shape sensitivity analysis and shape optimization in planar elasticity using the element free galerkin method abstract this paper demonstrates that the element free galerkin efg method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2d elasticity the continuum based variational equations for displacement sensitivities are derived and are subsequently discretized this approach allows one to avoid differentiating the efg shape functions the present formulation that employs a penalty method for imposing the essential boundary conditions can be easily extended to 3d and or non linear problems numerical examples are presented to show the capabilities of the current approach for calculating sensitivities the flexibility of the efg method that eliminates the element connectivity requirement of the finite element method fem permits solving shape optimization problems without re meshing the problem of shape optimization of a fillet is used to demonstrate this fact smoother stresses and better accuracy for points close to the boundary allow for a better efg solution compared to published results using the fem the boundary element method bem or the boundary contour method bcm furthermore for the efg approach grid optimization appears unnecessary

on the different formulations in linear bifurcation analysis of laminated cylindrical shells abstract the stability pattern of shells is governed by a set of nonlinear partial differential equations the solution procedure can be simplified and fast and accurate predictions of the critical buckling load obtained with the aid of a multilevel approach under this approach the lower levels are implemented by means of the perturbation technique with the nonlinear prebuckling deformation disregarded and a linear set of equations solved for each state it turns out however that in these circumstances the prediction may differ depending on the chosen formulation in an attempt to find the reasons for these differences the linear bifurcation buckling behavior of laminated cylindrical shells was examined via two well known formulations with u v w and w f as the unknowns a third mixed formulation was found the most reliable in predicting the buckling behavior

shape optimization using reproducing kernel particle method and an enriched genetic algorithm combining reproducing kernel particle method rkpm with the proposed multi family genetic algorithm mfga a novel approach to continuum based shape optimization problems is brought forward in this paper taking full advantage of the features of meshfree method and the merits of mfga the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely the effectiveness versatility and performance of the proposed approach are demonstrated via three 2 d numerical examples

color level sets a multi phase method for structural topology optimization with multiple materials in this paper we address the problem of structural shape and topology optimization in a multi material domain a level set method is employed as an alternative approach to the popular homogenization based methods of rule of mixtures for multi material modeling a multi phase level set model is adapted for material and topology representation this model eliminates the need for a material interpolation or phase mixing scheme it only requires m level set functions to represent a structure of n 2m different material phases in a principle similar to combining colors from the three primary colors therefore this multi phase model may be referred to as a color level set representation which has its unique benefits it is flexible to handle complex topologies it substantially reduces the number of model functions when n 3 it automatically avoids the problem of overlap between material phases of a conventional partitioning approach we describe numerical techniques for efficient and robust implementation of the method by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain this would separate the issues of accuracy in numerical calculations of the physical equation and in the level set model propagation a gradient projection method is described for incorporating multiple constraints in the problem finally the benefits and the advantages of the developed method are illustrated with several 2d examples of mean compliance minimization of multi material structures

mice multiple peak identification characterization and estimation summary mice multiple peak identification characterization and estimation is a procedure for estimating a lower bound of the number of frequency peaks and for estimating the frequency peak parameters the leading application is protein structure determination using nuclear magnetic resonance nmr experiments nmr frequency data are multiple peak data where each frequency peak corresponds to two connected atoms in the three dimensional protein structure we analyze the nmr frequency data through a series of steps a preliminary step for separating the signal from the background followed by identification of local maxima up to a noise level dependent threshold estimation of the frequency peak parameters using an iterative algorithm and detection of mixtures of peaks using hypothesis testing

an alternative root n consistent estimator for panel data binary choice models in this paper we present an alternative root n consistent estimator for panel data fixed effects binary choice models the proposed estimator relaxes one of the key conditions that are required for the consistency of the estimator proposed in honore and lewbel 2002 and is shown to be consistent and asymptotically normally distributed under some sufficient conditions an easy to compute consistent estimator for the asymptotic covariance is provided

linear interpolation with a nonparametric accelerated failure time model abstract assuming a nonparametric accelerated failure time model a method is proposed for extrapolating low stress response probabilities on negative sloping line segments in the stress failure time plane the method analogous to linear interpolation in dose response studies results in simultaneous extrapolation ahead in time and down in stress in the two sample two stress level setting a goodness of fit test of the nonparametric model is considered and two hypothesis tests are proposed each pertaining to a condition that in addition to the assumed model must be met for the method to be valid the method is illustrated with censored strand life data and some simulated examples are used to consider power and robustness the failure time model is a scale family with curvature constraints the failure probability is assumed to be a sigmoid function of the product of time and a sigmoid scaling function of stress time percentiles as functions of stress are assumed to be convex the goodness of fit

