an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

elastoplastic analysis by active macro zones with linear kinematic hardening and von mises materials in this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von mises materials under plane strain conditions is shown the proposed approach works with the symmetric galerkin boundary element method applied to multidomain problems using a mixed variables approach to obtain a more stringent solution the elastoplastic analysis is carried out as the response to the loads and the plastic strains the latter evaluated through the self equilibrium stress matrix this matrix is used both in the predictor phase for trial stress evaluation and in the corrector phase for solving a nonlinear global system which provides the elastoplastic solution of the active macro zones i e those zones collecting bem elements where the plastic consistency condition has been violated the simultaneous use of active macro zones gives rise to a nonlocal approach which is characterized by a large decrease in the plastic iteration number although the proposed strategy requires the inversion and updating of jacobian operators generally of big dimensions a strategy developed in order to reduce the computational efforts due to the use of this matrix in a recursive process is shown

a 3d finite element with planar symmetry for limit analysis computations abstract a formulation for finite element limit analysis of a certain class of 3d perfectly plastic solids governed by von mises plasticity condition is presented a planar symmetry constraint for both geometry and displacement field is assumed to analyze plane problems where the variable nature of transverse dissipation must be considered a mixed locking free and low distortion sensitive element is formulated on the basis of the natural approach the solution procedure exploits the kinematic theorem of limit analysis cast in the form of a minimum problem for a convex but non smooth dissipation functional applications to a notched specimen and to a bolted joint are presented to stress the importance of transverse effects in some problems commonly modeled as purely 2d

optimal circuits for parallel multipliers we present new design and analysis techniques for the synthesis of parallel multiplier circuits that have smaller predicted delay than the best current multipliers v g oklobdzija et al 1996 suggested a new approach the three dimensional method tdm for partial product reduction tree pprt design that produces multipliers that outperform the current best designs the goal of tdm is to produce a minimum delay pprt using full adders this is done by carefully modeling the relationship of the output delays to the input delays in an adder and then interconnecting the adders in a globally optimal way oklobdzija et al suggested a good heuristic for finding the optimal pprt but no proofs about the performance of this heuristic were given we provide a formal characterization of optimal pprt circuits and prove a number of properties about them for the problem of summing a set of input bits within the minimum delay we present an algorithm that produces a minimum delay circuit in time linear in the size of the inputs our techniques allow us to prove tight lower bounds on multiplier circuit delays these results are combined to create a program that finds optimal tdm multiplier designs using this program we can show that while the heuristic used by oklobdzija et al does not always find the optimal tdm circuit it performs very well in terms of overall pprt circuit delay however our search algorithms find better pprt circuits for reducing the delay of the entire multiplier

computation of limit loads for computing the collapse state of a perfect plastic continuum we suggest a mixed finite element approximation to the infinite dimensional mathematical programming problem of limit analysis the convergence of the limit load to the exact solution is discussed as well as solution methods for the discrete problem finally the method is applied to a classical problem in plane strain

an algorithm for shakedown analysis with nonlinear yield functions abstract this paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function firstly variational formulations for shakedown analysis of structures under variable loads are considered secondly the corresponding discrete forms are briefly recalled then the algorithm is derived by combining a newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility the proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models the numerical procedure is applied to a square plate with a circular hole under variable traction in two directions and the obtained approximations are compared with available results finally a rectangular plate with two small holes is considered in both plane strain and plane stress conditions all application use the mises condition without linearization

an upper bound limit analysis of mindlin plates using cs dsg3 method and second order cone programming the paper presents a numerical procedure for kinematic limit analysis of mindlin plate governed by von mises criterion the cell based smoothed discrete shear gap method cs dsg3 is combined with a second order cone optimization programming socp for determining the upper bound limit load of the mindlin plates the limit analysis problem of mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work this minimization problem is then transformed into an explicit form suitable for the solution using the socp the numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the mindlin plates cs dsg3 is combined with socp for determining upper bound limit load of mindlin plates limit analysis problem is transformed into an explicit form suitable for solution using socp and cs dsg3 numerical results show that cs dsg3 is free of shear locking and can provide reliable upper bound collapse multipliers for mindlin plates

conditions for optimality of the huffman algorithm a new general formulation of huffman tree construction is presented which has broad application recall that the huffman algorithm forms a tree in which every node has some associated weight by specifying at every step of the construction which nodes are to be combined to form a new node with a new combined weight we characterize a wide class of weight combination functions the quasilinear functions for which the huffman algorithm produces optimal trees under correspondingly wide classes of cost criteria in addition known results about huffman tree construction and related concepts from information theory and from the theory of convex functions are tied together suggestions for possible future applications are given

