dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative internal variable constitutive laws abstract reference is made to discrete finite element structural models formulated in terms of generalized variables the constitutive laws adopted are elastic plastic nonlinear hardening with internal variables and generally nonassociative the notion of reduced domain is employed as a generalization of a similar concept introduced in earlier developments of shakedown theory on this basis a unified theory is presented which encompasses necessary and separately sufficient conditions for shakedown by a static approach as a further generalization of classical melan s theorem bounds on various post shakedown quantities sufficient and necessary shakedown criteria by a kinematic approach as a further extension of neal symonds koiter theorem by suitable specializations and relaxations of the achievable results the criteria and bounding inequalities established here are formulated as mathematical programming problems in view of numerical applications

kinematical shakedown analysis with temperature dependent yield stress summary this paper describes a direct shakedown analysis of structures subjected to variable thermal and mechanical loading the classical kinematical shakedown theorem is modied to be implemented with any displacementbased nite elements the plastic incompressibility condition is imposed by the penalty function method the shakedown limit is found via a non linear mathematical programming procedure two numerical shakedown methods are developed and implemented to provide alternative numerical means the temperature dependent material model is included in theoretical and numerical calculation in a simple way its eect on shakedown limit is investigated the numerical examination for some pressure vessel structures subjected to thermal and mechanical loading shows a satisfying precision and eciency of the methods presented copyright 2001 john wiley sons ltd

quadri tilings of the plane we introduce quadri tilings and show that they are in bijection with dimer models on a family of graphs r arising from rhombus tilings using two height functions we interpret a sub family of all quadri tilings called triangular quadri tilings as an interface model in dimension 2 2 assigning critical weights to edges of r we prove an explicit expression only depending on the local geometry of the graph r for the minimal free energy per fundamental domain gibbs measure this solves a conjecture of kenyon invent math 150 409 439 2002 we also show that when edges of r are asymptotically far apart the probability of their occurrence only depends on this set of edges finally we give an expression for a gibbs measure on the set of all triangular quadri tilings whose marginals are the above gibbs measures and conjecture it to be that of minimal free energy per fundamental domain

the lee yang and polya schur programs i linear operators preserving stability in 1952 lee and yang proposed the program of analyzing phase transitions in terms of zeros of partition functions linear operators preserving non vanishing properties are essential in this program and various contexts in complex analysis probability theory combinatorics and matrix theory we characterize all linear operators on finite or infinite dimensional spaces of multivariate polynomials preserving the property of being non vanishing whenever the variables are in prescribed open circular domains in particular this solves the higher dimensional counterpart of a long standing classification problem originating from classical works of hermite laguerre hurwitz and polya schur on univariate polynomials with such properties

generalized domino shuffling the problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting perfect matchings of some subgraph of an aztec diamond graph an or more generally calculating the sum of the weights of all the matchings where the weight of a matching is equal to the product of the pre assigned weights of the constituent edges assumed to be non negative this article presents efficient algorithms that work in this context to solve three problems finding the sum of the weights of the matchings of a weighted aztec diamond graph an computing the probability that a randomly chosen matching of an will include a particular edge where the probability of a matching is proportional to its weight and generating a matching of an at random the first of these algorithms is equivalent to a special case of mihai ciucu s cellular complementation algorithm j combin theory ser a 81 1998 34 and can be used to solve many of the same problems the second of the three algorithms is a generalization of not yet published work of alexandru ionescu and can be employed to prove an identity governing a three variable generating function whose coefficients are all the edge inclusion probabilities this formula has been used duke math j 85 1996 117 as the basis for asymptotic formulas for these probabilities but a proof of the generating function identity has not hitherto been published the third of the three algorithms is a generalization of the domino shuffling algorithm presented in j algebraic combin 1 1992 111 it enables one to generate random diabolo tilings of fortresses and thereby to make intriguing inferences about their asymptotic behavior

