multicriteria planar location problems abstract given q different objective functions three types of single facility problems are considered lexicographic pareto and max ordering problems after discussing the interrelation between the problem types a complete characterization of lexicographic locations and some instances of pareto and max ordering locations is given the characterizations result in efficient solution algorithms for finding these locations the paper relies heavily on the theory of restricted locations developed by the same authors and can be further extended for instance to multi facility problems with several objectives the proposed approach is more general than previously published results on multicriteria planar location problems and is particularly suited for modelling real world problems

an algorithm for a constrained weber problem we present an algorithm for solving the weber problem when the set of feasible locations is the union of a finite number of convex polygons

the regularization method for an obstacle problem we give a relatively complete analysis for the regularization method which is usually used in solving non differentiable minimization problems the model problem considered in the paper is an obstacle problem in addition to the usual convergence result and a priori error estimates we provide a posteriori error estimates which are highly desired for practical implementation of the regularization method

quantitative error estimate in modeling the laminar stationary flow of a bingham fluid we present a quantitative a posteriori error estimate when the linear laminar stationary flow of a bingham fluid in a cylindrical pipe is modeled as a newtonian fluid the estimate is proved by using a complementary variational principle for the bingham fluid flow examples show that the estimate is effective

combinatorial algorithms for some 1 facility median problems in the plane abstract facility location problems in the plane are widely used tools of operations research in modeling real world problems in many of these problems restrictions have to be considered which correspond to regions in which a placement of new locations is forbidden this paper investigates restrictions in 1 facility median problems in the plane we introduce efficient algorithms for problems where the unrestricted problem can be solved in polynomial time the algorithms are of a combinatorial nature and reduce the search for an optimal solution of the restricted problem to a finite number of candidates the assumptions on the model are very weak we only require that the forbidden area is a union of pairwise disjoint convex sets

qualitative and numerical analysis of quasi static problems in elastoplasticity the quasi static problem of elastoplasticity with combined kinematic isotropic hardening is formulated as a time dependent variational inequality vi of the mixed kind that is it is an inequality involving a nondifferentiable functional and is imposed on a subset of a space this vi differs from the standard parabolic vi in that time derivatives of the unknown variable occur in all of its terms the problem is shown to possess a unique solution we consider two types of approximations to the vi corresponding to the quasi static problem of elastoplasticity semidiscrete approximations in which only the spatial domain is discretized by finite elements and fully discrete approximations in which the spatial domain is again discretized by finite elements and the temporal domain is discretized and the time derivative appearing in the vi is approximated in an appropriate way estimates of the errors inherent in the above two types of approximations in suitable sobolev norms are obtained for the quasi static problem of elastoplasticity in particular these estimates express rates of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and where appropriate of the time step size k a major difficulty in solving the problems is caused by the presence of the nondifferentiable terms we consider some regularization techniques for overcoming the difficulty besides the usual convergence estimates we also provide a posteriori error estimates which enable us to estimate the error by using only the solution of a regularized problem

a method for convex curve approximation abstract in this paper a new sandwich method is introduced to approximate a convex curve in r2 this method requires only function evaluation and the solution of a number of scalar optimization problems a quadratic convergence property of the method is established that is the total number of optimization problems solved is bounded by a constant multiple of the square root of the inverse of the given error an application to approximation of the efficient frontier of a bi criteria convex quadratic network program is given

approximation methods for non convex curves based on the triangle sandwich and block sandwich methods two approximation methods for non convex curves are considered in this paper numerical algorithms corresponding to these methods are developed and quadratic convergence properties of two methods in the original space are established application is given to the approximation of an efficient frontier of a bi criteria optimization problem

on the use of the varignon frame for single facility weber problems in the presence of convex barriers abstract this paper presents a new experimental approach to the weber problem in the presence of convex barriers by using the varignon frame the varignon frame is a mechanical system of strings weights and a board with holes that has been used to identify an optimal location for the classical weber problem we show through analytical results that the same analog can also be used for some of the weber problems in the presence of barriers some examples from the literature are revisited through experiments findings are compared to those found in the literature practical use of the analog is discussed as it provides rapid solutions allows for flexibility and enables one to visualize the problem