testing for monotonicity under endogeneity an application to the reservation wage function abstract this paper develops a test for monotonicity of nonparametric regression models under endogeneity which in its generality is novel in the literature the test statistic which is built upon a second order u process introduces correction terms based on control functions that purge the endogeneity the test has a non standard asymptotic distribution from which asymptotic critical values can directly be derived furthermore the test statistic is extended to accommodate multivariate exogenous regressors consistency against general alternatives is proved and the finite sample properties of the test are examined in a monte carlo experiment the test is used to formally assess the monotonicity of the reservation wage as a declining function of elapsed unemployment duration which has implications for underlying job search models this relationship is difficult to measure due to the simultaneity of both variables results for uk data indicate that reservation wage functions do in fact not decline monotonically thereby contradicting some partial equilibrium job search models

topology optimization in b spline space abstract in this paper we present a new form of density based topology optimization where the design space is restricted to the b spline space an arbitrarily shaped design domain is embedded into a rectangular domain in which tensor product b splines are used to represent the density field we show that with proper choice of b spline degrees and knot spans the b spline design space is free from checkerboards without extraneous filtering or penalty we further reveal that the b spline representation provides an intrinsic filter for topology optimization where the filter size is controlled by b spline degrees and knot spans this b spline filter is effective in removing numerical artifacts and controlling minimal feature length in optimized structures when the b spline basis functions span multiple analysis elements we demonstrate that the b spline filter is linear in storage cost and does not require neighboring element information further this b spline based density representation decouples the design representation of density distribution from the finite element mesh thus multi resolution designs can be obtained without re meshing the design domain in particular successive optimization with respect to design resolutions leads to topologically simple features obtainable in either coarse or fine design resolutions thus achieving a form of mesh independency with respect to design representation this approach is versatile in the sense a variety of finite element and isogeometric analysis techniques can be used for solution of equilibrium equations and a variety of projection methods can be used to approximate b spline density in analysis numerical studies have been conducted over several representative topology optimization problems including minimal compliance of mbb beams compliant mechanism inverters and heat conductions

topology optimization of fluid structure interaction problems in poroelasticity abstract this paper presents a method for applying topology optimization to fluid structure interaction problems in saturated poroelastic media the method relies on a multiple scale method applied to periodic media the resulting model couples the stokes flow in the pores of the structure with the deformation of the elastic skeleton through a macroscopic darcy type flow law the method allows to impose pressure loads for static problems through a one way coupling while transient problems are fully coupled modeling the interaction between fluid and solid the material distribution is determined by topology optimization in order to optimize the performance of a shock absorber and test the pressure loading capabilities and optimization of an internally pressurized lid

a level set based iga formulation for topology optimization of flexoelectric materials abstract this paper presents a design methodology based on a combination of isogeometric analysis iga level set and point wise density mapping techniques for topology optimization of piezoelectric flexoelectric materials the fourth order partial differential equations pdes of flexoelectricity which require at least c 1 continuous approximations are discretized using non uniform rational b spline nurbs the point wise density mapping technique with consistent derivatives is directly used in the weak form of the governing equations the boundary of the design domain is implicitly represented by a level set function the accuracy of the iga model is confirmed through numerical examples including a cantilever beam under a point load and a truncated pyramid under compression with different electrical boundary conditions finally we provide numerical examples demonstrating the significant enhancement in electromechanical coupling coefficient that can be obtained using topology optimization

large scale topology optimization using preconditioned krylov subspace methods with recycling summary the computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis we propose fast iterative solvers for large threedimensional topology optimization problems to address this problem since the linear systems in the sequence of optimization steps change slowly from one step to the next we can significantly reduce the number of iterations and the runtime of the linear solver by recycling selected search spaces from previous linear systems in addition we introduce a minres minimum residual method version with recycling and a short term recurrence to make recycling more efficient for symmetric problems furthermore we discuss preconditioning to ensure fast convergence we show that a proper rescaling of the linear systems reduces the huge condition numbers that typically occur in topology optimization to roughly those arising for a problem with constant density we demonstrate the effectiveness of our solvers by solving a topology optimization problem with more than a million unknowns on a fast pc