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

the arctic circle boundary and the airy process we prove that the appropriately rescaled boundary of the north polar region in the aztec diamond converges to the airy process the proof uses certain determinantal point processes given by the extended krawtchouk kernel we also prove a version of propp s conjecture concerning the structure of the tiling at the center of the aztec diamond 1 introduction and results domino tilings of the aztec diamond were introduced in 8 9 asymptotic properties of random domino tilings of the aztec diamond have been studied in 5 12 15 in particular in 12 the existence of the so called arctic circle was proved the arctic circle is the asymptotic boundary of the disordered so called temperate region of the tiling outside this boundary the tiling forms a completely regular brick wall pattern the methods in 12 combined with the results in 13 show that the fluctuations of the point of intersection of the boundary of the temperate region with a line converge to the tracy widom distribution of random matrix theory in this paper we extend this result to show that the fluctuations of the boundary around the arctic circle converges to the airy process introduced in 23 the paper is a continuation of the approach used in 14 and 15 where certain point processes with determinantal correlation functions 24 and the krawtchouk ensemble were used we will use the general techniques developed in 16 and investigate an extended point process which also has determinantal correlation functions given by a kernel which we call the extended krawtchouk kernel the aztec diamond an of order n is the union of all lattice squares m m 1 l l 1 m l 2 z that lie inside the region x1 y1 x1 y1

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

the emergence of the electrostatic field as a feynman sum in random tilings with holes we consider random lozenge tilings on the triangular lattice with holes q 1 q n in some fixed position for each unit triangle not in a hole consider the average orientation of the lozenge covering it we show that the scaling limit of this discrete field is the electrostatic field obtained when regarding each hole q i as an electrical charge of magnitude equal to the difference between the number of unit triangles of the two different orientations inside q i this is then restated in terms of random surfaces yielding the result that the average over surfaces with prescribed height at the union of the boundaries of the holes is in the scaling limit a sum of helicoids

arctic circles domino tilings and square young tableaux the arctic circle theorem of jockusch propp and shor asserts that uniformly random domino tilings of an aztec diamond of high order are frozen with asymptotically high probability outside the arctic circle inscribed within the diamond a similar arctic circle phenomenon has been observed in the limiting behavior of random square young tableaux in this paper we show that random domino tilings of the aztec diamond are asymptotically related to random square young tableaux in a more refined sense that looks also at the behavior inside the arctic circle this is done by giving a new derivation of the limiting shape of the height function of a random domino tiling of the aztec diamond that uses the large deviation techniques developed for the square young tableaux problem in a previous paper by pittel and the author the solution of the variational problem that arises for domino tilings is almost identical to the solution for the case of square young tableaux by pittel and the author the analytic techniques used to solve the variational problem provide a systematic guess free approach for solving problems of this type which have appeared in a number of related combinatorial probability models

a comparison between analytical calculations of the shakedown load by the bipotential approach and step by step computations for elastoplastic materials with nonlinear kinematic hardening abstract the class of generalized standard materials is not relevant to model the nonassociative constitutive equations the bipotential approach based on a possible generalization of fenchel s inequality allows the recovery of the flow rule normality in a weak form of an implicit relation this defines the class of implicit standard materials for such behaviours this leads to a weak extension of the classical bound theorems of the shakedown analysis in the present paper we recall the relevant features of this theory considering an elastoplastic material with nonlinear kinematic hardening rule we apply it to the problem of a sample in plane strain conditions under constant traction and alternating torsion in order to determine analytically the interaction curve bounding the shakedown domain the aim of the paper is to prove the exactness of the solution for this example by comparing it to step by step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level a reliable criterion to stop the computations is proposed the analytical and numerical solutions are compared and found to be closed one of each other moreover the method allows uncovering an additional 2 cycle shakedown curve that could be useful for the shakedown design of structure

algebraic arctic curves in the domain wall six vertex model the arctic curve i e the spatial curve separating ordered or frozen and disordered or temperate regions of the six vertex model with domain wall boundary conditions is discussed for the root of unity vertex weights in these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve some interesting examples are discussed in detail the upper bound on the maximal degree of the equation in a generic root of unity case is obtained

an iterative method for shakedown analysis abstract shakedown analysis for elastic perfect plastic structures is discussed and a fast incremental iterative solution method is proposed suitable for the fem analyses of large structures the theoretical motivations of the proposed method are discussed in detail and an example of its implementation is described with reference to plane frame analysis some numerical results are presented showing the numerical performances of the method

conformal invariance of loops in the double dimer model the dimer model is the study of random dimer covers perfect matchings of a graph a double dimer configuration on a graph mathcal g is a union of two dimer covers of mathcal g we introduce quaternion weights in the dimer model and show how they can be used to study the homotopy classes relative to a fixed set of faces of loops in the double dimer model on a planar graph as an application we prove that in the scaling limit of the uniform double dimer model on mathbb z 2 or on any other bipartite planar graph conformally approximating mathbb c the loops are conformally invariant