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

incremental elastoplastic analysis for active macro zones summary in this paper a strategy to perform incremental elastoplastic analysis using the symmetric galerkin boundary element method for multidomain type problems is shown the discretization of the body is performed through substructures distinguishing the bem elements characterizing the so called active macro zones where the plastic consistency condition may be violated and the macro elements having elastic behaviour only incremental analysis uses the well known concept of self equilibrium stress field here shown in a discrete form through the introduction of the influence matrix self stress matrix the nonlinear analysis does not use updating of the elastic response inside each plastic loop but at the end of the load increment only this is possible by using the self stress matrix both in the predictor phase for computing the stress caused by the stored plastic strains and in the corrector phase for solving a nonlinear global system which provides the elastoplastic solution of the active macro zones the use of active macro zones gives rise to a nonlocal and path independent approach which is characterized by a notable reduction of the number of plastic iterations the proposed strategy shows several computational advantages as shown by the results of some numerical tests reported at the end of this paper these tests were performed using the karnak sgbem code in which the present procedure was introduced as an additional module copyright 2012 john wiley sons ltd

the epsilon expansion from conformal field theory conformal multiplets of and 3 recombine at the wilson fisher xed point as a consequence of the equations of motion using this fact and other constraints from conformal symmetry we reproduce the lowest nontrivial order results for the anomalous dimensions of operators without any input from perturbation theory

a mixed formulation and mixed finite elements for limit analysis a mixed variational principle for the limit analysis of rigid perfectly plastic continua is discussed in which the nonlinear yield condition and the associated flow rule appear through a suitably defined penalty function a mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised affording a complete static and kinematic solution several results are presented in both structural and soil mechanics compared with previously available exact and numerical solutions

a general non linear optimization algorithm for lower bound limit analysis the non linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided the algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required as with interior point methods for linear programming the number of iterations is affected only little by the problem size some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non linear yield criteria copyright 2002 john wiley sons ltd

on critical exponents without feynman diagrams in order to achieve a better analytic handle on the modern conformal bootstrap program we re examine and extend the pioneering 1974 work of polyakov s which was based on consistency between the operator product expansion and unitarity as in the bootstrap approach this method does not depend on evaluating feynman diagrams we show how this approach can be used to compute the anomalous dimensions of certain operators in the o n model at the wilson fisher fixed point in 4 epsilon dimensions up to o epsilon 2

limit analysis with the dual affine scaling algorithm the collapse state of a rigid plastic material with the linearized mises yield condition is computed we use an infeasible point variant of the dual affine scaling algorithm for linear programming which is extremely efficient for this large sparse and ill conditioned problem for a classical test problem we obtain better results than previously both for the limit load and for the collapse fields thus setting a new standard for computations in limit analysis

a cell based smoothed finite element method for kinematic limit analysis this paper presents a new numerical procedure for kinematic limit analysis problems which incorporates the cell based smoothed finite element method with second order cone programming the application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort the non smooth optimization problem is formulated as a problem of minimizing a sum of euclidean norms ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm plane stress and plane strain problems governed by the von mises criterion are considered but extensions to problems with other yield criteria having a similar conic quadratic form or 3d problems can be envisaged

the use of qp free algorithm in the limit analysis of slope stability in many mountainous areas landslides and slope instabilities frequently occur after heavy rainfall and earthquake and result in enormous casualties and huge economic losses in order to mitigate the landslides hazard efficiently a method is required for a better understanding of stability analysis fortunately upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes and in this approach the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization in general the sqp type algorithms are used to solve this optimization problem however it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the sqp type algorithms fortunately a qp free algorithm based on penalty function and active set strategy can be globally convergent toward the kkt points with arbitrary starting point and the rate of convergence is local superlinear or even quadratic two classical problems of slope stability are solved by this qp free algorithm the results show that the qp free algorithm would be the better choice than sqp type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability

a sparsity exploiting variant of the bartels golub decomposition for linear programming bases we describe a sparsity exploiting variant of the bartels golub decomposition for linear programming bases it includes interchanges that whenever this is possible avoid the use of any eliminations with consequent fill ins when revising the factorization at an iteration test results on some medium scale problems are presented and comparisons made with the algorithm of forrest and tomlin

