minimum length scale control in structural topology optimization based on the moving morphable components mmc approach abstract a novel approach which can control the minimum length scale in topology optimization in a straightforward and explicit way is proposed in the present paper this approach is constructed under the so called moving morphable components mmc based solution framework where optimized structural topology can be found by changing the shapes and layout of a set of trapezoid shaped structural components on a fixed finite element mesh the extended finite element method xfem is employed for structural response analysis and shape sensitivity information is obtained by carrying out numerical integration along the structural boundary a precision definition of the minimum length scale of a structure is also suggested based on the proposed solution framework compared with existing approaches the proposed approach can achieve minimum length scale control by simply setting lower bounds on a set of geometric design variables only a small number of purely geometric constraints imposed on the sizes of intersection regions should be considered explicitly in order to get a complete minimum length scale control numerical examples demonstrate the effectiveness of the proposed method

use of higher order shape functions in the scaled boundary finite element method the scaled boundary finite element method is a novel semi analytical technique whose versatility accuracy and efficiency are not only equal to but potentially better than the finite element method and the boundary element method for certain problems this paper investigates the possibility of using higher order polynomial functions for the shape functions two techniques for generating the higher order shape functions are investigated in the first the spectral element approach is used with lagrange interpolation functions in the second hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones as in the p version of the finite element method to check the accuracy of the proposed procedures a plane strain problem for which an exact solution is available is employed a more complex example involving three scaled boundary subdomains is also addressed the rates of convergence of these examples under p refinement are compared with the corresponding rates of convergence achieved when uniform h refinement is used allowing direct comparison of the computational cost of the two approaches the results show that it is advantageous to use higher order elements and that higher rates of convergence can be obtained using p refinement instead of h refinement copyright 2005 john wiley sons ltd

fast and exact simulation of stationary gaussian processes through circulant embedding of the covariance matrix geostatistical simulations often require the generation of numerous realizations of a stationary gaussian process over a regularly meshed sample grid omega this paper shows that for many important correlation functions in geostatistics realizations of the associated process over m 1 equispaced points on a line can be produced at the cost of an initial fft of length 2m with each new realization requiring an additional fft of the same length in particular the paper first notes that if an m 1 times m 1 toeplitz correlation matrix r can be embedded in a nonnegative definite 2m times2m circulant matrix s exact realizations of the normal multivariate y sim cal n 0 r can be generated via ffts of length 2m theoretical results are then presented to demonstrate that for many commonly used correlation structures the minimal embedding in which m m is nonnegative definite extensions to simulations of stationary fields in higher dimensions are also provided and illustrated

plate spectral elements based upon reissner mindlin theory plate bending spectral elements based upon the reissner mindlin theory is developed for a rectangular plate numerical comparison studies for static and eigenvalue problems demonstrate the excellent performance and robustness of the present method the improvement in accuracy and computational efficiency in comparison with low order plate bending elements is remarkable and suggests that the proposed approach is an alternative to existing schemes

a simple and efficient space domain implementation of the turning bands method given a correlation function c x with x in rn the turning bands method tbm for n 2 and 3 constructs realizations of an n dimensional and stationary process y n o c x from appropriately summed line processes therefore an implementation of tbm calls naturally for fast and accurate generations of line realizations these have generally been generated by a spectral approach since the fourier transform of the line covariances is linked in a very simple fashion to the n dimensional fourier transform of c x however we show that in many instances a space domain implementation of tbm with line realizations obtained from a circulant embedding method has advantages over a spectral implementation in that without increase in computational costs 1 the line realizations display exactly the required covariance structure 2 knowledge of the spectral density of the process y is not required and 3 fine tuning of line process parameters is not needed

optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures we study dispersive effects of wave propagation in periodic media which can be modelled by adding a fourth order term in the homogenized equation the corresponding fourth order dispersive tensor is called burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion more precisely we consider the case of a two phase composite medium with an eightfold symmetry assumption of the periodicity cell in two space dimensions we obtain upper and lower bound for the dispersive properties along with optimal microgeometries

