sampling points in the enriched element and the size of the domain of influence doi of mls are investigated copyright 2005 john wiley sons ltd

a physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

sensitivity of subject specific models to errors in musculo skeletal geometry subject specific musculo skeletal models of the lower extremity are an important tool for investigating various biomechanical problems for instance the results of surgery such as joint replacements and tendon transfers the aim of this study was to assess the potential effects of errors in musculo skeletal geometry on subject specific model results we performed an extensive sensitivity analysis to quantify the effect of the perturbation of origin insertion and via points of each of the 56 musculo tendon parts contained in the model we used two metrics namely a local sensitivity index lsi and an overall sensitivity index osi to distinguish the effect of the perturbation on the predicted force produced by only the perturbed musculo tendon parts and by all the remaining musculo tendon parts respectively during a simulated gait cycle results indicated that for each musculo tendon part only two points show a significant sensitivity its origin or pseudo origin point and its insertion or pseudo insertion point the most sensitive points belong to those musculo tendon parts that act as prime movers in the walking movement insertion point of the achilles tendon lsi 15 56 osi 7 17 origin points of the rectus femoris lsi 13 89 osi 2 44 and as hip stabilizers insertion points of the gluteus medius anterior lsi 17 92 osi 2 79 insertion point of the gluteus minimus lsi 21 71 osi 2 41 the proposed priority list provides quantitative information to improve the predictive accuracy of subject specific musculo skeletal models

a regularized xfem model for the transition from continuous to discontinuous displacements this work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement as a model problem an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied a regularization of the displacement field is introduced depending on a scalar parameter the regularized solution is defined in a layer the emerging strain and stress fields are independently modelled using specific constitutive assumptions in particular it is shown that the mechanical work spent within the regularization layer can be interpreted as an interface work provided that a spring like constitutive law is adopted the accuracy of the integration procedures adopted for the stiffness matrix is assessed as highly non linear terms appear standard gauss quadrature is compared with adaptive quadrature and with a new technique based on an equivalent polynomial approach one and two dimensional results are reported for varying discretization size regularization parameter and constitutive parameters copyright 2007 john wiley sons ltd

an extended finite element method for a diffuse interface model this work presents an extended finite element method xfem for a diffuse interface model which describes interfacial phenomena of multi phase flow the diffuse interface has a non zero thickness over which the phase field variable changes continuously the diffuse interface thickness is typically very small compared to the observed domain size resulting in a high gradient solution in this work the finite element approximation of the phase field variable is locally enriched with a tangent hyperbolic function which characterizes a high gradient solution of the diffuse interface model we study a one dimensional advection and two diffusion problems and demonstrate the remarkable improvement of the solution by the local enrichment

on time integration in the xfem the extended finite element method xfem is often used in applications that involve moving interfaces examples are the propagation of cracks or the movement of interfaces in two phase problems this work focuses on time integration in the xfem the performance of the discontinuous galerkin method in time space time finite elements fes and time stepping schemes are analyzed by convergence studies for different model problems it is shown that space time fe achieve optimal convergence rates special care is required for time stepping in the xfem due to the time dependence of the enrichment functions in each time step the enrichment functions have to be evaluated at different time levels this has important consequences in the quadrature used for the integration of the weak form a time stepping scheme that leads to optimal or only slightly sub optimal convergence rates is systematically constructed in this work copyright 2009 john wiley sons ltd

a regularized xfem framework for embedded cohesive interfaces this work focuses on xfem modeling of elastodamaging interfaces characterized by regularized kinematics after regularization of the displacement discontinuity a process zone of finite width with continuous strain fields emerges the stress fields are independently energy deduced modeled via specific constitutive laws and subsequently introduced within the virtual work principle the methodology can address cohesive interfaces with vanishing and finite thickness in a unified way two dimensional results for a strain localization problem and several delamination tests are discussed in detail and compared with previous numerical experimental results

