predictive algorithms for neuromuscular control of human locomotion abstract the problem of quantifying muscular activity of the human body can be formulated as an optimal control problem the current methods used with large scale biomechanical systems are non derivative techniques these methods are costly as they require numerous integrations of the equations of motion additionally the convergence is slow making them impractical for use with large systems we apply an efficient numerical algorithm to the biomechanical optimal control problem using direct collocation with a trapezoidal discretization the equations of motion are converted into a set of algebraic constraint equations an augmented lagrangian formulation is used for the optimization problem to handle both equality and inequality constraints the resulting min max problem is solved with a generalized newton method in contrast to the prevalent optimal control implementations we calculate analytical first and second derivative information and obtain local quadratic convergence to demonstrate the efficacy of the method we solve a steady state pedaling problem with 7 segments and 18 independent muscle groups the computed muscle activations compare well with experimental emg data the computational effort is significantly reduced and solution times are a fraction of those of the non derivative techniques

some koszul rings from geometry abstract we give examples of koszul rings that arise naturally in algebraic geometry in the first part we prove a general result on koszul property associated to an ample line bundle on a projective variety specifically we show how koszul property of multiples of a base point free ample line bundle depends on its castelnuovo mumford regularity in the second part we give examples of koszul rings that come from adjoint line bundles on minimal irregular surfaces of general type

projective normality and syzygies of algebraic surfaces in this work we develop new techniques to compute koszul cohomology groups for several classes of varieties as applications we prove results on projective normality and syzygies for algebraic surfaces from more general results we obtain in particular the following a mukai s conjecture and stronger variants of it regarding projective normality and normal presentation for surfaces with kodaira dimension 0 and uniform bounds for higher syzygies associated to adjoint linear series b effective bounds along the lines of mukai s conjecture regarding projective normality and normal presentation for surfaces of positive kodaira dimension and c results on projective normality for pluricanonical models of surfaces of general type recovering and strengthening results by ciliberto and generalizations of them to higher syzygies in addition we also extend the above results to singular surfaces

an algorithm for the matrix free solution of quasistatic frictional contact problems a contact enforcement algorithm has been developed for matrix free quasistatic finite element techniques matrix free iterative solution algorithms such as non linear conjugate gradients cg and dynamic relaxation dr are desirable for large solid mechanics applications where direct linear equation solving is prohibitively expensive but in contrast to more traditional newton raphson and quasi newton iteration strategies the number of iterations required for convergence is typically of the same order as the number of degrees of freedom of the model it is therefore crucial that each of these iterations be inexpensive to per form which is of course the essence of a matrix free method in applying such methods to contact problems we emphasize here two requirements first that the treatment of the contact should not make an average equilibrium iteration considerably more expensive and second that the contact constraints should be imposed in such a way that they do not introduce spurious energy that acts against the iterative solver these practical concerns are utilized to develop an iterative technique for accurate constraint enforcement that is suitable for non linear conjugate gradient and dynamic relaxation iterative schemes copyright 1999 john wiley sons ltd

multiplier methods for engineering optimization multiplier methods used to solve the constrained engineering optimization problem are described these methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions the methods proposed in 1969 have been determined to be quite robust although not as efficient as other algorithms they can be more effective for some engineering applications such as optimum design and control oflarge scale dynamic systems since 1969 several modifications and extensions of the methods have been developed therefore it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications recent methods that are similar to the multiplier methods are also discussed these are continuous multiplier update exact penalty and exponential penalty methods

multigraded regularity and the koszul property abstract we give a criterion for the section ring of an ample line bundle to be koszul in terms of multigraded regularity we discuss applications to adjoint bundles on toric varieties as well as to polytopal semigroup rings

projective curves of degree codimension 2 in this article we study nondegenerate projective curves x subset mathbb p d 1 of degree d which are not arithmetically cohen macaulay note that x pi p widetilde x for a rational normal curve widetilde x subset mathbb p d and a point p in mathbb p d setminus widetilde x 2 our main result is about the relation between the geometric properties of x and the position of p with respect to widetilde x we show that the graded betti numbers of x are uniquely determined by the rank hbox rk widetilde x p of p with respect to widetilde x in particular x satisfies property n 2 p if and only if p leq quad rk widetilde x p 3 therefore property n 2 p of x is controlled by quad rk widetilde x p and conversely quad rk widetilde x p can be read off from the minimal free resolution of x this result provides a non linearly normal example for which the converse to theorem 1 1 in eisenbud et al compositio math 141 1460 1478 2005 holds also our result implies that for nondegenerate projective curves x subset mathbb p d 1 of degree d which are not arithmetically cohen macaulay there are exactly lfloor frac d 2 2 rfloor distinct betti tables

syzygies using vector bundles this paper studies syzygies of curves that have been embedded in projective space by line bundles of large degree the proofs take advantage of the relationship between syzygies and spaces of section of vector bundles associated to the given line bundles