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

the turning bands method for simulation of random fields using line generation by a spectral method the turning bands method tbm for the simulation of multidimensional random fields is presented these fields commonly occur in the monte carlo simulation of hydrologic processes particularly groundwater flow and mass transport the general tbm equations for two and three dimensional fields are derived with particular emphasis on the more complicated two dimensional case for stationary two dimensional fields the unidimensional line process is generated by a simple spectral method a technique which can be generally applied to any two dimensional covariance function and which is easily extended to anisotropic and areal averaged processes theoretically and by example the tbm is shown to be ergodic even for a finite number of lines and it is demonstrated that it rapidly converges to the true statistics of the field guidelines are presented for the selection of model parameters which will be helpful in the design of simulation experiments the tbm is compared to other methods in terms of cost and accuracy demonstrating that the tbm is as accurate as and much less expensive than multidimensional spectral techniques and more accurate than the most expensive approaches which use matrix inversion such as the nearest neighbor approach the unidimensional spectral technique presented here permits for the first time the inexpensive and accurate tbm simulation of any proper two dimensional covariance function and should be of some help in the stochastic analysis of hydrologic processes

shape optimization with a level set based mesh evolution method in this article we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process by means of a mesh amenable for mechanical analyses while retaining the whole versatility of the level set method when it comes to accounting for their evolution the key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one and conversely this notably brings into play an algorithm for generating the signed distance function to an arbitrary discrete domain and a mesh generation algorithm for implicitly defined geometries

analysis of orthotropic thick plates by meshless local petrov galerkin mlpg method a meshless local petrov galerkin mlpg method is applied to solve static and dynamic problems of orthotropic plates described by the reissner mindlin theory analysis of a thick orthotropic plate resting on the winkler elastic foundation is given too a weak formulation for the set of governing equations in the reissner mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied the meshless approximation based on the moving least squares mls method is employed in the numerical implementation the present computational method is applicable also to plates with varying thickness numerical results for simply supported and clamped plates are presented copyright 2006 john wiley sons ltd

shape optimization using the cut finite element method we present a cut finite element method for shape optimization in the case of linear elasticity the elastic domain is defined by a level set function and the evolution of the domain is obtained by

on multimodality of the likelihood in the spatial linear model summary a popular covariance scheme used for the spatial linear model in geostatistics has spherical form however the likelihood is not twice differentiable with respect to the range parameter and this raises some questions regarding the unimodality of the likelihood we compare the likelihoods of the spatial linear model for small samples under this scheme and the doubly geometric scheme also a power covariance with range parameter is proposed in view of potential multimodal likelihoods for small samples for this model a convenient profile likelihood is introduced and studied

a thin plate formulation without rotation dofs based on the radial point interpolation method and triangular cells a formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method rpim the deflection fields are approximated using the rpim shape functions which possess the kronecker delta property for easy impositions of essential boundary conditions three types of smoothing domains which are also serving as the numerical integrations domains are constructed based on the background three node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures the generalized smoothed galerkin weak form is then used to create the discretized system equations the essential boundary conditions of rotations are imposed in the process of constructing the curvature field and the translation boundary conditions are imposed as in the standard fem a number of numerical examples including both static and free vibration analysis are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures the results show that the present formulation can obtain very stable and accurate solutions even for the extremely irregular background cells