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

crc handbook of combinatorial designs balanced incomplete block designs and t designs2 v k l designs of small orderbibds with small block sizet designs t 3steiner systemssymmetric designsresolvable and near resolvable designslatin squares mols and orthogonal arrayslatin squaresmutually orthogonal latin squares mols incomplete molsorthogonal arrays of index more than oneorthogonal arrays of strength more than twopairwise balanced designspbds and gdds the basicspbds recursive constructionspbd closurepairwise balanced designs as linear spacespbds and gdds of higher indexpbds frames and resolvabilityother combinatorial designsassociation schemesbalanced part ternary designsbalanced tournament designsbhaskar rao designscomplete mappings and sequencings of finite groupsconfigurationscostas arrayscoveringscycle systemsdifference familiesdifference matricesdifference sets abeliandifference sets nonabeliandifference triangle setsdirected designsd optimal matricesembedding partial quasigroupsequidistant permutation arraysfactorial designsfrequency squaresgeneralized quadranglesgraph decompositions and designsgraphical designshadamard matrices and designshall triple systemshowell designsmaximal sets of molsmendelsohn designsthe oberwolfach problemordered designs and perpendicular arraysorthogonal designsorthogonal main effect planspackingspartial geometriespartially balanced incomplete block designsquasigroupsquasi symmetric designs r l designsroom squaresself orthogonal latin squares sols sols with a symmetric orthogonal mate solssom sequences with zero autocorrelationskolem sequencesspherical t designsstarterstrades and defining sets t m s netstuscan squarest wise balanced designsuniformly resolvable designsvector space designsweighing matrices and conference matriceswhist tournamentsyouden designs generalizedyouden squaresapplicationscodescomputer science selected applicationsapplications of designs to cryptographyderandomizationoptimality and efficiency comparing block designsgroup testingscheduling a tournamentwinning the lotteryrelated mathematics and computational methodsfinite groups and designsnumber theory and finite fieldsgraphs and multigraphsfactorizations of graphsstrongly regular graphstwo graphsclassical geometriesprojective planes nondesarguesiancomputational methods in design theoryindex

accuracy of three dimensional analysis of regularized singularities summary in computational mechanics the quadrature of discontinuous and singular functions is often required to avoid specialized quadrature procedures discontinuous and singular fields can be regularized however regularization changes the algebraic structure of the solving equations and this can lead to high errors we show how to acquire accurate and consistent results when regularization is carried out a three dimensional analysis of a tensile butt joint is performed through a regularized extended finite element method the accuracy obtained via gaussian quadrature is compared with that obtained by means of cubpack adaptive quadrature fortran tool the use of regularized functions with non compact and compact support is investigated through an error evaluation procedure based on the use of their fourier transform the proposed procedure leads to the remarkable conclusion that regularized delta functions with non compact support exhibit superior performance copyright 2014 john wiley sons ltd

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

arbitrary discontinuities in space time finite elements by level sets and x fem an enriched finite element method with arbitrary discontinuities in space time is presented the discontinuities are treated by the extended finite element method x fem which uses a local partition of unity enrichment to introduce discontinuities along a moving hyper surface which is described by level sets a space time weak form for conservation laws is developed where the rankine hugoniot jump conditions are natural conditions of the weak form the method is illustrated in the solution of first order hyperbolic equations and applied to linear first order wave and non linear burgers equations by capturing the discontinuity in time as well as space results are improved over capturing the discontinuity in space alone and the method is remarkably accurate implications to standard semi discretization x fem formulations are also discussed copyright 2004 john wiley sons ltd

higher order stable generalized finite element method the generalized finite element method gfem is a galerkin method where the trial space is obtained by augmenting the trial space of the standard finite element method fem by non polynomial functions called enrichments that mimic the local behavior of the unknown solution of the underlying variational problem the gfem has excellent approximation properties but its conditioning could be much worse than that of the fem however if the enrichments satisfy certain properties then the conditioning of the gfem is not worse than that of the standard fem and the gfem is referred to as the stable gfem sgfem in this paper we address the higher order sgfem that yields higher order convergence and suggest a specific modification of the enrichment function that guarantees the required conditioning yielding a robust implementation of the higher order sgfem

generating custom propagators for arbitrary constraints constraint programming cp is a proven set of techniques for solving complex combinatorial problems from a range of disciplines the problem is specified as a set of decision variables with finite domains and constraints linking the variables local reasoning propagation on the constraints is central to cp many constraints have efficient constraint specific propagation algorithms in this work we generate custom propagators for constraints these custom propagators can be very efficient even approaching and in some cases exceeding the efficiency of hand optimised propagators given an arbitrary constraint we show how to generate a custom propagator that establishes gac in small polynomial time this is done by precomputing the propagation that would be performed on every relevant subdomain the number of relevant subdomains and therefore the size of the generated propagator is potentially exponential in the number and domain size of the constrained variables the limiting factor of our approach is the size of the generated propagators we investigate symmetry as a means of reducing that size we exploit the symmetries of the constraint to merge symmetric parts of the generated propagator this extends the reach of our approach to somewhat larger constraints with a small run time penalty our experimental results show that compared with optimised implementations of the table constraint our techniques can lead to an order of magnitude speedup propagation is so fast that the generated propagators compare well with hand written carefully optimised propagators for the same constraints and the time taken to generate a propagator is more than repaid

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100