gradient bounds for wachspress coordinates on polytopes we derive upper and lower bounds on the gradients of wachspress coordinates defined over any simple convex d dimensional polytope p the bounds are in terms of a single geometric quantity h ast which denotes the minimum distance between a vertex of p and any hyperplane containing a nonincident face we prove that the upper bound is sharp for d 2 and analyze the bounds in the special cases of hypercubes and simplices additionally we provide an implementation of the wachspress coordinates on convex polyhedra using matlab and employ them in a three dimensional finite element solution of the poisson equation on a nontrivial polyhedral mesh as expected from the upper bound derivation the h 1 norm of the error in the method converges at a linear rate with respect to the size of the mesh elements

mode identification of volatility in time varying autoregression in many applications time series exhibit nonstationary behavior that might reasonably be modeled as a time varying autoregressive ar process in the context of such a model we discuss the problem of testing for modality of the variance function we propose a test of modality that is local and when used iteratively can be used to identify the total number of modes in a given series this problem is closely related to peak detection and identification which has applications in many fields we propose a test that under appropriate assumptions is asymptotically distribution free under the null hypothesis even though nonparametric estimation of the ar parameter functions is involved simulation studies and applications to real datasets illustrate the behavior of the test

structural shape and topology optimization using a meshless galerkin level set method summary this paper aims to propose a meshless galerkin level set method for shape and topology optimization of continuum structures to take advantage of the implicit free boundary representation scheme the design boundary is represented as the zero level set of a scalar level set function to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface compactly supported radial basis functions csrbfs are used to parameterize the level set function and construct the shape functions for meshfree approximations based on a set of unstructured field nodes the meshless galerkin method with global weak form is used to implement the discretization of the state equations this provides a pathway to unify the two different numerical stages in most conventional level set methods 1 the propagation of discrete level set function on a set of eulerian grid and 2 the approximation of discrete equations on a set of lagrangian mesh the original more difficult shape and topology optimization based on the level set equation is transformed into a relatively easier size optimization to which many efficient optimization algorithms can be applied the proposed level set method can describe the moving boundaries without remeshing for discontinuities the motion of the free boundary is just a question of advancing the discrete level set function in time by solving the size optimization several benchmark examples are used to demonstrate the effectiveness of the proposed method the numerical results show that the proposed method can simplify numerical process and avoid numerical difficulties involved in most conventional level set methods it is straightforward to apply the proposed method to more advanced shape and topology optimization problems copyright 2011 john wiley sons ltd

a simple test for moment inequality models with an application to english auctions abstract testable predictions of many economic models involve inequality comparisons between transformations of nonparametric functionals we introduce an econometric test for these types of restrictions based on one sided l p statistics that adapt asymptotically to the contact sets without having to directly estimate them monte carlo experiments show that our test is less conservative than procedures based on least favorable configurations and has power comparable to other contact set based procedures as an application we test for interdependence of bidders valuations in ascending auctions using usfs timber auction data we reject the independent private values model in favor of a model of correlated private values

approximate reanalysis in topology optimization despite rapid improvements in computer performance there is still room for advances in computational efficiency for handling structural optimization applications due to the high computational cost involved in the optimization process in general the total computational cost of the optimization procedure is governed by the complexity of three aspects the model the analysis and the optimization 1 solving problems that consider high complexities in all three aspects is presently somewhat limited in problem size thus motivating the search for methods and procedures that require reduced computational resources but yield high quality results in this paper the implementation of an approximate reanalysis method in topology optimization is investigated we apply the so called nested approach where optimization is performed in the design variables only and where the equilibrium equations are treated as function calls the goal is to reduce the computation involved in repeated solutions of the equilibrium equations which for large problems will dominate the computational cost of the whole process the approximate reanalysis performed here is based on the combined approximations ca approach proposed by kirsch 2 for linear static reanalysis and later used successfully also in vibration dynamic and nonlinear reanalysis the main feature of ca is the integration of a local series expansion in a global reduced basis solution when using ca for repeated structural analysis one can substantially reduce the number of required factorizations of the stiffness matrix and thus removing a significant portion of the computational effort in this study ca has been implemented for topology optimization of linear structures and the accuracy of the solutions obtained has been benchmarked against solutions presented in the literature 3 and 4 the relative efficiency of the method has been evaluated by comparing with the case in which all analysis equations are solved by a direct method there is a clear trade off between the accuracy and the efficiency of the approximate procedure both are mainly influenced by two parameters the frequency of full matrix decompositions and the number of vectors generated for the reduced basis more frequent decompositions will result in smaller changes in stiffness and therefore a more accurate approximation but at the cost of matrix factorizations similarly using more basis vectors will give a better representation of the actual solution but will increase the computational effort for all the trial cases considered the optimal designs and the objective values obtained by the approximate procedure were practically

a numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions we present a numerical algorithm for the construction of efficient high order quadratures in two and higher dimensions quadrature rules constructed via this algorithm possess positive weights and interior nodes resembling the gaussian quadratures in one dimension in addition rules can be generated with varying degrees of symmetry adaptable to individual domains we illustrate the performance of our method with numerical examples and report quadrature rules for polynomials on triangles squares and cubes up to degree 50 these formulae are near optimal in the number of nodes used and many of them appear to be new

convex clustering via l1 fusion penalization summary we study the large sample behaviour of a convex clustering framework which minimizes the sample within cluster sum of squares under an l1 fusion constraint on the cluster centroids this recently proposed approach has been gaining in popularity however its asymptotic properties have remained mostly unknown our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems we use this representation to provide a simple and intuitive formulation for the population clustering procedure we then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence the proof conducts a careful simultaneous analysis of a collection of m estimation problems whose cardinality grows together with the sample size on the basis of the new perspectives gained from the asymptotic investigation we propose a key post processing modification of the original clustering framework we show both theoretically and empirically that the resulting approach can be successfully used to estimate the number of clusters in the population using simulated data we compare the proposed method with existing number of clusters and modality assessment approaches and obtain encouraging results we also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single cell virology study

extended finite element method on polygonal and quadtree meshes in this paper we present mesh independent modeling of discontinuous flelds on polygonal and quadtree flnite element meshes this approach falls within the class of extended and generalized flnite element methods where the partition of unity framework is used to introduce additional enrichment functions within the classical displacement based flnite element approximation for crack modeling a discontinuous function and the two dimensional asymptotic crack tip flelds are used as enrichment functions linearly complete partition of unity approximations are adopted on polygonal convex and nonconvex elements and quadtree meshes excellent agreement with reference solution results is obtained for mixed mode stress intensity factors on benchmark crack problems and crack growth simulations without remeshing are conducted on polygonal and quadtree meshes to reveal the potential of the proposed techniques in computational failure mechanics

numerically determined enrichment functions for the extended finite element method and applications to bi material anisotropic fracture and polycrystals strain singularities appear in many linear elasticity problems a very fine mesh has to be used in the vicinity of the singularity in order to obtain acceptable numerical solutions with the finite element method fem special enrichment functions describing this singular behavior can be used in the extended finite element method x fem to circumvent this problem these functions have to be known in advance but their analytical form is unknown in many cases li et al described a method to calculate singular strain fields at the tip of a notch numerically a slight modification of this approach makes it possible to calculate singular fields also in the interior of the structural domain we will show in numerical experiments that convergence rates can be significantly enhanced by using these approximations in the x fem the convergence rates have been compared with the ones obtained by the fem this was done for a series of problems including a polycrystalline structure copyright 2010 john wiley sons ltd

a generalized finite element method for polycrystals with discontinuous grain boundaries summary we present a generalized finite element method for the analysis of polycrystals with explicit treatment of grain boundaries grain boundaries and junctions understood as loci of possible displacement discontinuity are inserted into finite elements by exploiting the partition of unity property of finite element shape functions consequently the finite element mesh does not need to conform to the polycrystal topology the formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach the proposed methodology can also be used for branched and intersecting cohesive cracks and comparisons are made to a related approach int j numer meth engng 2000 48 1741 copyright 2006 john wiley sons ltd

shape optimization directly from cad an isogeometric boundary element approach using t splines abstract we develop a t spline isogeometric boundary element method igabem simpson et al 2012 scott et al 2013 simpson et al 2014 to shape sensitivity analysis and gradient based shape optimization in three dimensional linear elasticity contrary to finite element based isogeometric analysis iga approaches no parametrization of the volume is required hence the iterative optimization algorithm can be implemented directly from cad without any mesh generation or postprocessing step for returning the resulting structure to cad designers t splines also guarantee a water tight geometry without the manual geometrical repair work as with non uniform rational b splines nurbs we demonstrate the worth of the method by analysing problems with and without analytical solutions including engineering examples involving complex shapes additionally we provide all the derivations of the required sensitivities and the details pertaining to the geometries examined in the benchmarking to provide helpful reference problems for 3d shape optimization

linear smoothed polygonal and polyhedral finite elements the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method in this work we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes the main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain this new strain is then used in the computation of the stiffness matrix the convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations the accuracy is also improved and all the methods tested pass the patch test to machine precision