upscaling of permeability of anisotropic heterogeneous formations 1 the general framework in numerical simulations of flow through heterogeneous formations the domain is partitioned into numerical elements the solution requires assigning physical properties to each numerical block the process of transferring information from the scale of actual heterogeneity to that of the numerical elements is known as upscaling we consider steady one phase flow and the only property of interest is the permeability which is regarded as a random space function and the same is true for the upscaled conductivity in this paper we establish the necessary and sufficient conditions to be satisfied by upscaling the necessary conditions are expressed with the aid of the global response of the formation e g the total flux caused by a constant pressure head drop applied on the boundaries the requirement is that the expected value and the variance of the total flux are the same in the actual and upscaled domains these are supplemented by local conditions which stipulate that space averages of flow variables over the numerical blocks in the upscaled domain tend to those in the actual formation when the elements size tends to 0 the result of this analysis is that the upscaled permeability must be such as to ensure the equality in a statistical sense between the space averaged dissipation in the two media by assuming an unbounded domain average uniform flow and stationarity simplified relationships between the moments of the dissipation in the upscaled and actual media are derived it is shown that the effective permeability of the two media is the same the approach is illustrated for stratified formations for which exact composition rules are possible even in this simple case the upscaled permeability is a tensor characterized at second order by two mean components and three covariance functions

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

velocity extension for the level set method and multiple eigenvalues in shape optimization in the context of structural optimization by the level set method we propose an extension of the velocity of the underlying hamilton jacobi equation the gradient method is endowed with a hilbertian structure based on the h1 sobolev space numerical results for compliance minimization and mechanism design show a strong improvement of the rate of convergence of the level set method another important application is the optimization of multiple eigenvalues

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

a new formulation for transmissivity estimation with improved global convergence properties a new formulation is proposed for the estimation of transmissivity in confined aquifers based on head measurements this formulation consists of a formulation which minimizes a weighted residual norm of the gradient of the measured and observed head the weighting is the square of the estimated transmissivity we show by theoretical analysis and numerical experimentation the improved global convergence properties and characteristics of stability under head measurement uncertainty exhibited by the new formulation we conclude that the new formulation may be superior to conventional head residual formulations or may be useful as an added term to conventional formulations the formulation is further demonstrated by a field scale application to the friuli aquifer in italy

semi lagrangian methods for level set equations a new numerical method for solving geometric moving interface problems is presented the method combines a level set approach and a semi lagrangian time stepping scheme which is explicit yet unconditionally stable the combination decouples each mesh point from the others and the time step from the cfl stability condition permitting the construction of methods which are efficient adaptive and modular analysis of a linear one dimensional model problem suggests a surprising convergence criterion which is supported by heuristic arguments and confirmed by an extensive collection of two dimensional numerical results the new method computes correct viscosity solutions to problems involving geometry anisotropy curvature and complex topological events

pq adaptive solid finite elements for three dimensional plates and shells this article presents a pq adaptive finite element procedure for three dimensional computation of thin walled structures like plates and shells the approach is based on a hexahedral element with high order shape functions the polynomial degree of the shape functions in the three spatial directions of the element is adjusted by means of an adaptive procedure to this end a hierarchical error indicator is applied to automatically control the polynomial degree q in thickness and p in the in plane direction of plate and shell like structures the efficiency and reliability of the proposed adaptive method is demonstrated using two numerical examples

a level set based topology optimization method targeting metallic waveguide design problems in this paper we propose a level set based topology optimization method targeting metallic waveguide design problems where the skin effect must be taken into account since the metallic waveguides are generally used in the high frequency range where this effect critically affects performance one of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal to implement this approach we develop a boundary tracking scheme for the arbitrary lagrangian eulerian ale mesh pertaining to the zero iso contour of the level set function that is given in an eulerian mesh and impose dirichlet boundary conditions at the nodes on the zero iso contour in the ale mesh to compute the electric field since the ale mesh accurately tracks the zero iso contour at every optimization iteration the electric field is always appropriately computed during optimization for the sensitivity analysis we compute the nodal coordinate sensitivities in the ale mesh and smooth them by solving a helmholtz type partial differential equation the obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the eulerian mesh and the level set function is updated based on the computed normal velocity finally the utility of the proposed method is discussed through several numerical examples copyright 2011 john wiley sons ltd

a quadratic assumed natural strain curved triangular shell element abstract in this paper a six node triangular c 0 curved shell element is developed by the assumed natural or covariant strain ans method all the sampled natural strains are optimal with respect to the derivative of a prescribed cubic field in a subparametric element numerical examinations reveal that the element shows no sign of locking passes all the patch tests and yields satisfactory accuracy