an efficient solution method for weber problems with barriers based on genetic algorithms in this paper we consider the problem of locating one new facility with respect to a given set of existing facilities in the plane and in the presence of convex polyhedral barriers it is assumed that a barrier is a region where neither facility location nor travelling are permitted the resulting non convex optimization problem can be reduced to a finite series of convex subproblems which can be solved by the weiszfeld algorithm in case of the weber objective function and euclidean distances a solution method is presented that by iteratively executing a genetic algorithm for the selection of subproblems quickly finds a solution of the global problem visibility arguments are used to reduce the number of subproblems that need to be considered and numerical examples are presented

on an elastic plastic problem etude d un probleme elastoplastique de valeur limite quasi statique pour des corps pouvant etre discretement heterogenes et elastiquement anisotropes dont le comportement plastique est regi par des fonctions de deformation lineaires par morceaux dependantes de l histoire du materiau et par des lois de durcissement couplees existence unicite et regularite d une solution faible convergence des solutions d elements finis

topology optimization of incompressible media using mixed finite elements abstract we present an alternative formulation for the topology optimization of structures made of incompressible materials a topic that cannot be tackled using most of the approaches of the current literature that are mainly based on displacement finite elements that are well known to be affected by the locking phenomenon a way out of the problem has recently been proposed in sigmund and clausen 2007 o sigmund p m clausen topology optimization using a mixed formulation an alternative way to solve pressure load problems comput methods appl mech engrg 196 13 16 2007 1874 1889 based on a displacement pressure finite element discretization the approach presented here consists in a truly mixed variational formulation coupled to a mixed fem discretization that uses the composite element of johnson and mercier for the discretization of the stress field by so doing the continuous and discrete inf sup conditions of the problem are automatically met even in the presence of incompressible materials a few numerical studies are presented to validate the theoretical framework for which the well known method of moving asymptotes mma is adopted for the numerical optimization of the problem different topologies in plane stress and plane strain conditions are presented with particular attention to the convergence of the last ones to pure 0 1 designs some forthcoming investigations are eventually highlighted including the solution of stress constrained topology optimization problems that find in the truly mixed setting their natural environment and the extension of the present formulation to deal with pressure load structural problems

a convergence analysis of a p version finite element method for one dimensional elastoplasticity problem with constitutive laws based on the gauge function method in this paper we will give a p version finite element method for the one dimensional nonlinear elastoplasticity problem a family of admissible constitutive laws based on the so called gauge function method is introduced first and then a p version semi discretization scheme is presented we show that the existence and uniqueness of the solution for the semi discrete problem can be guaranteed by using some special properties of the constitutive law finally we show that as the polynomial degree of the elements bf p to infty oo the solution of the semi discrete problem will converge to the solution of the continuous problem the p version convergence analysis given here is only for one dimensional problems with a linear hardening constitutive law hypothesis however it also gives us a very useful idea for the study of the hp version finite element method for the one dimensional problem with more general constitutive laws or even two dimensional problems

multiobjective solution of the uncapacitated plant location problem abstract in this paper we consider the discrete multiobjective uncapacitated plant location problem we present an exact and an approximate approach to obtain the set of non dominated solutions the two approaches resort to dynamic programming to generate in an efficient way the non dominated solution sets the solution methods that solve the problems associated with the generated states are based on the decomposition of the problem on two nested subproblems we define lower and upper bound sets that lead to elimination tests that have shown to have a high performance computational experiments on a set of test problems show the good performance of the proposal

on the uniqueness of optimal solutions in continuous location theory abstract this paper deals with the uniqueness of an optimal solution in general continuous single facility minisum and minimax location problems we define the concept of an s norm and obtain general conditions which guarantee the existence of a unique optimal location some consequences for the uniqueness of optimal locations in multi facility location problems are discussed

analysis of the brezzi pitkaranta stabilized galerkin scheme for creeping flows of bingham fluids in this paper we propose and analyze a finite element scheme for a class of variational nonlinear and nondifferentiable mixed inequalities including balance equations governing incompressible creeping flows of bingham fluids for numerical efficiency reasons equal order piecewise linear approximations are used for both velocity and pressure and the numerical scheme is stabilized by a brezzi pitkaranta perturbation term we obtain error estimates of the same order as for stable discretizations namely h1 2 for velocity and pressure solutions in htwod and hun respectively a decomposition coordination algorithm to solve the discrete nonlinear algebraic system is presented together with its convergence properties finally numerical tests are performed the solution of the problem under consideration presents particular regularity properties that are shown to permit convergence order improvement to h log h 1 2 this estimate is confirmed by numerical results