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

unilateral contact of two solids subject to large deformations formulation and existence results the approach that is currently the most widely used for formulating the unilateral frictionless contact between two deformable solids involves two key elements the orthogonal projection of one potential contact material surface on another and the action reaction principle of contact forces in the present paper we investigate this approach in the general case of large deformations and study unilateral frictionless boundary value problems of elasticity formulated by means of it the conditions for the orthogonal projection to be unique or further a c 1 diffeomorphism are established an extended action reaction principle is explicitly given for the forces acting on a pair of potential contact surfaces assuming the solids under consideration can be described by polyconvex hyperelastic laws we formulate the associated unilateral frictionless boundary value problem as a minimum principle and show the existence of a solution to it

higher syzygies of ruled varieties over a curve let x be a ruled variety over a smooth projective curve c with the projection morphism x c in this paper we study higher syzygies of very ample line bundles on x each embedding of x is fiberwise a veronese embedding and our first result is to clarify the relation between property np of very ample line bundles on x and that of the veronese embedding more precisely letting h be the tautological line bundle of x assume that the a uple veronese embedding of a fiber satisfies property np we prove that line bundles on x of the form ah b satisfy property np if deg b is sufficiently large theorem 1 1 also we get some partial answer for the converse corollary 3 7 from this observation we improve butler s result in d c butler normal generation of vector bundles over a curve j differential geom 39 1994 1 34 for ruled scrolls ruled surfaces and veronese surface fibrations

on the solvability of closest point projection procedures in contact analysis analysis and solution strategy for surfaces of arbitrary geometry abstract the uniqueness and existence of the closest point projection procedure widely used in contact mechanics are analyzed in the current article first a projection domain for c 2 continuous surfaces is created based on the geometrical properties of surfaces then any point from the projection domain has a unique projection onto the given surface it is shown that in order to construct a continuous projection domain for arbitrary globally c 1 or c 0 continuous surfaces a projection routine should be generalized and also include a projection onto a curved edge and onto corner points criteria of uniqueness and existence of the corresponding projection routine are given and discussed from the geometrical point of view some examples showing the construction of the projection domain as well as the necessity of a generalized projection routine are given

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

a contact smoothing method for arbitrary surface meshes using nagata patches abstract this paper presents a contact surface smoothing method combined with the node to segment discretization technique to solve large deformation frictional contact problems between deformable bodies the nagata patch interpolation is used to smooth the surface mesh providing a master surface with quasi g 1 continuity between patches moreover the local support of the interpolation method allows to deal with surface meshes of arbitrary topology regular and irregular finite element discretizations as well as hybrid meshes the non physical oscillations in the contact force evolution induced by the faceted contact surface representation are reduced using the proposed smoothing method furthermore the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces while providing an important improvement in convergence behaviour four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method the results show a significant improvement in the accuracy robustness and performance of the numerical simulations using the smoothing approach when compared with the piecewise faceted contact surface description

some results on rational surfaces and fano varieties this is the publisher s version also available electronically from http www degruyter com view j crll 2001 2001 issue 538 crll 2001 068 crll 2001 068 xml

on syzygies of non complete embedding of projective varieties let x be a non degenerate not necessarily linearly normal projective variety in mathbb p r recently the generalization of property np to non linearly normal projective varieties have been considered and its algebraic and geometric properties are studied extensively one of the generalizations is the property nd p for the saturated ideal ix eisenbud et al in compos math 141 1460 1478 2005 and the other is the property n p s for the graded module of the twisted global sections of mathcal o x 1 kwak and park in j reine angew math 582 87 105 2005 in this paper we are interested in the algebraic and geometric meaning of properties n p s for every p 0 and the syzygetic behaviors of isomorphic projections and hyperplane sections of a given variety with property n p s