the topological asymptotic for pde systems the elasticity case the aim of the topological sensitivity analysis is to obtain an asymptotic expansion of a design functional with respect to the creation of a small hole in this paper such an expansion is obtained and analyzed in the context of linear elasticity for general functionals and arbitrary shaped holes by using an adaptation of the adjoint method and a domain truncation technique the method is general and can be easily adapted to other linear pdes and other types of boundary conditions

implementation of the three dimensional turning bands random field generator numerical techniques to generate replicates of spatially correlated random fields are often used to synthesize sets of highly variable physical quantities in stochastic models of naturally heterogeneous systems within the realm of hydrologic research for example such tools are widely used to develop hypothetical rainfall distributions hydraulic conductivity fields fracture set properties and other surface or subsurface flow parameters the turning bands method is one such algorithm which generates two and three dimensional fields by combining values found from a series of one dimensional simulations along lines radiating outward from a coordinate origin previous work with two dimensional algorithms indicates that radial lines evenly spaced about the unit circle lead to enhanced convergence properties the same can be said for the three dimensional models but it is more difficult to choose an arbitrary number of evenly spaced lines about the unit sphere the current investigation shows that the use of larger numbers of randomly oriented lines 100 can enhance the performance of the three dimensional algorithm this improved performance is needed to effectively simulate problems characterized by full three dimensionality and or anisotropy in either monte carlo or single realization applications use of a large number of lines will also reduce the presence of a distortion effect manifested as linelike patterns in the field increased computational costs can be reduced by employing a fast fourier transform technique to generate the line processes

a smoothed finite element method for plate analysis a quadrilateral element with smoothed curvatures for mindlin reissner plates is proposed the curvature at each point is obtained by a non local approximation via a smoothing function the bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells numerical results show that the proposed element is robust computational inexpensive and simultaneously very accurate and free of locking even for very thin plates the most promising feature of our elements is their insensitivity to mesh distortion

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

trefftz method for kirchhoff plate bending problems kirchhoff plate bending problems were studied by both the trefftz direct and indirect approximations in which non singular complete trefftz functions are used as the weighting and or trial functions the trefftz direct method involved only the quantities of engineering interest numerical results are given to show the efficiency and the excellent accuracy of the present method

shape optimization of dirichlet boundaries based on weighted b spline finite cell method and level set function abstract this paper addresses extended shape optimization problems where structural supports i e dirichlet boundaries and free boundaries are simultaneously optimized unlike traditional fem the weighted b spline finite cell method fcm is applied as structural analysis tool and combined with the level set function lsf to take into account dirichlet boundary condition dbc automatically through penalization of the displacement field the proposed shape optimization method achieves a comprehensive integration of fixed grid b spline shape function and level set function as both the structure and dirichlet boundaries are described in the form of lsf any modification of dirichlet boundaries can be made in a straightforward way as easily as free boundaries by changing continuous design variables meanwhile the computing accuracy is ensured within the framework of fixed grid owing to the quadtree refinements of boundary cells stress related shape optimization problems are finally solved to demonstrate the merit and validity of the proposed optimization method in dealing with shape optimization of dirichlet boundaries