upper bound limit analysis using discontinuous velocity fields abstract a new method for computing rigorous upper bounds under plane strain conditions is described it is based on a linear three noded triangular element which has six unknown nodal velocities and a fixed number of unknown plastic multiplier rates and uses the kinematic theorem to define a kinematically admissible velocity field as the solution of a linear programming problem unlike existing formulations which permit only a limited number of velocity discontinuities whose directions of shearing must be specified a priori the new formulation permits velocity discontinuities at all edges shared by adjacent triangles and the directions of shearing are found automatically the variation of the velocity jump along each discontinuity is described by an additional set of four unknowns all of the unknowns are subject to the constraints imposed by an associated flow rule and the velocity boundary conditions the objective function corresponds to the dissipated power or some related load parameter of interest and is minimised to yield the desired upper bound since plastic deformation may occur not only in the discontinuities but also throughout the triangular elements as well the method is capable of modelling complex velocity fields accurately and typically produces tight upper bounds on the true limit load the formulation is applicable to materials whose strength is cohesive frictional purely cohesive and uniform or purely cohesive and linearly varying and thus quite general the new procedure is very efficient and always requires fewer elements than existing methods to obtain useful upper bound solutions moreover because of the extra degrees of freedom introduced by the discontinuities the linear elements no longer need to be arranged in a special pattern to model incompressible behaviour accurately

extended finite element method for plastic limit load computation of cracked structures summary the extended finite element method is extended to allow computation of the limit load of cracked structures in the paper it is demonstrated that the linear elastic tip enrichment basis with and without radial term r may be used in the framework of limit analysis but the six function enrichment basis based on the well known hutchinson rice rosengren asymptotic fields appears to be the best the discrete kinematic formulation is cast in the form of a second order cone problem which can be solved using highly efficient interior point solvers finally the proposed numerical procedure is applied to various benchmark problems showing that the present results are in good agreement with those in the literature copyright 2015 john wiley sons ltd

lower bound limit analysis by using the efg method and non linear programming intended to avoid the complicated computations of elasto plastic incremental analysis limit analysis is an appealing direct method for determining the load carrying capacity of structures on the basis of the static limit analysis theorem a solution procedure for lower bound limit analysis is presented firstly making use of the element free galerkin efg method rather than traditional numerical methods such as the finite element method and boundary element method the numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration the reduced basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self equilibrium stress subspaces with very low dimensions the self equilibrium stress field is expressed by a linear combination of several self equilibrium stress basis vectors with parameters to be determined these self equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto plastic incremental analysis the complex method is used to solve these non linear programming sub problems and determine the maximal load amplifier numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the efg method and non linear programming copyright 2007 john wiley sons ltd

a non linear programming method approach for upper bound limit analysis this paper presents a finite element model based on mathematical non linear programming in order to determine upper bounds of colapse loads of a mechanical structure the proposed formulation is derived within a kinematical approach framework employing two simultaneous and independent field approximations for the velocity and strain rate fields the augmented lagrangian is used to establish the compatibility between these two fields in this model only continuous velocity fields are used uzawa s minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate the use of this technique allows to bypass the complexity of the non linear aspects of the problem since non linearity is addressed as a set of small local subproblems of optimization for each finite element the obtained model is quite versatile and suitable for solving a wide range of collapse problems this paper studies 3d strut and tie structures 2d plane strain stress and 3d solid problems copyright 2007 john wiley sons ltd

a steepest edge active set algorithm for solving sparse linear programming problems a steepest edge active set algorithm is described which is suitable for solving linear programming problems where the constraint matrix is sparse and has more rows than columns the algorithm uses a steepest edge criterion for selecting the search direction at each iteration and recurrence relations are derived which enable it to execute efficiently the canonical form for the active set method is convenient for many applications and may be exploited to devise a simple crash procedure which is employed prior to phase one a complete two phase algorithm which incorporates the crash procedure is outlined only one artificial variable is needed to determine if the linear programming problem has a feasible solution in phase one some computational results are given to illustrate the effectiveness of the algorithm for a range of sparse linear programming problems comparisons between the steepest edge criterion and the traditional dantzig criterion suggest that the former usually requires fewer iterations and often leads to substantial savings for large problems

lower bound limit analysis by the symmetric galerkin boundary element method and the complex method abstract a solution procedure for lower bound limit analysis is presented making use of the symmetric galerkin boundary element method sgbem rather than of finite element method the self equilibrium stress fields are expressed by linear combination of several basic self equilibrium stress fields with parameters to be determined these basic self equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains obtained through elastic plastic incremental analysis the complex method is used to solve nonlinear programming and determine the maximal load amplifier the numerical results show that it is efficient and accurate to solve limit analysis problems by using the sgbem and the complex method