large deformation frictional contact mechanics continuum formulation and augmented lagrangian treatment absract a complete methodology for the formulation and solution of unilateral contact problem with non associated threshold friction between solids undergoing large deformations is presented the approach includes a continuum contact mechanics model combined with an augmented lagrangian method for treating the contact and friction inequality constraints the main developments are a precise statement of the incremental contact minimization problem the exact computations of the first and second variations of the normal gap and the tangential slip velocity and an extension of the augmented lagrangian formulation for frictional contact problems from the discrete to the continuum framework the corresponding saddle point functional first variation mixed virtual work and second variation exact linearization are given the development are illustrated by numerical simulations of frictional contact problems between rigid elastic and elastoplastic bodies a new severe benchmark for large slip frictional contact elements is also proposed

a family of simple two pass dual formulations for the finite element solution of contact problems simple stable unbiased algorithms for two pass two body contact have until now eluded researchers in computational mechanics this work examines the subject starting from an interpolation scheme proposed in an earlier work this method though stable and unbiased results in an exceedingly complex algorithm in three dimensions motivated by the need for simplicity a new formulation of the contact problem is introduced which results in a family of simple stable geometrically unbiased elements the starting point of these elements is any algorithm which is stable for the signorini problem a number of example problems are presented to compare the performance of the elements

an augmented lagrangian method for discrete large slip contact problems reference lmaf article 1993 001view record in web of science record created on 2005 09 14 modified on 2017 05 10

algorithms for the analysis of 3d finite strain contact problems from the constraint imposition aspects in 3d to friction regularization various ideas are exposed in this paper a variation of the rockafellar lagrangian is proposed which results in continuous second order derivatives if lagrange multiplier estimates are greater or equal than one this fact allows the adoption of a full second order i e lagrange newton method avoiding sequential unconstrained minimization techniques an algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods a modified constraint definition to deal with non smooth situations is presented aspects of friction implementation including a regularization scheme which ensures stepwise objectivity are detailed finally several illustrative examples are carried out with success

uzawa and newton algorithms to solve frictional contact problems within the bi potential framework this paper is concerned with the numerical modeling of three dimensional unilateral contact problems in elastostatics with coulomb friction laws we propose a newton like algorithm to solve the local contact non linear equations within the bi potential framework the piecewise continuous contact tangent matrices are explicitly derived a comparative study is made between the newton algorithm and the previously developed uzawa algorithm a test example is included to demonstrate the developed algorithms and to highlight their performance

united elements method for general contact impact problems abstract this work presents the details of a finite element based numerical method to analyse general contact impact problems called united elements method uem in contrast to usual methods that is lagrange multipliers and penalty function this method is conceptual suitable for computer programming and free from inherent deficiencies of those methods the key points of this procedure are elimination of the normal degree of freedom of the contactor node from the system energy potential functional in terms of target surface motion and proper calculation of target element unbalanced forces to incorporate the contact constraints after a review on classic formulations the mathematical and matrix presentation of the united element stiffness matrix are discussed solution of some examples adopting a newton raphson based solution together with a normal return scheme support the capability and accuracy of the procedure in static and dynamic problems

on higher syzygies of ruled surfaces ii abstract in this article we continue the study of property n p of irrational ruled surfaces begun in e park on higher syzygies of ruled surfaces math ag 0401100 trans amer math soc in press let x be a ruled surface over a curve of genus g 1 with a minimal section c 0 and the numerical invariant e when x is an elliptic ruled surface with e 1 it is shown in f j gallego b p purnaprajna higher syzygies of elliptic ruled surfaces j algebra 186 1996 626 659 that there is a smooth elliptic curve e x such that e 2 c 0 f and we prove that if l pic x is in the numerical class of a c 0 b f and satisfies property n p then c l c 0 and e l e satisfy property n p and hence a b 3 p and a 2 b 3 p this gives a proof of the relevant part of gallego purnaprajna conjecture in f j gallego b p purnaprajna higher syzygies of elliptic ruled surfaces j algebra 186 1996 626 659 when g 2 and e 0 we prove some effective results about property n p let l pic x be a line bundle in the numerical class of a c 0 b f our main result is about the relation between higher syzygies of x l and those of c l c where l c is the restriction of l to c 0 in particular we show the followings 1 if e g 2 and b a e 3 g 2 then l satisfies property n p if and only if b a e 2 g 1 p 2 when c is a hyperelliptic curve of genus g 2 l is normally generated if and only if b a e 2 g 1 and normally presented if and only if b a e 2 g 2 also if e g 2 then l satisfies property n p if and only if a 1 and b a e 2 g 1 p