estimation of aquifer parameters under transient and steady state conditions 1 maximum likelihood method incorporating prior information in this series of three papers a method is presented to estimate the parameters of groundwater flow models under steady and nonsteady state conditions the parameters include values and directions of principal hydraulic conductivities or transmissivities in anisotropic media specific storage or storativity interior and boundary recharge or leakage rates coefficients of head dependent interior and boundary sources and boundary heads in transient situations the initial head distribution can also be estimated if the system is originally at a steady state paper 1 of the series discusses some of the advantage in treating the inverse problem statistically and in regularizing its solution by means of penalty criteria based on prior estimates of the parameters the inverse problem is posed in the framework of maximum likelihood theory cast in a manner that accounts for prior information about the parameters since not all the factors which contribute to the prior errors can be quantified statistically at the outset the covariance matrices of these errors are expressed in terms of several parameters which if unknown can be estimated jointly with the hydraulic parameters by a stagewise optimization process when transient head data are separated by a fixed time interval the temporal structure of these data is approximated by a lag one autoregressive model with a correlation coefficient that can be treated as another unknown parameter estimation errors are analyzed by examining the lower bound of their covariance matrix in the eigenspace paper 1 concludes by suggesting that certain model identification criteria developed in the time series literature all of which are based on the maximum likelihood concept might be useful for selecting the best groundwater model or the best method of parameterizing a particular model among a number of given alternatives

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

higher order mitc general shell elements two mixed interpolated general shell finite elements for non linear analysis a 9 node element and a 16 node element are presented the elements are based on the mixed interpolation of tensorial components mitc approach in which the covariant strain component fields for the in plane and shear actions are interpolated and tied to the also interpolated displacement field both the 9 node element referred to as the mitc9 element and the 16 node element referred to as the mitc16 element are tested numerically and found to have high predictive capabilities

the p version of the finite element method for three dimensional curved thin walled structures in this paper we present an implementation of a three dimensional p version for structural problems of solids with almost arbitrarily curved surfaces applying the blending function method complex structures can often be modelled by a few p elements being the basis for a higher order approximation numerical examples will demonstrate that the p version with anisotropic ansatz spaces allows to predict the structural behaviour of three dimensional plates and shells with approximately the same amount of degrees of freedom as in the two dimensional case yet significantly more accurate due to the three dimensional model furthermore it is advantageous to compute complex structures exclusively with three dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three dimensional solid elements using the p version with anisotropic ansatz spaces the whole structure can be efficiently discretized with solid elements even if the aspect ratio of the elements becomes very large copyright 2001 john wiley sons ltd

a cut finite element method for the bernoulli free boundary value problem we develop a cut finite element method for the bernoulli free boundary problem the free boundary represented by an approximate signed distance function on a fixed background mesh is allowed to i

incorporating topological derivatives into level set methods the aim of this paper is to investigate the use of topological derivatives in combination with the level set method for shape reconstruction and optimization problems we propose a new approach generalizing the standard speed method which is obtained by using a source term in the level set equation that depends on the topological derivative of the objective functional the resulting approach can be interpreted as a generalized fixed point iteration for the optimality system with respect to topological and shape variations moreover we apply the new approach for a simple model problem in shape reconstruction where the topological derivative can be computed without additional effort finally we present numerical tests related to this model problem which demonstrate that the new method based on shape and topological derivative successfully reconstructs obstacles in situations where the standard level set approach fails

a new plate bending element based on orthogonal polynomials expansion of the curvature field a new approach to derive finite elements for the thin plate model is presented the proposed method approximates compatible kirchhoff formulations by means of orthogonal polynomials expansion of the curvature field depending only on the element boundary traces with respect to the compatible formulation the proposed method produces elements that beneficially underestimate the deformation energy a simple triangular element is developed and investigated from both the theoretical and the numerical point of view and numerically compared with other two well known elements copyright 2007 john wiley sons ltd

generalization of the twist kirchhoff theory of plate elements to arbitrary quadrilaterals and assessment of convergence abstract we generalize the recently introduced twist kirchhoff theory of rectangular plate elements to arbitrary quadrilateral elements a key feature is the use of raviart thomas vector field approximations for rotations to preserve continuity of the normal components of the rotation vector across mesh edges we employ the piola transformation to map the rotations from the parent domain to the physical domain these elements possess a unique combination of efficiency and robustness in that minimal quadrature rules are sufficient to guarantee stability without rank deficiency in particular only one point gauss quadrature is required for the lowest order element in the twist kirchhoff family we numerically study the convergence and accuracy of the first two members of the twist kirchhoff family of quadrilateral elements on square rhombic and circular plate problems