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

a second quantized kolmogorov chentsov theorem via the operator product expansion we establish a direct connection between two fundamental topics one in probability theory and one in quantum field theory the first topic is the problem of pointwise multiplication of random schwartz distributions which has been the object of recent progress thanks to hairer s theory of regularity structures and the theory of paracontrolled distributions introduced by gubinelli imkeller and perkowski the second topic is wilson s operator product expansion which is a general property of models of quantum field theory and a cornerstone of the bootstrap approach to conformal field theory our main result is a general theorem for the almost sure construction of products of random distributions by mollification and suitable additive as well as multiplicative renormalizations the hypothesis for this theorem is the operator product expansion with precise bounds for pointwise correlations we conjecture these bounds to be universal features of quantum field theories with gapped dimension spectrum our theorem can accommodate logarithmic corrections anomalous scaling dimensions and even lack of translation invariance however it only applies to fields with short distance singularities that are milder than white noise as an application we provide a detailed treatment of a scalar conformal field theory of mean field type i e the fractional massless free field also known as the fractional gaussian field

a quadratically convergent method for minimizing a sum of euclidean norms we consider the problem of minimizing a sum of euclidean norms f x sum nolimits i 1 m r i x here the residuals r i x are affine functions fromr n tor 1 n 1 2 m 2 this arises in a number of applications including single and multi facility location problems the functionf is in general not differentiable atx if at least oner i x is zero

limit state solutions based upon linear elastic solutions with a spatially varying elastic modulus abstract the paper describes an iterative method of determining the limit state of a perfectly plastic body for the von mises yield condition a sequence of incompressible linear elastic solutions are defined with a spatially varying shear modulus which provide a sequence of upper bounds to the limit load which monotonically reduce and converge to the limit state solution for a discretized solution generated by a rayleigh ritz method the sequence converges to the least upper bound associated with the class of displacement fields an example of a finite element implementation method is given and applied to the limit state of a cracked body a method for accelerated convergence is described for problems where the plastic region forms a small proportion of the total volume of the body

computation of the collapse state in limit analysis using the lp primal affine scaling algorithm abstract the object of this work is twofold the first goal is to demonstrate that for the duality problem of limit analysis with linearized yield condition the lp primal affine scaling algorithm shows properties which are significantly different from those of the simplex method and that as a consequence of this better results can be obtained the second goal is to compute the collapse state for a classical and hard problem in plane strain tension of a rectangular bar with symmetric thin cuts both the collapse multiplier and collapse fields are computed to a better accuracy and detail than previously

kinematic limit analysis of frictional materials using nonlinear programming abstract in this paper a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming limit analysis and the conventional displacement based finite element method the analysis is based on a general yield function which can take the form of the mohr coulomb or drucker prager criterion by using an associated flow rule a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization the plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained the nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation the calculation is based entirely on kinematically admissible velocities without calculation of the stress field the finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint the objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load an effective direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem the effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples

relations between short range and long range ising models we perform a numerical study of the long range lr ferromagnetic ising model with power law decaying interactions j ensuremath propto r ensuremath d ensuremath ensuremath sigma on both a one dimensional chain d 1 and a square lattice d 2 we use advanced cluster algorithms to avoid the critical slowing down we first check the validity of the relation connecting the critical behavior of the lr model with parameters d ensuremath sigma to that of a short range sr model in an equivalent dimension d we then study the critical behavior of the d 2 lr model close to the lower critical ensuremath sigma uncovering that the spatial correlation function decays with two different power laws the effect of the subdominant power law is much stronger than finite size effects and actually makes the estimate of critical exponents very subtle by including this subdominant power law the numerical data are consistent with the standard renormalization group rg prediction by sak phys rev b 8 281 1973 thus making not necessary and unlikely according to occam s razor the recent proposal by picco arxiv 1207 1018 of having a new set of rg fixed points in addition to the mean field one and the sr one