bisecant and trisecant curves on ruled surfaces abstract in this paper we study numerical classes of integral curves on a ruled surface p e associated to a stable bundle e the nef cone of a ruled surface is generated by the classes of a minimal section c 0 and a fiber f we compute the smallest integer b such that the class k c 0 b f contains a multisecant curve for k 2 and 3 also we find its consequence on the lange stability of s y m k e

second order optimal control algorithm for complex systems the solution to large scale optimal control problems characterized by complex dynamics and extended time periods is often computationally demanding we present a solution algorithm with favourable local convergence properties as a way to reduce simulation times this method is based on using a trapezoidal direct collocation to convert the differential equations into algebraic constraints the resulting constrained minimization problem is then solved with an augmented lagrangian formulation to accommodate both equality and inequality constraints in contrast to the prevalent optimal control software implementations we calculate analytical first and second derivatives we then apply a generalized newton method to the augmented lagrangian formulation solving for all unknowns simultaneously the computational costs of the hessian formation and matrix solution remain manageable as the system size increases due to the sparsity of all tensor quantities likewise the total iterations for convergence scale well due to the local quadratic convergence of the generalized newton method we demonstrate the method with an inverted pendulum problem and a neuromuscular control problem with complex dynamics and 18 forcing functions the optimal control solutions are successfully found in both examples we obtain quadratic convergence rates in the neighbourhood of the solution copyright 2002 john wiley sons ltd

on syzygies of calabi yau varieties and varieties of general type abstract we establish projective normality property n p and effective very ampleness for line bundles on a calabi yau variety as well as for pluricanonical bundles of a variety of general type we also prove a result on the degrees of generators of canonical rings under the condition that the image of the canonical map has minimal degree

geometric properties of 2d and 3d unilateral large slip contact operators abstract in order to treat the unilateral frictionless large slip contact between a deformable body and a smooth rigid obstacle geometrical properties associated to smooth curves 2d and surfaces 3d are investigated starting from basic differential geometry properties of smooth 2d curves the kinematics of node to node or node to facet contact is generalized the projection of a potential contactor point striker on any parametrizable curve and its first variation are derived expressions for the contact gap and its first and second variations are then calculated to obtain force equilibrium conditions and associated consistent linearization these results are extended to 3d geometries intrinsic properties of smooth surfaces related to their first and second fundamental forms are introduced and serve to characterize the projection of a striker on the surface the signed contact gap and its first two variations are then expressed explicitly these results are specialized to the particular case where cubic hermite curves and surfaces are considered the resulting contact element features are illustrated with a hertz contact benchmark problem and with a 3d model of the human patella knee cap sliding over the femur during knee flexion

newton okounkov bodies on projective bundles over curves in this article we study newton okounkov bodies on projective vector bundles over curves inspired by wolfe s estimates used to compute the volume function on these varieties we compute all newton okounkov bodies with respect to linear flags moreover we characterize semi stable vector bundles over curves via newton okounkov bodies

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

applying nagata patches to smooth discretized surfaces used in 3d frictional contact problems the accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved this paper presents a smoothing method applicable to 3d contact surfaces discretized with an arbitrary mesh topology the quadratic nagata patch interpolation is adopted to define the smooth surface the resulting contact surface passes through all nodes of the mesh while providing a smooth description with at least g 1 continuity at the nodes and quasi g 1 continuity between the patches thus the proposed method avoids the non physical oscillations in the contact force which are induced by the traditionally used faceted contact surfaces description when slave nodes slide over several master segments moreover it allows the accurate evaluation of kinematic variables leading to important improvements in terms of convergence rate within the newton raphson iteration loop the developed global and local contact search algorithms designed for contact surfaces described by nagata patches are described in detail three numerical examples were selected to illustrate the advantages of the proposed smoothing method including a complex industrial example of sheet metal forming process the results show the significant improvements attained with the proposed approach in terms of efficiency robustness and accuracy when compared with the traditional faceted contact surfaces description 2014 published by elsevier b v

singular riccati equations stabilizing large scale systems in this paper we discuss the convergence of a stabilization algorithm based on a singular version of the discrete riccati difference equation this method is particularly appealing for large scale linear time invariant dynamical systems since one can nicely exploit the sparsity of such systems in order to reduce the complexity of the algorithm