studies in the history of probability and statistics xlix on the matern correlation family summary handcock stein 1993 introduced the matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field we document the varied history of this family which includes contributions by eminent physical scientists and statisticians

new rectangular plate elements based on twist kirchhoff theory abstract we introduce a new framework for the development of thin plate finite elements the twist kirchhoff theory a family of rectangular plate elements is derived that takes advantage of the special structure of this new theory particular attention is focused on the lowest order member of the family an eight degree of freedom four node element with mid side rotations whose stiffness matrix is exactly computed with one point gaussian quadrature we prove a convergence theorem for it and various error estimates these are also generalized to the higher order elements in the family numerical tests corroborate the theoretical results

level set methods for optimization problems involving geometry and constraints i frequencies of a two density inhomogeneous drum many problems in engineering design involve optimizing the geometry to maximize a certain design objective geometrical constraints are often imposed in this paper we use the level set method devised in osher and sethian j comput phys 79 12 1988 the variational level set calculus presented in zhao et al j comput phys 127 179 1996 and the projected gradient method as in rudin et al physica d 60 259 1992 to construct a simple numerical approach for problems of this type we apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry our numerical results are quite promising we expect to use this approach to deal with a wide class of optimal design problems in the future

stochastic models that separate fractal dimension and the hurst effect fractal behavior and long range dependence have been observed in an astonishing number of physical biological geological and socioeconomic systems time series profiles and surfaces have been characterized by their fractal dimension a measure of roughness and by the hurst coefficient a measure of long memory dependence both phenomena have been modeled and explained by self affine random functions such as fractional gaussian noise and fractional brownian motion the assumption of statistical self affinity implies a linear relationship between fractal dimension and hurst coefficient and thereby links the two phenomena this article introduces stochastic models that allow for any combination of fractal dimension and hurst coefficient associated software for the synthesis of images with arbitrary prespecified fractal properties and power law correlations is available the new models suggest a test for self affinity that assesses coupling and decoupling of local and global behavior

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

damage and fracture evolution in brittle materials by shape optimization methods this paper is devoted to a numerical implementation of the francfort marigo model of damage evolution in brittle materials this quasi static model is based at each time step on the minimization of a total energy which is the sum of an elastic energy and a griffith type dissipated energy such a minimization is carried over all geometric mixtures of the two healthy and damaged elastic phases respecting an irreversibility constraint numerically we consider a situation where two well separated phases coexist and model their interface by a level set function that is transported according to the shape derivative of the minimized total energy in the context of interface variations hadamard method and using a steepest descent algorithm we compute local minimizers of this quasi static damage model initially the damaged zone is nucleated by using the so called topological derivative we show that when the damaged phase is very weak our numerical method is able to predict crack propagation including kinking and branching several numerical examples in 2d and 3d are discussed

on structural shape optimization using an embedding domain discretization technique summary this contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique the evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization we consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements exterior elements and elements intersected by the physical domain boundary a selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component thereby we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration as it is the case for a standard lagrangian approach to structural shape optimization still we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process in order to avoid irregular and impracticable design updates we consider a geometric regularization technique to render feasible descent directions for the course of the optimization this article is protected by copyright all rights reserved

a fast and exact method for multidimensional gaussian stochastic simulations to generate multidimensional gaussian random fields over a regular sampling grid hydrogeologists can call upon essentially two approaches the first approach covers methods that are exact but computationally expensive e g matrix factorization the second covers methods that are approximate but that have only modest computational requirements e g the spectral and turning bands methods in this paper we present a new approach that is both exact and computationally very efficient the approach is based on embedding the random field correlation matrix r in a matrix s that has a circulant block circulant structure we then construct products of the square root s1 2 with white noise random vectors appropriate sub vectors of this product have correlation matrix r and so are realizations of the desired random field the only conditions that must be satisfied for the method to be valid are that 1 the mesh of the sampling grid be rectangular 2 the correlation function be invariant under translation and 3 the embedding matrix s be nonnegative definite these conditions are mild and turn out to be satisfied in most practical hydrogeological problems implementation of the method requires only knowledge of the desired correlation function furthermore if the sampling grid is a d dimensional rectangular mesh containing n points in total and the correlation between points on opposite sides of the rectangle is vanishingly small the computational requirements are only those of a fast fourier transform fft of a vector of dimension 2dn per realization thus the cost of our approach is comparable with that of a spectral method also implemented using the fft in summary the method is simple to understand easy to implement and is fast