a primal dual algorithm for shakedown analysis of structures abstract the paper describes a primal dual algorithm for shakedown analysis of structures with the use of kinematically admissible finite elements starting from koiter kinematic theorem a primal dual optimization condition is established by adopting static terms as complementary variables newton like iterations are performed to give both upper and quasi lower bounds of the load factor that converge rapidly to the accurate solution of shakedown limit

tacnode gue minor processes and double aztec diamonds we study determinantal point processes arising in random domino tilings of a double aztec diamond a region consisting of two overlapping aztec diamonds at a turning point in a single aztec diamond where the disordered region touches the boundary the natural limiting process is the gue minor process increasing the size of a double aztec diamond while keeping the overlap between the two aztec diamonds finite we obtain a new determinantal point process which we call the tacnode gue minor process this process can be thought of as two colliding gue minor processes as part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode gue minor process we find the inverse kasteleyn matrix for the dimer model version of the double aztec diamond

numerical shakedown analysis of damaged structures a numerical method is proposed to predict the failure of mechanical structures it is based on the generalization of the classical static shakedown theorem to damaged inelastic structures ductile plastic damage is taken into account by using the models of lemaitre and shichun hua the obtained results are compared in the special case of limit analysis to those obtained by incremental methods

double aztec diamonds and the tacnode process discrete and continuous non intersecting random processes have given rise to critical infinite dimensional diffusions like the airy process the pearcey process and variations thereof it has be

shakedown analysis in poroplasticity by linear programming static lower bound and kinematic upper bound theorems for shakedown analysis and limit analysis as special case are presented for two phase fully saturated poroplastic solids in a context characterized by the following features quasi static non associative non softening perfect or hardening poroplasticity piecewise linearized yield loci and hardening constant permeability linear fluid transport law small deformations non traditional galerkin finite element discretization with reference to cyclic periodic external actions numerical examples centred on linear programming evidence the computational potentialities and limitations of direct non evolutive methods of integrity assessment according to limit state design concepts in poroplasticity copyright 2000 john wiley sons ltd

consistent shakedown theorems for materials with temperature dependent yield functions abstract the elastic shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic plastic rate independent associative material models with temperature dependent yield functions assuming the yield functions convex in the stress temperature space a thermodynamically consistent small deformation thermo plasticity theory is provided in which the set of state and evolutive variables includes the temperature and the plastic entropy rate within the latter theory the known static prager s and kinematic konig s shakedown theorems which hold for yield functions convex in the stress space are restated in an appropriate consistent format in contrast with the above known theorems the restated theorems provide dual lower and upper bound statements for the shakedown limit loads additionally the latter theorems can be expressed in terms of only dominant thermo mechanical loads generally the vertices of a polyhedral load domain in which the loadings are allowed to range the shakedown limit load evaluation problem is discussed together with the related shakedown limit state of the structure a few numerical applications are presented

shakedown state simulation techniques based on linear elastic solutions abstract the paper extends an iterative method previously applied to the determination of the limit state of a perfectly plastic body 5 to the determination of the shakedown limit state of a body subjected to a cyclic history of mechanical load and temperature a convergence proof is presented for a particular class of problems where the magnitude of a mechanical load at the shakedown limit is found as the limit of a sequence of monotonically reducing upper bounds an implementation of the method in a finite element scheme is discussed and examples of the application of the method to sample problems are presented

asymptotics of uniformly random lozenge tilings of polygons gaussian free field we study large scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice for a class of polygons which allows arbitrarily large number of sides we show that these fluctuations are asymptotically governed by a gaussian free massless field this complements the similar result obtained in kenyon comm math phys 281 2008 675 709 about tilings of regions without frozen facets of the limit shape in our asymptotic analysis we use the explicit double contour integral formula for the determinantal correlation kernel of the model obtained previously in petrov asymptotics of random lozenge tilings via gelfand tsetlin schemes 2012 preprint

a note on dimer models and mckay quivers we give one formulation of a procedure of hanany and vegh j high energy phys 0710 029 35 2007 which takes a lattice polygon as an input and produces a set of isoradial dimer models we study the case of lattice triangles in detail and discuss the relation with coamoebas following feng et al adv theor math phys 12 3 489 545 2008

effects of softening in elastic plastic structural dynamics softening understood as unstable behaviour of material or structural components is considered herein for its possible consequences on the overall behaviour of discrete dynamic models of elastic plastic beam structures in the absence of geometric effects it is shown that multiplicity of incremental solutions response bifurcations and manifestations of overall instability may occur the bifurcated responses may exhibit different scenarios for the same excitation e g shakedown or local damage up to failure an insight into and criteria for such occurrences are achieved by formulating the rate and the finite increment problem as linear complementarity problems period doubling and deterministic chaos under harmonic excitation are observed when reversible holonomic softening behaviour is assumed the strong sensitivity of the phenomena investigated with respect to the choice of the structural model is pointed out the findings are elucidated by illustrative examples