normal presentation on elliptic ruled surfaces from the introduction let x be an irreducible projective variety and l a very ample lline bundle on x whose complete linear series defines l x p h0 l let s 1 m 0 smh0 x l and let r l l1 n 0 h0 x l n be the homogeneous coordinate ring associated to l then r is a finitely generated graded module over s so it has a minimal graded free resolution we say that the line bundle l is normally generated if the natural maps smh0 x l h0 x l m are surjective for all m 2 if l is normally generated then we say that l satisfies property np if the matrices in the free resolution of r over s have linear entries until the p th stage in particular property n1 says that the homogeneous ideal i of x in p h0 l is generated by quadrics a line bundle satisfying property n1 is also called normally presented let r kr1r2 be a graded algebra over a field k the algebra r is a koszul ring iff torri k k has pure degree i for all i in this article we determine exactly theorem 4 2 which line bundles on an elliptic ruled surface x are normally presented as a corollary we show that mukai s conjecture is true for the normal presentation of the adjoint linear series for an elliptic ruled surface in section 5 of this article we show that if l is normally presented on x then the homogeneous coordinate ring associated to l is koszul we also give a new proof of the following result due to butler if deg l 2g 2 on a curve x of genus g then l embeds x with koszul homogeneous coordinate ring

on higher syzygies of ruled surfaces we study higher syzygies of a ruled surface x over a curve of genus g with the numerical invariant e let l picx be a line bundle in the numerical class of ac 0 bf we prove that for 0 2g 1 p by using these facts we obtain mukai type results for ample line bundles at we show that k x a 1 a q satisfies property np when 0 e g 3 2 and q g 2e 1 p or when e g 3 2 and g p 4 therefore we prove mukai s conjecture for ruled surface with e g 3 2 we also prove that when x is an elliptic ruled surface with e 0 l satisfies property n p if and only if a 1 and b ae 3 p

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

numerical aspects of different kalman filter implementations a theoretical analysis is made of the error propagation due to numerical roundoff for four different kalman filter implementations the conventional kalman filter the square root covariance filter the square root information filter and the chandrasekhar square root filter an experimental analysis is performed to validate the new insights gained by the theoretical analysis

a contact finite element formulation for biological soft hydrated tissues as part of the highly complex numerical simulation of human joints a finite element formulation for contact between layers of articular cartilage has been developed a biphasic description of the cartilage is used where the material is considered to be a porous permeable solid matrix with fluid flowing through it governing equations and contact boundary conditions are summarized for this material before developing the finite element formulation from a galerkin weighted residual statement lagrange multipliers are introduced to enforce the two kinetic continuity equations across the contact surface and an iterative scheme is employed to determine the current contact area numerical examples are presented which demonstrate both that the appropriate continuity across the contact surface is enforced and that the contact surface definition is accurate

a cell based smoothed finite element method for multi body contact analysis using linear complementarity formulation abstract in this paper the cell based smoothed finite element using quadrilateral elements cs fem is used for 2d contact problems which are converted into linear complementarity problems lcps which can be solved efficiently using the lemke method the modified coulomb friction contact model with tangential strength and normal adhesion is considered which models sticking slipping contacting departing and bonding debonding processes in a unified formulation smoothed galerkin weak form with contact boundary is deduced in which the stiffness is implemented using the cs fem with 1 smoothing domain 1sd 2sd 3sd 4sd 8sd and 16sd for each element contact interface equations are discretized through contact point pairs that are constructed using a master slave surface algorithm intensive numerical examples are given to investigate the effects of contact parameters on contact behaviors and examine the effectiveness of the proposed approach the numerical results of cs fem models are compared with that of fem q4 model which demonstrates that all cs fem models are softer than fem q4 model the strain energy solutions obtained using several cs fem models are monotonically decreasing with the number of the sds for each element increasing the upper bound solutions in strain energy can be obtained using a cs fem 1sd model in our examples while the lower bound solutions are obtained using cs fem 16sd model or fem q4 with fem q4 solution being the lowest

a dynamic lagrangian frequency time method for the vibration of dry friction damped systems abstract a new frequency time domain procedure the dynamic lagrangian mixed frequency time method dlft is proposed to calculate the non linear steady state response to periodic excitation of structural systems subject to dry friction damping in this formulation the dynamic lagrangians are defined as the non linear contact forces obtained from the equations of motion in the frequency domain with the adjunction of a penalization on the difference between the interface displacements calculate by the non linear solver in the frequency domain and those calculated in the time domain from the non linear contact forces thus accounting for coulomb friction and non penetration conditions the dynamic lagrangians allow one to solve for the non linear forces between two points in contact without using artifacts such as springs the new dlft method is thus particularly well suited to handling finite element models of structures in frictional contact as it does not require a special model for the contact interface dynamic lagrangians are also better suited to frequency domain friction problems than the traditional time domain method of augmented lagrangians furthermore a reduction of the non linear system to relative interface displacements is introduced to decrease the computation time the dlft method is validated for a beam in contact with a flexible dry friction element connected to ground for frictional constraints that feature two dimensional relative motion results are also obtained for a large scale structural system with a large number of one dimensional dry friction dampers the dlft method is shown to be accurate and fast and it does not suffer from convergence problems at least in the examples studied