jackknife multiplier bootstrap finite sample approximations to the u process supremum with applications this paper is concerned with finite sample approximations to the supremum of a non degenerate u process of a general order indexed by a function class we are primarily interested in situations where the function class as well as the underlying distribution change with the sample size and the u process itself is not weakly convergent as a process such situations arise in a variety of modern statistical problems we first consider gaussian approximations namely approximate the u process supremum by the supremum of a gaussian process and derive coupling and kolmogorov distance bounds such gaussian approximations are however not often directly applicable in statistical problems since the covariance function of the approximating gaussian process is unknown this motivates us to study bootstrap type approximations to the u process supremum we propose a novel jackknife multiplier bootstrap jmb tailored to the u process and derive coupling and kolmogorov distance bounds for the proposed jmb method all these results are non asymptotic and established under fairly general conditions on function classes and underlying distributions key technical tools in the proofs are new local maximal inequalities for u processes which may be useful in other problems we also discuss applications of the general approximation results to testing for qualitative features of nonparametric functions based on generalized local u processes

a high order mixed polygonal finite element for incompressible stokes flow analysis abstract this paper presents a new high order mixed scheme of polygonal finite element method pfem for incompressible flow computation the system of polygonal basis functions with bubble enriched functions is applied to represent the fluid velocity field while the pressure field is approximated by the set of polygonal basis functions the new element is named as minipe from a practical point of view the present element naturally satisfies the well known inf sup condition the numerical tests of the incompressible fluid flow problems governed by stokes equation systems are presented to verify the performance quality of proposed method with respect to the stability and convergence rate

testing monotonicity of a regression function we consider the problem of testing monotonicity of the regression function in a nonparametric regression model we introduce test statistics that are functionals of a certain natural u process we study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for gaussian processes we show that the tests are consistent against general alternatives

gauss green cubature and moment computation over arbitrary geometries we have implemented in matlab a gauss like cubature formula over arbitrary bivariate domains with a piecewise regular boundary which is tracked by splines of maximum degree p spline curvilinear polygons the formula is exact for polynomials of degree at most 2n 1 using n cmn 2 nodes 1 c p m being the total number of points given on the boundary it does not need any decomposition of the domain but relies directly on univariate gauss legendre quadrature via green s integral formula several numerical tests are presented including computation of standard as well as orthogonal moments over a nonstandard planar region

testing functional inequalities abstract this paper develops tests for inequality constraints of nonparametric regression functions the test statistics involve a one sided version of l p type functionals of kernel estimators 1 p drawing on the approach of poissonization this paper establishes that the tests are asymptotically distribution free admitting asymptotic normal approximation in particular the tests using the standard normal critical values have asymptotically correct size and are consistent against general fixed alternatives furthermore we establish conditions under which the tests have nontrivial local power against pitman local alternatives some results from monte carlo simulations are presented

construction of polygonal interpolants a maximum entropy approach in this paper we establish a link between maximizing information theoretic entropy and the construction of polygonal interpolants the determination of shape functions on n gons n 3 leads to a non unique under determined system of linear equations the barycentric co ordinates i which form a partition of unity are associated with discrete probability measures and the linear reproducing conditions are the counterpart of the expectations of a linear function the i are computed by maximizing the uncertainty h 1 2 n i log i subject to the above constraints the description is expository in nature and the numerical results via the maximum entropy maxent formulation are compared to those obtained from a few distinct polygonal interpolants the maximum entropy formulation leads to a feasible solution for i in any convex or non convex polygon this study is an instance of the application of the maximum entropy principle wherein least biased inference is made on the basis of incomplete information copyright 2004 john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 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

parallelized structural topology optimization for eigenvalue problems a parallel topology optimization method is proposed to deal with large scale structural eigenvalue related design problems while existing parallel methods have been employed mainly for finite element analysis the present work deals with the entire parallel process of analysis and topology optimization using a parallel processing technique in the framework of the physical domain decomposition method the sensitivity analysis and design variable update are performed independently in each subdomain with minimum data communication among subdomains a successive estimation strategy over design iterations is proposed to expedite the design optimization process the preconditioned conjugate gradient method and the subspace iteration method are used as parallel solvers several numerical examples are considered to show the scalability and effectiveness of the present parallel approach in handling large scale design problems