computing limit loads by minimizing a sum of norms this paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition such as for example the von mises condition after discretization with the finite element method using divergence free elements for the plastic flow the kinematic formulation reduces to the problem of minimizing a sum of euclidean vector norms subject to a single linear constraint this is a nonsmooth minimization problem since many of the norms in the sum may vanish at the optimal point recently an efficient solution algorithm has been developed for this particular convex optimization problem in large sparse form the approach is applied to test problems in limit analysis in two different plane models plane strain and plates in the first case more than 80 of the terms in the objective function are zero in the optimal solution causing extreme ill conditioning in the second case all terms are nonzero in both cases the method works very well and problems are solved which are larger by at least an order of magnitude than previously reported the relative accuracy for the solution of the discrete problems measured by duality gap and feasibility is typically of the order 10 8

an optimal allocation of carry save adders in arithmetic circuits carry save adder csa is one of the most widely used components for fast arithmetic in industry this paper provides a solution to the problem of finding an optimal timing allocation of csas in arithmetic circuits namely we present a polynomial time algorithm which finds an optimal timing csa allocation for a given arithmetic expression we then extend our result for csa allocation to the problem of optimizing arithmetic expressions across the boundary of design hierarchy by introducing a new concept called auxiliary ports our algorithm can be used to carry out the csa allocation step optimally and automatically and this can be done within the context of a standard rtl synthesis environment

automatic mesh refinement in limit analysis a strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method in the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition the approach is tested on standard problems in plane strain including the classical punch problem very accurate results are obtained with the use of moderate computational power

infinite chiral symmetry in four dimensions we describe a new correspondence between four dimensional conformal field theories with extended supersymmetry and two dimensional chiral algebras the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four dimensional theory infinite chiral symmetry has far reaching consequences for the spectral data correlation functions and central charges of any four dimensional theory with mathcal n 2 superconformal symmetry

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

a numerical approach for limit analysis of orthotropic composite laminates a numerical approach for limit analysis of structures whose constituent material exhibits orthotropic behaviour is presented and discussed attention is focused on orthotropic composite laminates under plane stress conditions the proposed approach is an extension in the context of orthotropic materials of the linear matching method lmm the latter is based on a sequence of linear analyses performed on the analysed structure made of a fictitious linear viscous material with spatially varying moduli here the lmm is applied to structures made of materials obeying the tsai wu criterion an appropriate choice of the fictitious material which in this case is assumed linear viscous orthotropic and suffering a distribution of assigned initial stresses reduces the number of parameters to be spatially varied thus rendering the whole procedure applicable and reliable the results obtained are highly promising as witnessed by a number of numerical examples which are carried out to verify the effectiveness of the proposed approach copyright 2006 john wiley sons ltd

a polytree based adaptive approach to limit analysis of cracked structures abstract we in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures the key idea is to develop a general refinement algorithm based on a so called polytree mesh structure the method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones which are considered as special cases also polytree meshes are conforming and can be regarded as a generalization of quadtree meshes for the aim of this paper we restrict our main interest in plane strain limit analysis to von mises type materials yet its extension to a wide class of other solid mechanics problems and materials is completely possible to avoid volumetric locking we propose an approximate velocity field enriched with bubble functions using wachspress coordinates on a primal mesh and design carefully strain rates on a dual mesh level an adaptive mesh refinement process is guided by an l 2 norm based indicator of strain rates through numerical validations we show that the present method reaches high accuracy with low computational cost this allows us to perform large scale limit analysis problems favorably

locking free discontinuous finite elements for the upper bound yield design of thick plates summary this work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of reissner mindlin thick plates in shear bending interaction the main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields in particular it has been demonstrated for 2d plane stress plane strain or 3d limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates for this reason discontinuous interpolations of the transverse velocity and the rotation fields for reissner mindlin plates are proposed the subsequent discrete minimization problem is formulated as a second order cone programming problem and is solved using the industrial software package mosek a comprehensive study of the shear locking phenomenon is also conducted and it is shown that discontinuous elements avoid such a phenomenon quite naturally whereas continuous elements cannot without any specific treatment this particular aspect is confirmed through numerical examples on classical benchmark problems and the so obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates copyright 2015 john wiley sons ltd

bootstrapping conformal field theories with the extremal functional method the existence of a positive linear functional acting on the space of differences between conformal blocks has been shown to rule out regions in the parameter space of conformal field theories cfts we argue that at the boundary of the allowed region the extremal functional contains in principle enough information to determine the dimensions and operator product expansion ope coefficients of an infinite number of operators appearing in the correlator under analysis based on this idea we develop the extremal functional method efm a numerical procedure for deriving the spectrum and ope coefficients of cfts lying on the boundary of solution space we test the efm by using it to rederive the low lying spectrum and ope coefficients of the two dimensional ising model based solely on the dimension of a single scalar quasiprimary char22 no virasoro algebra required our work serves as a benchmark for applications to more interesting less known cfts in the near future