approximation of convex curves with application to the bicriterial minimum cost flow problem abstract an approximation of an explicity or implicity given convex curve in the plane is given by two piecewise linear outer and inner curves to compute these three rules for choosing the supporting points are proposed and it is shown for two of them that the projective distance between inner and outer approximation decreases quadratically with the number of supporting points this method is applied to approximate the efficient point curve of the bicriterial minimum cost flow problem which is a piecewise linear convex curve that may have an exponential number of breakpoints in the worst case

restricted center problems under polyhedral gauges abstract given a finite set ex ex 1 ex 2 ex m in the plane and a forbidden region r we want to find a point x r such that max m 1 m w m m x ex m is minimized this is a variant of the well known continuous center problem where we measure the distance with polyhedral gauges the unit ball of a polyhedral gauge may be any convex polyhedron containing the origin in its interior this large class of distance functions allows very general practical settings such as asymmetry to be modeled each ex m is allowed to have its own gauge m and the forbidden region r enables us to include negative information which means defining the infeasible region explicitly instead of the feasible region in the model efficient algorithms and structural properties for this non convex optimization problem based on combinatorial and geometrical methods are presented a classification scheme for location problems is also introduced

variational principles and convergence of finite element approximations of a holonomic elastic plastic problem it is shown that a boundary value problem based on a holonomic elastic plastic constitutive law may be formulated equivalently as a variational inequality of the second kind a regularised form of the problem is analysed and finite element approximations are considered it is shown that solutions based on finite element approximation of the regularised problem converge

the shift operator technique for so 7 in an su 2 3 basis ii applications reduced matrix elements of the tensor operator which forms part of so 7 generator basis are calculated for the three respective classes of so 7 representations v 0 0 v n0 v 0 1 v n0 0 0 v v n0 the calculation is based on the relations between quadratic products of shift operators established in a previous paper by the same authors

a quasistatic frictional problem with normal compliance a friction and contact problem will be considered for an elastic solid body which under the influence of volume and surface forces is in contact with a rigid foundation

facility location in the presence of forbidden regions i formulation and the case of euclidean distance with one forbidden circle abstract a constrained form of the weber problem is formulated in which no path is permitted to enter a prespecified forbidden region r of the plane using the calculus of variations the shortest path between two points x y r which does not intersect r is determined if d x y is unconstrained distance we denote the shortes distance along a feasible path by d x y the constrained weber problem is then given points x j r and positive weights wj j 1 2 n find a point x r such that f x n j 1 d x x j is a minimum an algorithm is formulated for the solution of this problem when d x y is euclidean distance and r is a single circular region numerical results are presented

a new fixed point algorithm for hardening plasticity based on non linear mixed variational inequalities moving from the seminal papers of han and reddy we propose a fixed point algorithm for the solution of hardening plasticity two dimensional problems the continuous problem may be classified as a mixed non linear non differentiable variational inequality of the second type and is discretized by means of a truly mixed finite element scheme one of the main peculiarities of our approach is the use of the composite triangular element of johnson and mercier for the approximation of the stress field the non differentiability is coped with via regularization whereas the non linearity is approached with a fixed point iterative strategy numerical results are proposed that investigate the sensitivity of the approach with respect to the mesh size and the regularization parameter e the simplicity of the proposed fixed point scheme with respect to more classical return mapping approaches seems to represent one of the key features of our algorithm copyright 2003 john wiley sons ltd

locating least distant lines in the plane in this paper we deal with locating a line in a plane given a set of existing facilities represented by points in the plane our objective is to find a straight line l minimizing the sum of weighted distances to the existing facilities or minimizing the maximum weighted distance to the existing facilities respectively we show that for all distance measures derived from norms one of the lines minimizing the sum objective contains at least two of the existing facilities for the center objective we always get an optimal line which is at maximum distance from at least three of the existing facilities if all weights are equal there is an optimal line which is parallel to one facet of the convex hull of the existing facilities

an optimal algorithm for intersecting line segments in the plane the main contribution of this work is an o n log n k time algorithm for computing all k intersections among n line segments in the plane this time complexity is easily shown to be optimal within the same asymptotic cost our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment if any lies right above or below each intersection and each endpoint the algorithm has been implemented and performs very well the storage requirement is on the order of n k in the worst case but it is considerably lower in practice to analyze the complexity of the algorithm an amortization argument based on a new combinatorial theorem on line arrangements is used