probability distributions related to tilings of non convex polygons in this paper we study random lozenge tilings of non convex polygonal regions the interaction of the non convexities cuts leads to new kernels and thus new statistics for the tiling fluctuations near these regions this paper gives new probability distributions and joint probability distributions for the fluctuation of tiles along lines in between the cuts

bulk universality for random lozenge tilings near straight boundaries and for tensor products we prove that the asymptotic of the bulk local statistics in models of random lozenge tilings is universal in the vicinity of straight boundaries of the tiled domains the result applies to uniformly random lozenge tilings of large polygonal domains on triangular lattice and to the probability measures describing the decomposition in gelfand tsetlin bases of tensor products of representations of unitary groups in a weaker form our theorem also applies to random domino tilings

tilings of non convex polygons skew young tableaux and determinantal processes this paper studies random lozenge tilings of general non convex polygonal regions we show that the pairwise interaction of the non convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations the precise geometrical figure here consists of a hexagon with cuts along opposite edges for this model we take limits when the size of the hexagon and the cuts tend to infinity while keeping certain geometric data fixed in order to guarantee sufficient interaction between the cuts in the limit we show in this paper that the kernel for the finite tiling model can be expressed as a multiple integral where the number of integrations is related to the fixed geometric data above the limiting kernel is believed to be a universal master kernel

twisted relative trace formulae with a view towards unitary groups we introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of langlands et al in the quadratic case and the relative trace formula of jacquet and lai certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven including the relevant fundamental lemma in the biquadratic case using recent work of jacquet lapid and their collaborators and the rankin selberg integral representation of the asai l function obtained by flicker using the theory of jacquet piatetskii shapiro and shalika we give the following application let e f be a totally real quadratic extension with gal e f let u be a quasi split unitary group with respect to a cm extension m f and let u res e f u under suitable local hypotheses we show that a cuspidal cohomological automorphic representation of u whose asai l function has a pole at the edge of the critical strip is nearly equivalent to a cuspidal cohomological automorphic representation of u that is u distinguished in the sense that there is a form in the space of admitting a nonzero period over u this provides cohomologically nontrivial cycles of middle dimension on unitary shimura varieties analogous to those on hilbert modular surfaces studied by harder langlands and rapoport

dimer problem on the cylinder and torus institute of mathematics academia sinica nsfc 10771086 10671162 fujian province university nsc nsc96 2115 m 001 005

a variational principle for domino tilings 1 1 description of results a domino is a 1 x 2 or 2 x 1 rectangle and a tiling of a region by dominos is a way of covering that region with dominos so that there are no gaps or overlaps in 1961 kasteleyn kal found a formula for the number of domino tilings of an m x n rectangle with mn even as shown in figure 1 for rm n 68 temperley and fisher tf used a differenit method and arrived at the same result at almost exactly the same time both lines of calculation showed that the logarithm of number of tilings divided by the number of dominos in a tiling that is mn 2 converges to 2g 7r 0 58 here g is catalan s constant on the other hand in 1992 elkies et al eklp studied domino tilings of regions they called aztec diamonds figure 2 shows an aztec diamond of order 48 and showed that the logarithm of the number of tilings divided by the number of dominos converges to the smaller number log 2 2 0 35 thus even though the region in figure 1 has slightly smaller area than the region in figure 2 the former has far more domino tilings for regions with other shapes neither of these asymptotic formulas may apply in the present paper we consider simply connected regions of arbitrary shape we give an exact formula for the limiting value of the logarithm of the number of tilings per unit area as a function of the shape of the boundary of the region as the size of the region goes to infinity in particular we show that computation of this limit is intimately linked with an understanding of long range variations in the local statistics of random domino tilings such variations can be seen by comparing figures 1 and 2 each of the two tilings is random in the sense that the algorithm pwi that was used to create it generates each of the possible tilings of the region being tiled with the same probability hence one can expect each tiling to be qualitatively typical of the overwhelming majority of tilings of the region in