on the approximation in the smoothed finite element method sfem this letter aims at resolving the issues raised in the recent short communication int j numer meth engng 2008 76 8 1285 1295 doi 10 1002 nme 2460 and answered by int j numer meth engng 2009 doi 10 1002 nme 2587 by proposing a systematic approximation scheme based on non mapped shape functions which both allows to fully exploit the unique advantages of the smoothed finite element method sfem comput mech 2007 39 6 859 877 doi 10 1007 s00466 006 0075 4 commun numer meth engng 2009 25 1 19 34 doi 10 1002 cnm 1098 int j numer meth engng 2007 71 8 902 930 comput meth appl mech engng 2008 198 2 165 177 doi 10 1016 j cma 2008 05 029 comput meth appl mech engng 2007 submitted int j numer meth engng 2008 74 2 175 208 doi 10 1002 nme 2146 comput meth appl mech engng 2008 197 13 16 1184 1203 doi 10 1016 j cma 2007 10 008 and resolve the existence linearity and positivity deficiencies pointed out in int j numer meth engng 2008 76 8 1285 1295 we show that wachspress interpolants a rational basis for function approximation academic press inc new york 1975 computed in the physical coordinate system are very well suited to the sfem especially when elements are heavily distorted obtuse interior angles the proposed approximation leads to results that are almost identical to those of the sfem initially proposed in comput mech 2007 39 6 859 877 doi 10 1007 s00466 006 0075 4 these results suggest that the proposed approximation scheme forms a strong and rigorous basis for the construction of sfems copyright 2009 john wiley sons ltd

isogeometric topology optimization using trimmed spline surfaces in the present work a new spline based topology optimization using trimmed spline surfaces and the isogeometric analysis is proposed in the proposed approach the trimmed surface analysis which can treat topologically complex spline surfaces using trimming information provided by cad systems is employed for structural response analysis and sensitivity calculation in the topology optimization the outer and inner boundaries of design models are represented by a spline surface and trimming curves design variables used in this approach are the coordinates of control points of a spline surface and those of trimming curves new sensitivity formulations for the control points in the trimmed surface analysis are proposed and their efficiency and accuracy are verified the creation of new inner fronts during optimization is allowed for the topological flexibility an inner front merging algorithm is also presented the proposed spline based topology optimization is used to solve some benchmarking problems design space dependency which is one of serious shortcomings in conventional topology optimization approaches is naturally eliminated by the proposed spline based optimization design dependent load problems which are difficult to treat with conventional grid based topology optimization methods are easily dealt with by the proposed one it is also shown that post processing effort for converting to cad model is eliminated by using the same spline information in numerical analysis and design optimization

testing noisy numerical data for monotonic association rank correlation measures are intended to measure to which extent there is a monotonic association between two observables while they are mainly designed for ordinal data they are not ideally suited for noisy numerical data in order to better account for noisy data a family of rank correlation measures has previously been introduced that replaces classical ordering relations by fuzzy relations with smooth transitions thereby ensuring that the correlation measure is continuous with respect to the data the given paper briefly repeats the basic concepts behind this family of rank correlation measures and investigates it from the viewpoint of robust statistics then on this basis we introduce a framework of novel rank correlation tests an extensive experimental evaluation using a large number of simulated data sets is presented which demonstrates that the new tests indeed outperform the classical variants in terms of type ii error rates without sacrificing good performance in terms of type i error rates this is mainly due to the fact that the new tests are more robust to noise for small samples the gaussian rank correlation estimator turned out to be the best choice in situations where no prior knowledge is available about the data whereas the new family of robust gamma test provides an advantage in situations where information about the noise distribution is available an implementation of all robust rank correlation tests used in this paper is available as an r package from the cran repository

polygon scaled boundary finite elements for crack propagation modelling summary an automatic crack propagation modelling technique using polygon elements is presented a simple algorithm to generate a polygon mesh from a delaunay triangulated mesh is implemented the polygon element formulation is constructed from the scaled boundary finite element method sbfem treating each polygon as a sbfem subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks stress intensity factors are computed directly from their definitions without any nodal enrichment functions an automatic remeshing algorithm capable of handling any n sided polygon is developed to accommodate crack propagation the algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths the efficiency of the polygon sbfem in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features the predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature copyright 2012 john wiley sons ltd

bayesian spatial monotonic multiple regression we consider monotonic multiple regression for contiguous regions the regression functions vary regionally and may exhibit spatial structure we develop bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump markov chain monte carlo techniques spatial dependence is incorporated by a flexible prior distribution which is tuned using cross validation and bayesian optimization we derive the mean and variance of the prior induced by the marked point process approach asymptotic results show consistency of the estimated functions posterior realizations enable variable selection the detection of discontinuities and prediction in simulations and in an application to a norwegian insurance data set our methodology shows better performance than existing approaches

large scale topology optimization in 3d using parallel computing we consider large scale topology optimization of elastic continua in 3d using the regularized intermediate density control introduced in 1 the nested approach is used i e equilibrium is solved at each iteration to get a high quality resolution of realistic designs in 3d problems involving several hundreds of thousand finite elements are solved in order to deal with problems of this size parallel computing is used in combination with domain decomposition the equilibrium equations are solved by a preconditioned conjugate gradient algorithm and the optimization part is solved using sequential convex programming several numerical results obtained from computations performed on a cray parallel computer are presented