the maximin line problem with regional demand abstract given a family p p 1 p m of m polygonal regions possibly intersecting in the plane we consider the problem of locating a straight line l intersecting the convex hull of p and such that mink d pk l is maximal we give an algorithm that solves the problem in time o m2 n log m log n using o m2 n space where n is the total number of vertices of p1 pm the previous best running time for this problem was o n2 j janardan f p preparata widest corridor problems nordic journal of computing 1 1994 231 245 we also improve the known complexity for several variants of this problem which include a three dimensional version the maximin plane problem the weighted problem and considering measuring distance different to the euclidean one

extremum properties of finite step solutions in elastoplasticity with nonlinear mixed hardening abstract the class of elastic plastic constitutive laws assumed herein can be described as follows we envisage y 1 yield criteria or modes which define the current yield surface each yield function consists of two addends an effective stress and a yield limit y 1 y the former is an order one positively homogeneous function of the difference between the stresses ii and reference stresses ii which are generally nonlinear functional of the plastic strain history so that kinematic hardening is accounted for the yield limit y is generally a nonlinear function of y nondecreasing internal variables so that another hardening mechanism which may reduce to isotropic hardening is accommodated in the model the rates of these variables play the role of plastic multipliers in the flow rule a finite step in the geometrically linear evolutive analysis of such solids is defined according to the backward difference or stepwise holonomic strategy for approximate time integration for the finite step boundary value problem thus arising various extremum characterizations of solutions are established and the underlying constitutive restrictions are pointed out and discussed

an adaptive finite element method for bingham fluid flows around a cylinder the numerical modeling of the steady flow of a yield stress fluid around a cylinder is presented three categories of yielded regions are exhibited the asymptotic behavior when the cylinder gets close to the wall is investigated the resolution of variational inequalities describing the flow is based on the augmented lagrangian method and a mixed finite element method the localization of yield surfaces is approximated by an anisotropic auto adaptive mesh procedure

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

constrained anisotropic elastic materials in unilateral contact with or without friction we consider time independent problems of linear homogeneous anisotropic elasticiy for materials with internal constraints that are in frictional or frictionless contact with a rigid support

a numerical study of holonomic approximations to problems in plasticity the incremental holonomic boundary value problem in elastoplasticity has been shown to be characterized by a variational inequality the problem may be approximated however by a perturbed minimization problem characterized by a variational equality this formulation is used as the basis for constructing finite element approximations of the original boundary value problem leading to a system of non linear algebraic equations procedures for solving these equations are described and numerical results are presented and compared with those obtained using a conventional approach

placing a finite size facility with a center objective on a rectangular plane with barriers abstract this paper addresses the finite size 1 center placement problem on a rectangular plane in the presence of barriers barriers are regions in which both facility location and travel through are prohibited the feasible region for facility placement is subdivided into cells along the lines of larson and sadiq r c larson g sadiq facility locations with the manhattan metric in the presence of barriers to travel operations research 31 4 1983 652 669 to overcome complications induced by the center minimax objective we analyze the resultant cells based on the cell corners we study the problem when the facility orientation is known a priori we obtain domination results when the facility is fully contained inside 1 2 and 3 cornered cells for full containment in a 4 cornered cell we formulate the problem as a linear program however when the facility intersects gridlines analytical representation of the distance functions becomes challenging we study the difficulties of this case and formulate our problem as a linear or nonlinear program depending on whether the feasible region is convex or nonconvex an analysis of the solution complexity is presented along with an illustrative numerical example

a variational theory for finite step elasto plastic problems abstract an extended version ofgeneralized standard elasto plastic material is considered in the framework of an internal variable theory of associated plasticity according to a backward difference scheme for time integration of the flow rule a finite step structural problem is formulated in a geometrically linear range convex analysis and a brand new potential theory for monotone multivalued operators are shown to provide the natural mathematical setting for the derivation of the related variational formulation a general stationarity principle is obtained and then specialized to obtain a minimum principle in terms of displacements plastic strains and internal variables a critical comparison with an analogous minimum principle recently proposed in literature is performed showing the inadequacy of classical procedures in deriving non smooth variational formulations

an output sensitive algorithm for computing visibility the visibility graph of a set of nonintersecting polygonal obstacles in the plane is an undirected graph whose vertex set consists of the vertices of the obstacles and whose edges are pairs of vertices u v such that the open line segment between u and v does not intersect any of the obstacles the visibility graph is an important combinatorial structure in computational geometry and is used in applications such as solving visibility problems and computing shortest paths this paper presents an algorithm that computes the visibility graph of a set of obstacles in time o e n log n where e is the number of edges in the visibility graph and n is the total number of vertices in all the obstacles