corner percolation on ℤ2 and the square root of 17 we consider a four vertex model introduced by balint toth a dependent bond percolation model on 2 in which every edge is present with probability 1 2 and each vertex has exactly two incident edges perpendicular to each other we prove that all components are finite cycles almost surely but the expected diameter of the cycle containing the origin is infinite moreover we derive the following critical exponents the tail probability diameter of the cycle of the origin n n and the expectation mathbb e length of a typical cycle with diameter n n with gamma 5 sqrt 17 4 0 219 ldots and delta sqrt 17 1 4 1 28 ldots the value of comes from a singular sixth order ode while the relation 3 2 corresponds to the fact that the scaling limit of the natural height function in the model is the additive brownian motion whose level sets have hausdorff dimension 3 2 we also include many open problems for example on the conformal invariance of certain linear entropy models

dimers and amoebae we study random surfaces which arise as height functions of random perfect matchings a k a dimer configurations on a weighted bipartite doubly periodic graph g embedded in the plane we derive explicit formulas for the surface tension and local gibbs measure probabilities of these models the answers involve a certain plane algebraic curve which is the spectral curve of the kasteleyn operator of the graph for example the surface tension is the legendre dual of the ronkin function of the spectral curve the amoeba of the spectral curve represents the phase diagram of the dimer model further we prove that the spectral curve of a dimer model is always a real curve of special type namely it is a harnack curve this implies many qualitative and quantitative statement about the behavior of the dimer model such as existence of smooth phases decay rate of correlations growth rate of height function fluctuations etc

coupling functions for domino tilings of aztec diamonds the inverse kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics in this paper we consider three different weightings of domino tilings of the aztec diamond and show using recurrence relations that we can compute the inverse kasteleyn matrix these weights are the one periodic weighting where the horizontal edges have one weight and the vertical edges have another weight the qvol weighting which corresponds to multiplying the product of tile weights by q if we add a box to the height function and the two periodic weighting which exhibits a flat region with defects in the center

log gases on quadratic lattices via discrete loop equations and q boxed plane partitions abstract we study a general class of log gas ensembles on shifted quadratic lattices we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are gaussian with a universal covariance we apply our general results to analyze the asymptotic behavior of a q boxed plane partition model introduced by borodin gorin and rains in particular we show that the global fluctuations of the height function on a fixed slice are described by a one dimensional section of a pullback of the two dimensional gaussian free field our approach is based on a q analogue of the schwinger dyson or loop equations which originate in the work of nekrasov and his collaborators and extends the methods developed by borodin gorin and guionnet to quadratic lattices

bessel identities in the waldspurger correspondence over a p adic field in this paper we develop the local theory for a jacquet s relative trace formula the local theory is essential to the application of the trace formula it is an identity of bessel and relative bessel distributions we show that the relative bessel distribution attached to a distinguished that is self contragradient unitary representation of gl 2 k where k is a p adic field is given by a locally integrable function namely the relative bessel function we compute the relative bessel function for principal series complementary series and special representations we also show that the bessel distributions associated to unitary irreducible admissible representations of the double covers of gl 2 k and sl 2 k are given by a locally integrable bessel functions we compute these bessel functions for principal series complementary series and special representations finally we obtain the waldspurger correspondence via bessel identities between relative bessel functions on gl 2 k and bessel functions on the double cover of sl 2 k the bessel identity also implies the identity between bessel and relative bessel distributions

fluctuations of an atomic ledge bordering a crystalline facet when a high symmetry facet joins the rounded part of a crystal the step line density vanishes as square root of r with r denoting the distance from the facet edge this means that the ledge bordering the facet has a lot of space to meander as caused by thermal activation we investigate the statistical properties of the border ledge fluctuations in the scaling regime they turn out to be non gaussian and related to the edge statistics of gaussian unitary ensemble multimatrix models

shakedown analysis of structures made of materials with temperature dependent yield stress in this work the shakedown of structures made of materials with temperature dependent yield stress is considered under some restrictions on the thermal loading condition the yield stress is linearized and shakedown theorems are established based on these linearized shakedown theorems the shakedown limit is formulated as a problem of convex optimization an algorithm is built to compute shakedown limits numerical tests show good agreement with analytic solutions and experimental data

limit shapes and the complex burgers equation in this paper we study surfaces in r 3 that arise as limit shapes in random surface models related to planar dimers these limit shapes are surface tension minimizers that is they minimize a functional of the form h dx dy among all lipschitz functions h taking given values on the boundary of the domain the surface tension has singularities and is not strictly convex which leads to formation of facets and edges in the limit shapes we find a change of variables that reduces the euler lagrange equation for the variational problem to the complex inviscid burgers equation complex hopf equation the equation can thus be solved in terms of an arbitrary holomorphic function which is somewhat similar in spirit to weierstrass parametrization of minimal surfaces we further show that for a natural dense set of boundary conditions the holomorphic function in question is in fact algebraic the tools of algebraic geometry can thus be brought in to study the minimizers and especially the formation of their singularities this is illustrated by several explicitly computed examples