buckling of laminated cylindrical shells in terms of different theories and formulations bifurcation buckling analysis of laminated cylindrical shells is presented on the basis of three different shell theories donnell s donnell l h stability of thin walled tubes under torsion naca tr 479 1933 sanders s sanders j l jr nonlinear theories of thin shells quarterly journal on applied mathematics vol 21 no 1 1963 pp 21 36 and timoshenko s timoshenko s theory of elastic stability mcgraw hill new york 1961 formulations in terms of the displacement components and of the airy stress function and normal displacement are examined the partial differential equations are derived via the variational principle and solved with variables expanded in fourier series in the circumferential direction and presented as finite differences in the axial direction the buckling behavior of an angle ply laminated cylindrical shell under different modes of loading was investigated parametrically showing in contrast to its isotropic counterparts a discrepancy between the two formulations

a polytree based adaptive polygonal finite element method for topology optimization summary we propose a highly effective approach using a novel adaptive methodology to perform topology optimization with polygonal meshes called polytree meshes polytree is a hierarchical data structure based on the principle of recursive spatial decomposition of each polygonal element with n nodes into n 1 arbitrary new polygonal elements enabling more efficient utilization of unstructured meshes and arbitrary design domains in topology optimization in order to treat hanging nodes after each optimization loop we define the wachspress coordinate on a reference element and then utilize an affine map to obtain shape functions and their gradients on arbitrary polygons with n vertices and m hanging nodes called side nodes as the polygonal element with n m vertices the polytree meshes do not only improve the boundary description quality of the optimal result but also reduce the computational cost of optimization process in comparison with the use of uniformly fine meshes several numerical examples are investigated to show the high effectiveness of the proposed method this article is protected by copyright all rights reserved

buckling analysis of laminated cylindrical shells with arbitrary noncircular cross section buckling analysis of laminated cylindrical shells with noncircular cross section of arbitrary closed shape is presented the equations in terms of the normal displacement and airy stress function of the donnell type are derived via the hu washizu mixed formulation the curvature which is a function of the circumferential coordinate is expanded in fourier series the circumferential dependence is eliminated by a combination of fourier expansion and galerkin s method the resulting ordinary differential equations are then reduced to matrix equations by the use of finite differences the configurational aspect is investigated parametrically unlike the circular cylindrical shells coupling of the wave number in the circumferential direction is significantly high

improving multiresolution topology optimization via multiple discretizations summary unlike the traditional topology optimization approach that uses the same discretization for finite element analysis and design optimization this paper proposes a framework for improving multiresolution topology optimization imtop via multiple distinct discretizations for 1 finite elements 2 design variables and 3 density this approach leads to high fidelity resolution with a relatively low computational cost in addition an adaptive multiresolution topology optimization amtop procedure is introduced which consists of selective adjustment and refinement of design variable and density fields various two dimensional and three dimensional numerical examples demonstrate that the proposed schemes can significantly reduce computational cost in comparison to the existing element based approach copyright 2012 john wiley sons ltd

reducing dimensionality in topology optimization using adaptive design variable fields topology optimization methodologies typically use the same discretization for the design variable and analysis meshes analysis accuracy and expense are thus directly tied to design dimensionality and optimization expense this paper proposes leveraging properties of the heaviside projection method hpm to separate the design variable field from the analysis mesh in continuum topology optimization hpm projects independent design variables onto element space over a prescribed length scale a single design variable therefore influences several elements creating a redundancy within the design that can be exploited to reduce the number of independent design variables without significantly restricting the design space the algorithm begins with sparse design variable fields and adapts these fields as the optimization progresses the technique is demonstrated on minimum compliance maximum stiffness problems solved using continuous optimization and genetic algorithms for the former the proposed algorithm typically identifies solutions having objective functions within 1 of those found using full design variable fields computational savings are minor to moderate for the minimum compliance formulation with a single constraint and are substantial for formulations having many local constraints when using genetic algorithms solutions are consistently obtained on mesh resolutions that were previously considered intractable copyright 2009 john wiley sons ltd