a prange hellinger reissner type finite element formulation for small strain elasto plasticity abstract in this contribution we propose a mixed variational formulation of the prange hellinger reissner type for elasto plasticity at small strains here the displacements and the stresses are interpolated independently which are balanced within the variational functional by the relation of the elastic strains and the partial derivative of the complementary stored energy with respect to the stresses for the elasto plastic material behavior a von mises yield criterion is considered where we restrict ourselves w l o g to linear isotropic hardening in the proposed formulation we enforce the constraints arising from plasticity point wise in contrast to the element wise realization of the plastic return mapping algorithm suggested in simo et al 1989 the performance of the new formulation is demonstrated by the analysis of several benchmark problems here we compare the point wise treatment of elasto plasticity with the original element wise formulation of simo et al 1989 furthermore we derive an algorithmic consistent treatment for plane stress as well as for plane strain condition

a projected weiszfeld algorithm for the box constrained weber location problem abstract the weber problem consists of finding a point in r n that minimizes the weighted sum of distances from m points in r n that are not collinear an application that motivated this problem is the optimal location of facilities in the 2 dimensional case a classical method to solve the weber problem proposed by weiszfeld in 1937 is based on a fixed point iteration in this work we generalize the weber location problem considering box constraints we propose a fixed point iteration with projections on the constraints and demonstrate descending properties it is also proved that the limit of the sequence generated by the method is a feasible point and satisfies the kkt optimality conditions numerical experiments are presented to validate the theoretical results

finding shortest paths in the plane in the presence of barriers to travel for any lp norm abstract this paper develops an efficient algorithm for the computation of the shortest paths between given sets of points origins and destinations in the plane when these paths are constrained not to cross any of a finite set of polygonal open or closed barriers it is proved that when distances are measured by an 1p norm with 1 it is also shown that optimal solutions when distances are measured according to the rectilinear or max norm i e lp norm with p 1 or p can be deduced from the results of the algorithm

a bi objective median location problem with a line barrier the multiple objective median problem momp involves locating a new facility with respect to a given set of existing facilities so that a vector of performance criteria is optimized a variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier such barriers like rivers highways borders or mountain ranges are frequently encountered in practice in this paper theory of an momp with line barriers is developed as this problem is nonconvex but specially structured a reduction to a series of convex optimization problems is proposed the general results lead to a polynomial algorithm for finding the set of efficient solutions the algorithm is proposed for bicriteria problems with different measures of distance

a family of higher order mixed finite element methods for plane elasticity the dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the raviart thomas mixed finite elements for a scalar second order elliptic equation estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inl 2 and optimal order negative norm estimates are obtained inh s for a range ofs depending on the index of the finite element space an optimal order estimate inl for the displacement error is given also a quasioptimal estimate is derived in an appropriate space all estimates are valid uniformly with respect to the compressibility and apply in the incompressible case the formulation of the elements is presented in detail

modeling cohesive crack growth via a truly mixed formulation an alternative approach for cohesive crack growth in elastic media is proposed standard methods move from displacement based formulations that are enriched to handle discontinuities in the inherently continuous displacement field the herein adopted formulation is conversely based on a truly mixed discretization that has stresses as main regular variables while discontinuous displacements play the role of lagrangian multipliers the approach directly handles the analysis of propagating cohesive cracks in elastic media through the appropriate inclusion of interface energy terms that enrich the formulation when a crack is growing notably no edge element is introduced but simply the inherent discontinuity of the displacement field is taken advantage of furthermore the continuity of traction vectors is imposed in an exact fashion within the formulation and not as an additional weak constraint as classically done the work has the main aim of investigating the features of the approach through numerical simulations that refer to well known experimental results on concrete specimens the capability of modeling size effect is firstly tested in case of a pure mode i growth the accuracy of truly mixed stress interpolation is also exploited to recover crack path and to handle energy dissipation in mixed mode simulations

the variational formulation and solution of problems of finite strain elastoplasticity based on the use of a dissipation function the solution of initial boundary value problems involving finite elastoplastic deformations is discussed the formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function a generalized midpoint rule is used to obtain an incremental problem a variational form of which is derived the finite element method is used for spatial discretization and an algorithm to solve the resulting discrete problem is developed this algorithm has the predictor corrector structure common to most solution procedures for problems in plasticity methods for imposing the plastic incompressibility constraint are investigated solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors

on the finite element method for mixed variational inequalities arising in elastoplasticity we analyze the finite element method for a class of mixed variational inequalities of the second kind which arises in elastoplastic problems an abstract variational inequality of which the elast

a reduction result for location problems with polyhedral barriers abstract in this paper we consider the problem of locating one new facility in the plane with respect to a given set of existing facilities where a set of polyhedral barriers restricts traveling this non convex optimization problem can be reduced to a finite set of convex subproblems if the objective function is a convex function of the travel distances between the new and the existing facilities like e g the median and center objective functions an exact algorithm and a heuristic solution procedure based on this reduction result are developed

gbsss the generalized big square small square method for planar single facility location abstract big square small square is a geometrical branch and bound algorithm devised by p hansen et al or 33 1251 1265 for the solution of constrained planar minisum single facility location problems with l p norms and continuous non decreasing costfunctions the method basically works by splitting the studied planar region into squares and either rejecting or further processing these squares by the evaluation of a lower bound we present a modified version of this algorithm aimed at correcting a small failure to converge accelerating the calculations minimising the information to be stored and most importantly determining a region of near optimality furthermore the method is applicable to any planar single facility problem with distances measured by mixed norms and as an objective any continuous function of the distances this includes nearly all the models which have been proposed in the literature

on the construction of optimal mixed finite element methods for the linear elasticity problem the mixed finite element method for the linear elasticity problem is considered we propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement the ideas are applied in some examples

so 2n 1 in an so 2n 3 su 2 su 2 basis ii detailed study of the symmetric representations of the so 7 group for pt i see ibid vol 15 p 2665 76 1982 the so 7 down arrow su 2 3 reduction is analysed in detail explicit forms for the different su 2 generators and the remaining ones are derived using the results of the previous paper basis states describing the symmetric irreducible unitary representations are introduced expressions for the reduced matrix elements of the occurring generators with respect to these basis states are determined

on a class of spinor representations of so 7 the reduction of the irreducible representations v 0 0 1 of so 2n 1 with respect to su 2 su 2 so 2n 3 is considered for the n 3 case all the reduced matrix elements of the so 7 generators in the su 2 2 so 3 basis are calculated with the use of recursion relations

analysis of some mixed finite element methods for plane elasticity equations we analyze some mixed finite element methods based on rectangular elements for solving the two dimensional elasticity equations we prove error estimates for a method proposed by taylor and zienkiewicz and for some new variants of the known equilibrium methods a numerical example is given demonstrating the performance of the various algorithms considered 1 introduction in the numerical solution of problems of continuum mechanics the stresses are normally of primary interest in the elastic region it is therefore natural to design the numerical algorithms so that the stresses can be obtained directly without first computing the displacements such methods can be derived from the dual variational formulation of the elasticity problem the corresponding finite element algorithms are usually formulated as mixed methods where both the displacements and the stresses are first approximated and the displacements are then eliminated from the discrete equations in many cases the elimination can be rather effectively done using penalty perturbation techniques or their iterative variants cf 3 11 12 the best known finite element methods of the above type are the so called equilibrium methods first proposed by fraejis de veubeke 17 cf also 14 16 18 and analyzed theoretically by johnson and mercier 9 cf also 8 in these methods one uses specific composite elements which allow the equilibrium condi tion between the stresses and the volume load to be satisfied exactly in the case where the volume load is zero

an efficient algorithm for facility location in the presence of forbidden regions abstract this paper investigates a constrained form of the classical weber problem specifically we consider the problem of locating a new facility in the presence of convex polygonal forbidden regions such that the sum of the weighted distances from the new facility to n existing facilities is minimized it is assumed that a forbidden region is an area in the plane where travel and facility location are not permitted and that distance is measured using the euclidean distance metric a solution procedure for this nonconvex programming problem is presented it is shown that by iteratively solving a series of unconstrained problems this procedure terminates at a local optimum to the original constrained problem numerical examples are presented

algebraic properties of location problems with one circular barrier abstract the consideration of barriers to travel plays an increasingly important role in the transportation and location literature in one of the classical papers on location problems with barriers katz and cooper eur j oper res 6 1981 166 considered the weber problem often also referred to as median problem with one circular barrier region considering the same problem we develop new structural results showing that the set of feasible solutions can be subdivided into a polynomial number of cells of algebraic invariance on every convex subset of which the generally non convex objective function is convex these results imply improved exact and heuristic solution procedures based on convex optimization methods