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

a note on upper bound formulations in limit analysis summary in this paper we study some recent formulations for the computation of upper bounds in limit analysis we show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound nor does it provide a velocity field that satisfies the normality rule everywhere we show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power we derive a formulation that furnishes a strict upper bound of the load factor which in fact coincides with a formulation reported in the literature from the analysis of these formulations we propose a post process which consists in computing exactly the dissipation power for the optimum upper bound velocity field this post process may further reduce the strict upper bound of the load factor in particular situations finally we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap copyright 2012 john wiley sons ltd

discontinuous velocity domain splitting in limit analysis abstract we present a new limit analysis method originated in ionescu and lachand robert 2005 and called discontinuous velocity domain splitting method dvds dvds is a mesh free method which focuses on the strain localization and completely neglect the bulk deformations it considers the kinematic variational principle on a special class of virtual velocity fields to get an upper bound of the limit load to construct this class of virtual velocity fields the rigid plastic body is splinted into simple connected sub domains and on each such sub domain a rigid motion is associated the discontinuous collapse flow velocity field results in localized deformations only located at the boundary of the sub domains in the numerical applications of the dvds method we introduce a numerical technique based on a level set description of the partition of the rigid plastic body and on genetic minimization algorithms for the anti plane flow of a von mises material dvds is exact in solving the limit analysis problem the collapse flow is a rigid motion of a sub domain the associated deformation rate is localized on the smooth boundary of the moving sub domain representing the fracture surface in the case of in plane deformation of pressure insensitive materials the internal boundaries of the sub domains are parts of circles or straight lines tangent to the collapse velocity jumps in this case dvds reduces to the block decomposition method which was intensively used to get analytical upper bounds of the limit loads when applied to the two notched tensile problem of a von mises material dvds gives excellent results with a low computational cost furthermore dvds was applied to model collapse in pressure sensitive plastic materials illustrative examples for homogenous and heterogeneous coulomb and cam clay materials shows that dvds gives excellent prediction of limit loads and on the collapse flow

quadratic velocity linear stress interpolations in limit analysis summary we compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis the aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them two of these interpolations are used in limit analysis for the first time in this article the inequalities in the proposition are also demonstrated via numerical applications to this end the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements copyright 2014 john wiley sons ltd

limit analysis of orthotropic structures based on hill s yield condition abstract the limit analysis problem which permits the direct computation of the limit load of rigid perfectly plastic solids and structures is considered with reference to anisotropic materials as a starting step attention is focused on hill s orthotropic condition for which an explicit expression of the dissipation power in terms of strain rates is established on this basis numerical procedures successfully employed in the isotropic von mises case can be used in this context as some examples illustrate

a numerical method for plastic limit analysis of 3 d structures abstract based on the upper bound theorem of plasticity the 3 d limit analysis of rigid perfectly plastic structures is formulated as a discrete nonlinear mathematical programming problem with only equality constraints by means of the finite element technique the penalty function method is used to deal with the plastic incompressibility condition a direct iterative algorithm is employed in solving this formulation at each step of the iteration the rigid and plastic zones are continually distinguished the respective constraint conditions are imposed on them and the goal function is modified appropriately the numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function and the incompressibility of plastic deformation are overcome the limit load multiplier and the associated velocity field computed by the iteration procedure converge monotonically to the upper bounds of real solutions the numerical procedure has been used to carry out the limit analysis for cylindrical shells with part through slot type defects under internal pressure numerical examples are given to demonstrate the applicability of the procedure

computation of limit and shakedown loads using a node based smoothed finite element method summary this paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node based smoothed fem in combination with a primal dual algorithm an associated primal dual form based on the von mises yield criterion is adopted the primal dual algorithm together with a newton like iteration are then used to solve this associated primal dual form to determine simultaneously both approximate upper and quasi lower bounds of the plastic collapse limit and the shakedown limit the present formulation uses only linear approximations and its implementation into finite element programs is quite simple several numerical examples are given to show the reliability accuracy and generality of the present formulation compared with other available methods copyright 2011 john wiley sons ltd