an iteration algorithm for kinematic shakedown analysis abstract this paper investigates the computational shakedown analysis of an elastic plastic body subjected to a set of loads varying within a given domain using an ellipsoid yield surface an iteration algorithm based on a kinematic formulation is proposed to approach the shakedown load the convergence of the algorithm is guaranteed this algorithm can be applied to shakedown problems with strainhardening and certain geometric effects numerical examples are presented to illustrate the validity of the present method

on a conjecture of jacquet about distinguished representations of gl n in this paper we prove a conjecture of jacquet about supercuspidal representations of gln k distinguished by gln k or by un k for k a quadratic unramified extension of a non archimedean local field k

a unified approach for variationally consistent finite elements in elastoplasticity abstract a general variationally consistent approach for elastoplastic finite element analysis is presented a weak formulation of the finite step i e in terms of finite increments elastoplastic boundary value problem is obtained by enforcing the stationarity of a mixed functional of hu washizu type a peculiarity of the present formulation is that the constitutive equations are expressed in weak form also all fields are then independently discretized in terms of so called generalized variables the result is a set of non linear algebraic equations a subset of which can be interpreted as the backward difference time integrated constitutive law of the finite element an iterative procedure where all calculations are at the element and not at the gauss point level resting on newton raphson scheme is proposed for the solution of the governing equations it is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation

three dimensional limit analysis of rigid blocks assemblages part ii load path following solution procedure and validation a novel solution procedure for the non associated limit analysis of rigid blocks assemblages is proposed this proposal produces better solutions than previously proposed procedures and it is also able to provide an insight into the structural behaviour prior to failure the limit analysis model proposed in part i of this paper and the solution procedure are validated through illustrative examples in three dimensional masonry piers and walls the use of limit analysis for three dimensional problems incorporating non associated flow rules and a coupled yield surface is novel in the literature

incremental shakedown analysis in the case of thermal effects a new method of performing the shakedown analysis of structures subjected to variable repeated loads and temperature fields is presented the method employs the standard incremental elastic plastic finite element algorithm and is based upon a cyclic repetition of piecewise proportional paths that contain all the vertices of the load temperature variation domain a numerical example illustrates the approach

planar dimers and harnack curves in this article we study the connection between dimers and harnack curves discovered in 15 we prove that every harnack curve arises as a spectral curve of some dimer model we also prove that the space of harnack curves of given degree is homeomorphic to a closed octant and that the areas of the amoeba holes and the distances between the amoeba tentacles give these global coordinates we characterize harnack curves of genus zero as spectral curves of isoradial dimers and also as minimizers of the volume under their ronkin function with given boundary conditions

numerical shakedown analysis of axisymmetric sandwich shells an upper bound formulation shakedown analysis of axisymmetric elastic perfectly plastic sandwich shells is performed here using a new upper bound formulation based on a special form of koiter s theorem concerning piecewise linearized yield surfaces starting from finite element techniques and the tresca sandwich yield condition shakedown analysis is reduced to a linear programming problem which is solved by a powerful simplex algorithm numerical results are given for a number of examples and a comparison is made with a previously computed lower bound formulation

dynamics of 2 1 dimensional sos surfaces above a wall slow mixing induced by entropic repulsion we study the glauber dynamics for the 2 1 d solid on solid model above a hard wall and below a far away ceiling on an l times l box of z 2 with zero boundary conditions at large inverse temperature beta it was shown by bricmont el mellouki and frohlich 1986 that the floor constraint induces an entropic repulsion effect which lifts the surface to an average height h asymp 1 beta log l as an essential step in understanding the effect of entropic repulsion on the glauber dynamics we determine the equilibrium height h to within an additive constant h 1 4 beta log l o 1 we then show that starting from zero initial conditions the surface rises to its final height h through a sequence of metastable transitions between consecutive levels the time for a transition from height h ah a in 0 1 to height h 1 is roughly exp c l a for some constant c 0 in particular the mixing time of the dynamics is exponentially large in l i e t mix geq e c l we also provide the matching upper bound t mix leq e c l requiring a challenging analysis of the statistics of height contours at low temperature and new coupling ideas and techniques finally to emphasize the role of entropic repulsion we show that without a floor constraint at height zero the mixing time is no longer exponentially large in l