finite element analysis of a holonomic elastic plastic problem a thorough analysis of the finite element method is given for a holonomic elastic plastic problem an inequality of the cea s lemma type is proved which is the basis of error estimates for various finite element solutions difficulty caused by a non differentiable term in the problem can be overcome by using two convergent procedures an iterative procedure and a regularization procedure an a posteriori quantitative error estimate is derived for the regularized solution

fuzzy group decision making for facility location selection the selection of a facility location among alternative locations is a multicriteria decision making problem including both quantitative and qualitative criteria the conventional approaches to facility location problem tend to be less effective in dealing with the imprecise or vagueness nature of the linguistic assessment under many situations the values of the qualitative criteria are often imprecisely defined for the decision makers the aim of the paper is to solve facility location problems using different solution approaches of fuzzy multi attribute group decision making the paper includes four different fuzzy multi attribute group decision making approaches the first one is a fuzzy model of group decision proposed by blin the second is the fuzzy synthetic evaluation the third is yager s weighted goals method and the last one is fuzzy analytic hierarchy process although four approaches have the same objective of selecting the best facility location alternative they come from different theoretic backgrounds and relate differently to the discipline of multi attribute group decision making these approaches are extended to select the best facility location alternative by taking into account quantitative and qualitative criteria a short comparative analysis among the approaches and a numeric example to each approach are given

convergence of approximations to the primal problem in plasticity under conditions of minimal regularity this work considers semi and fully discrete approximations to the primal problem in elastoplasticity the unknowns are displacement and internal variables and the problem takes the form of an evolution variational inequality strong convergence of time discrete as well as spatially and fully discrete approximations is established without making any assumptions of regularity over and above those established in the proof of well posedness of this problem

so 2n 1 in an so 2n 3 su 2 su 2 basis i reduction of the symmetric representations the branching rule for the reduction of symmetric irreducible unitary representations iur of the simple lie group so 2n 1 into iur of its maximal subgroup so 2n 3 x su 2 x su 2 is established for all n or 3 after the particular case n 3 is analysed in detail a general proof is presented which is valid for all n or 3 all branching rules n 3 4 can be summed up in one formula also a dimension verification is carried out the generators of so 2n 1 not belonging to the semi simple subgroup can be combined into a mixed tensor spinor representation with respect to the simple groups which occur in the direct product the precise nature of that representation is indicated and discussed

a class of generalized mixed variational hemivariational inequalities i existence and uniqueness results abstract we investigate a generalized lagrange multiplier system in a banach space called a mixed variational hemivariational inequality mvhvi for short which contains a hemivariational inequality and a variational inequality first we employ the minty technique and a monotonicity argument to establish an equivalence theorem which provides three different equivalent formulations of the inequality problem without compactness for one of operators in the problem a general existence theorem for mvhvi is proved by using the fan knaster kuratowski mazurkiewicz principle combined with methods of nonsmooth analysis furthermore we demonstrate several crucial properties of the solution set to mvhvi which include boundedness convexity weak closedness and continuity finally a uniqueness result with respect to the first component of the solution for the inequality problem is proved by using the ladyzhenskaya babuska brezzi lbb condition all results are obtained in a general functional framework in reflexive banach spaces

a numerical analysis of a class of problems in elastodynamics with friction on utilise les methodes d elements finis pour analyser le comportement dynamique de corps lineairement elastiques ayant une partie de leurs frontieres soumise au frottement et a des tractions normales prescrites on etablit des estimations d erreur on presente un algorithme de resolution des problemes a deux dimensions et on decrit plusieurs essais numeriques

a new locking free equilibrium mixed element for plane elasticity with continuous displacement interpolation with reference to plane elastic problems we first show that using the johnson and mercier jm element c johnson b mercier numer math 30 1978 103 for the stresses and an h 1 piecewise linear interpolation for the displacements leads to a severe locking when the lamcoefficient k tends to infinity i e in the case of an incompressible material motivated by the need to have a continuous displacement field that emerges in several engineering applica tions we use an eigenvalue argument to prove that locking is due to the presence of the element average pressure among the degrees of freedom we therefore relax the incompressibility constraint by introducing a quadrilateral macroelement basically consisting of two adjacent jm triangles sharing the same average pressure in a sense switching from a locking t1p0 approximation to a locking free q1p0 numerical tests on the pathological cook cantilever are performed to assess the validity of the proposed approach in which comparisons between the newly devised element and the original jm element with l 2 displacements are presented 2001 published by elsevier science b v