numerical limit analysis solutions for the bearing capacity factor nγ abstract numerical limit analyses are applied to evaluate the self weight bearing capacity factor for a rigid surface footing with a smooth or rough interface to isolate the effect of the self weight on the bearing capacity the soil is modeled as a cohesionless frictional mohr coulomb material assuming an associated flow rule the true collapse load is bracketed to within 3 42 by computing rigorous lower and upper bound solutions using recently developed limit analysis methods lyamin and sloan 2002a upper bound limit analysis using linear finite elements and non linear programming international journal for numerical and analytical methods in geomechanics 26 2 181 lyamin and sloan 2002b lower bound limit analysis using linear finite elements and non linear programming international journal for numerical methods in engineering 55 5 573 with these sharp bounds the average bearing capacity factor provides an excellent estimate of the exact bearing capacity factor that can be used with confidence for design purposes the numerical formulations of both the upper and the lower bound theorems are obtained by means of finite elements and solved using efficient non linear mathematical programming schemes the solutions presented in the form of graphs are compared against existing semi empirical expressions and numerical solutions an approximate analytical expression for n is suggested at the end of the paper

an edge based finite element method es fem with adaptive scaled bubble functions for plane strain limit analysis abstract this paper deals with critical roles of cubic bubble functions for the edge based finite element method es fem formulation within the framework of the kinematic theorem for predicting the plastic collapse loads of structures we show that the bubble function can be scaled by a non zero coefficient alpha while the volumetric locking is entirely eliminated based on this finding the present method is designed in a very small value with a bubble function that is maximum at the center of the element this can lead to the loss of the partition of unity for easy reference the present method is termed as bes fem the significant advantage of the present method lies in the rigorous treatment of the volumetric locking free that can occur in the fully plastic range the bes fem works well with high efficiency by using triangular meshes it achieves both simplicity and computational efficiency for implementation into packages of plastic limit analyses in case of bes fem the locking issue can be solved conveniently by two schemes 1 the usual piecewise linear displacements enriched with a cubic bubble function on a primal mesh of triangular elements and 2 a projection operator of strain rates through a dual mesh associated with the edges in the mesh the optimization formulation of finite element limit analysis is written in the form of a second order cone programming socp the well established interior point solvers can be exploited efficiently the bes fem using a small number of integration points enables to solve the large scale optimization problems efficiently in addition an adaptive meshing procedure based on an alternative indicator of dissipation is also derived to further enhance the quality of the solution without increasing significantly the number of degrees of freedom of the model numerical results show the robustness of the proposed method

formulation and solution of some plasticity problems as conic programs abstract the application of conic programming to some traditionally difficult plasticity problems is considered convenient standard forms for conic programming of both limit and incremental elastoplastic analysis are given the types of yield criteria that can be treated by conic programming is discussed and it is shown that the three dimensional mohr coulomb criterion can be cast as a set of conic constraints thus facilitating efficient treatment by dedicated algorithms finally the performance of a number of mixed finite elements is evaluated together with a state of the art second order cone programming algorithm

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

a new discontinuous upper bound limit analysis formulation summary a new upper bound formulation of limit analysis of two and three dimensional solids is presented in contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers however by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions also kinematically admissible discontinuities which have previously been shown to be very efficient are given an interpretation in terms of stresses this allows for a much simpler implementation and in contrast to existing formulations extension to arbitrary yield criteria in two and three dimensions is straightforward finally the capabilities of the new method are demonstrated through a number of examples copyright 2005 john wiley sons ltd

upper and lower bounds in limit analysis adaptive meshing strategies and discontinuous loading summary upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimisation problems the membership constraints for von mises and mohrcoulomb plasticity criteria are written as a set of quadratic constraints which permits to solve the optimisation problem using specific algorithms for second order conic program socp from the stress field at the lower bound and the velocities at the upper bound we construct a novel error estimate based on elemental and edge contributions to the bound gap these contributions are employed in an adaptive remeshing strategy that is able to reproduce fan type mesh patterns around points with discontinuous surface loading the solution of this type of problems is analysed in detail and from this study some additional meshing strategies are also described we particularise the resulting formulation and strategies to two dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature copyright c 2007 john wiley sons ltd