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

a p version mitc finite element method for reissner mindlin plates with curved boundaries we consider the approximation of reissner mindlin plates with curved boundaries using a p version mitc finite element method we describe in detail the formulation and implementation of the method and emphasize the need for a piola type map in order to handle the curved geometry of the elements the results of our numerical computations demonstrate the robustness of the method and suggest that it gives near exponential convergence when the error is measured in the energy norm for the robust computation of quantities of engineering interest such as the shear force the proposed method yields very satisfactory results without the need for any additional post processing comparisons are made with the standard finite element formulation with and without post processing

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

sleipnnir a multiscale particle level set method for newtonian and non newtonian interface flows abstract we present in this paper a multiscale micro macro particle level set method for newtonian and non newtonian interface flows the technique termed sleipnnir semi lagrangian ensemble implementation of particle level set for newtonian and non newtonian interfacial rheology uses the finite element method in a semi lagrangian framework for the discretization of the governing equations capturing the free surface by means of a particle level set strategy where all involved magnitudes are computed sharply surface tension effects are considered via the laplace beltrami operator using a fully explicit or semi implicit technique with a second order accurate reinitialization procedure to ensure the signed distance property non newtonian fluids are tackled by means of a stochastic variance reduced kinetic modeling approach in which the polymer stress tensor is retrieved making use of compactly supported radial basis functions for randomly scattered data interpolation we carry out numerical tests to highlight the versatility robustness and accuracy of the proposed scheme through a series of bubble dynamics experiments in a 2d setup for large density and viscosity ratios and featuring strong purely elastic effects relevant to engineering applications

structural boundary design via level set and immersed interface methods we develop and test an algorithmic approach to the boundary design of elastic structures the goal of our approach is two fold first to develop a method which allows one to rapidly solve the two dimensional lam equations in arbitrary domains and compute for example the stresses and second to develop a systematic way of modifying the design to optimize chosen properties at the core our approach relies on two distinct steps given a design we first apply an explicit jump immersed interface method to compute the stresses for a given design shape we then use a narrow band level set method to perturb this shape and progress towards an improved design the equations of 2d linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers this effectively reduces the dimensionality of the problem by one once the stresses are found the level set method which represents the design structure through an embedded implicit function is used in the second step to alter the shape with velocities depending on the stresses in the current design criteria are provided for advancing the shape in an appropriate direction and for correcting the evolving shape when given constraints are violated

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

a level set method for vibration and multiple loads structural optimization abstract we extend the level set method for shape and topology optimization to new objective functions such as eigenfrequencies and multiple loads this method is based on a combination of the classical shape derivative and of the osher sethian level set algorithm for front propagation in two and three space dimensions we maximize the first eigenfrequency or we minimize a weighted sum of compliances associated to different loading configurations the shape derivative is used as an advection velocity in a hamilton jacobi equation for changing the shape this level set method is a low cost shape capturing algorithm working on a fixed eulerian mesh and it can easily handle topology changes

a new triangular discrete kirchhoff plate shell element we present a new 6 node triangular bending element called dktp based on a discrete kirchhoff model a corresponding new flat shell element dltp having quadratic variation of in plane displacement is also presented this element has 6 degrees of freedom u v w x y z at each corner node and 3 degrees of freedom u v w at each mid side node detailed numerical experimentation is presented to demonstrate the efficiency and reliability of these elements