dynamic plasticity models the evolution of an elastic plastic material is modeled as an initial boundary value problem consisting of the dynamic momentum equation coupled with a constitutive law for which the hysteretic dependence between stress and strain is described by a system of variational inequalities this system is posed as an evolution equation in hilbert space for which is proved the existence and uniqueness of three classes of solutions which are distinguished by their regularity

error bounds for the approximative solution of restricted planar location problems abstract facility location problems in the plane play an important role in mathematical programming when looking for new locations in modeling real world problems we are often confronted with forbidden regions that are not feasible for the placement of new locations furthermore these forbidden regions may have complicated shapes even if we require them to be convex it may be more useful or even necessary to use approximations of such forbidden regions when trying to solve location problems in this paper we develop error bounds for the approximative solution of restricted planar location problems using the so called sandwich algorithm the number of approximation steps required to achieve a specified error bound is analyzed as examples of these approximation schemes we discuss round norms and polyhedral norms computational tests are also included

an optimal adaptive algorithm for the approximation of concave functions motivated by the study of parametric convex programs we consider approximation of concave functions by piecewise affine functions using dynamic programming we derive a procedure for selecting the knots at which an oracle provides the function value and one supergradient the procedure is adaptive in that the choice of a knot is dependent on the choice of the previous knots it is also optimal in that the approximation error in the integral sense is minimized in the worst case

a new mixed formulation for elasticity we propose a new mixed variational formulation for the equations of linear elasticity it does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations

the minisum and minimax location problems revisited the minisum minimax problem consists of locating a single facility in the plane with the aim of minimizing the sum of the weighted distances the maximum weighted distance to m given points we present two solution methods for generalized versions of these problems in which i location is restricted to the union of a finite number of convex polygons ii distances are approximated by norms that may differ with the given points and iii transportation costs are increasing and continuous functions of distance computational experience is described

multiple objective minimum cost flow problems a review in this paper theory and algorithms for solving the multiple objective minimum cost flow problem are reviewed for both the continuous and integer case exact and approximation algorithms are presented in addition a section on compromise solutions summarizes corresponding results the reference list consists of all papers known to the authors which deal with the multiple objective minimum cost flow problem

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

the effect of transformations on the approximation of univariate convex functions with applications to pareto curves in the literature methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed we study the effect of the use of increasing convex or increasing concave transformations on the approximation of univariate convex functions in this paper we show that these transformations can be used to construct upper and lower bounds for nonconvex functions moreover we show that by using such transformations of the input variable or the output variable we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations we show that these transformations can be applied to the approximation of a convex pareto curve that is associated with a convex bi objective optimization problem

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

finding efficient solutions for rectilinear distance location problems efficiently abstract given n planar existing facility locations a planar new facility location x is called efficient if there is no other location y for which the rectilinear distance between y and each existing facility is at least as small as between x and each existing facility and strictly less for at least one existing facility rectilinear distances are typically used to measure travel distances between points via rectilinear aisles or street networks we first present a simple arrow algorithm based entirely on geometrical analysis that constructs all efficient locations we then present a row algorithm which is of order n log n that constructs all efficient locations and establish that no alternative algorithm can be of a lower order

nonlinear complementarity functions for plasticity problems with frictional contact in this paper a unifying framework for the numerical treatment of frictional contact in combination with elastoplasticity with hardening is presented both kinds of problems lead to the mathematical structure of variational inequalities which are discretized by introducing additional variables for the contact stresses or the deviatoric stresses leading to a mixed formulation by defining a family of nonlinear complementarity functions which can be applied to both frictional and plastic yield conditions these inequality constraints are reformulated as equalities combined with the equilibrium equations a system of nonlinear equations is obtained that is solved in terms of a semismooth newton method to obtain a larger domain of convergence and better stability properties the introduction of additional scaling parameters is motivated and their benefit to the convergence of the scheme is demonstrated due to the locality of the contact and plastic constraints the resulting method can be interpreted as a primal dual active set strategy furthermore for linear hardening laws our method is a generalization of the well known radial return algorithm which is obtained for a special suboptimal choice of the plastic scaling parameters the efficiency and the generality of the proposed quasi newton scheme is demonstrated by several numerical examples including the simulation of a three dimensional contact problem with several elastoplastic bodies exponential isotropic hardening and coulomb friction