smooth c1 interpolations for two dimensional frictional contact problems finite deformation contact problems are associated with large sliding in the contact area thus in the discrete problem a slave node can slide over several master segments standard contact formulations of surfaces discretized by low order finite elements leads to sudden changes in the surface normal field this can cause loss of convergence properties in the solution procedure and furthermore may initiate jumps in the velocity field in dynamic solutions furthermore non smooth contact discretizations can lead to incorrect results in special cases where a good approximation of the contacting surfaces is needed in this paper a smooth contact discretization is developed which circumvents most of the aformentioned problems a smooth deformed surface with no slope discontinuities between segments is obtained by a c1 continuous interpolation of the master surface different forms of discretizations are possible among these are bezier hermitian or other types of spline interpolations in this paper we compare two formulations which can be used to obtain smooth normal and tangent fields for frictional contact of deformable bodies the formulation is developed for two dimensional applications and includes finite deformation behaviour examples show the performance of the new discretization technique for contact copyright 2001 john wiley sons ltd

conservative discretization of contact impact problems for nearly rigid bodies abstract a discretization scheme for contact impact problems related to modeling of gears is proposed the problem is first discretized in time and then a variational formulation for the resulted one step problem is developed a finite element discretization completes the discretization process the scheme is a reinterpretation of the general simo laursen chavla algorithm in the context of the rigid body motion superimposed with small elastic deformation it conserves precisely the linear momentum and total energy and approximately the angular momentum the discretization method is illustrated with two numerical examples the standard 1d impact problem for an elastic rod and a 2d model problem of an elastic wheel bouncing within a constraining box

contact treatment in isogeometric analysis with nurbs abstract we study nurbs based isogeometric analysis of contact problems and compare with standard c 0 continuous lagrange finite elements a knot to surface kts algorithm is developed to treat the contact constraints with nurbs contact surface discretizations qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems quantitative studies based on the hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard kts approach the improved mortar based kts algorithm delivers robust and accurate results for nurbs discretizations based on numerical examples we conclude that nurbs based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over c 0 continuous finite elements

an augmented lagrangian technique combined with a mortar algorithm for modelling mechanical contact problems summary a finite element formulation for three dimensional 3d contact mechanics using a mortar algorithm combined with a mixed penalty duality formulation from an augmented lagrangian approach is presented in this method no penalty parameter is introduced for the regularisation of the contact problem the contact approach based on the mortar method gives a smooth representation of the contact forces across the bodies interface and can be used in arbitrarily curved 3d configurations the projection surface used for integrating the equations is built using a local cartesian basis defined in each contact element a unit normal to the contact surface is defined locally at each element simplifying the implementation and linearisation of the equations the displayed examples show that the algorithm verifies the contact patch tests exactly and is applicable to large displacements problems with large sliding motions copyright 2012 john wiley sons ltd

some effects of property n p on the higher normality and defining equations of nonlinearly normal varieties for a smooth projective variety x p embedded by the complete linear system property np has been studied for a long time 5 11 12 10 etc on the other hand castelnuovo mumford regularity conjecture and related problems have been focused for a projective variety which is not necessarily linearly normal 2 13 15 17 20 etc this paper aims to explain the influence of property np on higher normality and defining equations of a smooth variety embedded by sub linear system also we prove a claim about property np of surface scrolls which is a generalization of green s work in 11 about property np for curves

a complementary energy formulation of no tension masonry like solids in the present work a complementary energy formulation for the solution of the static equilibrium problem of no tension solids is presented the main feature of the work is systematic use of the augmented lagrangian approach for the regularisation of the nonsmooth and nondifferentiable anelastic deformation potential the proposed formulation is applied to derive a finite element formulation using the subspace of the self equilibrated stresses as primal variables the code implements the augmented lagrangian algorithm for the determination of the inelastic deformations some numerical examples are included to illustrate the performance of the proposed approach