an evolutionary topology optimization approach with variationally controlled growth abstract previous works of junker and hackl 2016 have presented a variational growth approach to topology optimization in which the problem of checkerboarding was suppressed by means of a discontinuous regularization scheme this approach did not require additional filter techniques and also optimization algorithms were not needed any more however growth approaches to topology optimization demand some limitations in order to avoid a global and simultaneous generation of mass the limitation has been achieved by a rather simple approach with restricted possibilities for controlling in this contribution we eliminate this drawback by introducing a lagrange multiplier to control the total mass within the model space for each iteration step this enables us to achieve directly controlled growth behavior and even find optimized structures for prescribed structure volumes furthermore a modified growth approach which we refer to as the lagrange shift approach results a numerically stable model that is easy to handle after the derivation of the approach we present numerical solutions for different boundary problems that demonstrate the potential of our model

a polytree based adaptive polygonal finite element method for multi material topology optimization abstract this study presents a polytree based adaptive methodology for multi material topology optimization mmtop polytree data structure is introduced as a general recursive multi level mesh that is automatically refined in processing based on error analysis in order to resolve hanging nodes in element edges the wachspress coordinate is employed on a reference element before using a mapping scheme to obtain shape functions and their derivatives for any polygons a new definition of filter radius is also proposed to improve the efficiency of filters and optimized results the combination of polytree meshes and adaptive filters not only clarifies the interfaces between material phases including void phase but also decreases the computing time of the overall process in comparison to using the regular fine meshes several benchmark and practical problems are considered to show distinct features of the proposed method

implementation of regularized isogeometric boundary element methods for gradient based shape optimization in two dimensional linear elasticity the present work addresses shape sensitivity analysis and optimization in two dimensional elasticity with a regularized isogeometric boundary element method igabem non uniform rational b splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations with the advantage of tight integration of design and analysis the application of igabem in shape optimization reduces the mesh generation regeneration burden greatly the work is distinct from the previous literatures in igabem shape optimization mainly in two aspects 1 the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives which were the main implementation difficulty in igabem and 2 although based on the same computer aided design cad model the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh thus achieving a balance between less design variables for efficiency and refined mesh for accuracy this technique was initially used in isogeometric finite element method and was incorporated into the present igabem implementation

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

numerical integration over arbitrary polygonal domains based on schwarz christoffel conformal mapping this paper presents a new numerical integration technique oil arbitrary polygonal domains the polygonal domain is mapped conformally to the unit disk using schwarz christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used this method eliminates the need for a two level isoparametric mapping usually required moreover the positivity of the jacobian is guaranteed numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

virtual and smoothed finite elements a connection and its application to polygonal polyhedral finite element methods summary we show both theoretically and numerically a connection between the smoothed finite element method sfem and the virtual element method and use this approach to derive stable cheap and optimally convergent polyhedral fem we show that the stiffness matrix computed with one subcell sfem is identical to the consistency term of the virtual element method irrespective of the topology of the element as long as the shape functions vary linearly on the boundary using this connection we propose a new stable approach to strain smoothing for polygonal polyhedral elements where instead of using sub triangulations we are able to use one single polygonal polyhedral subcell for each element while maintaining stability for a similar number of degrees of freedom the proposed approach is more accurate than the conventional sfem with triangular subcells the time to compute the stiffness matrix scales with the o dofs 1 1 in case of the conventional polygonal fem while it scales as o dofs 0 7 in the proposed approach the accuracy and the convergence properties of the sfem are studied with a few benchmark problems in 2d and 3d linear elasticity copyright 2015 john wiley sons ltd

distribution free tests of stochastic monotonicity this article proposes an omnibus test for monotonicity of nonpara metric conditional distributions and its moments unlike previous proposals our method does not require smooth estimation of the derivatives of nonparametric curves and it can be implemented even when probability densities do not exist in fact we only require continuity of the marginal distributions under the null and xed alternatives distinguishing features of our approach are that critical values are pivotal under the null in nite samples and the test is invariant to any monotonic continuous transformation of the explanatory variable the test sta tistic is the sup norm of the dierence between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate the resulting test is able to detect local alternatives converging to the null at the parametric rate n 1 2 with n the sample size the article also discusses several applications and extensions of the proposal these include testing monotonicity of general conditional moments and the extension to multivariate explanatory variables the nite sample performance of the test is examined by means of a monte carlo experiment

virtual elements for linear elasticity problems we discuss the application of virtual elements to linear elasticity problems for both the compressible and the nearly incompressible case virtual elements are very close to mimetic finite differences see for linear elasticity l beirao da veiga m2an math model numer anal 44 2010 pp 231 250 and in particular to higher order mimetic finite differences as such they share the good features of being able to represent in an exact way certain physical properties conservation incompressibility etc and of being applicable in very general geometries the advantage of virtual elements is the ductility that easily allows high order accuracy and high order continuity