exponential time differencing with embedded runge kutta adaptive step control we have presented the first embedded runge kutta exponential time differencing rketd methods of fourth order with third order embedding and fifth order with third order embedding for non rosenbrock type nonlinear systems a procedure for constructing rketd methods that accounts for both order conditions and stability is outlined in our stability analysis the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before an effective time stepping strategy based on reducing both etd function evaluations and rejected steps is described comparisons of performance with adaptive stepping integrating factor if are carried out on a set of canonical partial differential equations the shock fronts of burgers equation interacting kdv solitons ks controlled chaos and critical collapse of two dimensional nls

shape optimization using adaptive shape refinement a large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information this effort increases dramatically with an increase in the number of variables used to represent the shape an adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape the method is demonstrated with a simple representative test case

stability and stabilization of two time scale switched systems in discrete time in this technical note stability and stabilization of two time scale switched linear systems in the singular perturbation form are addressed in discrete time we show that under an arbitrary switching rule stability of the slow and fast switched subsystems is not sufficient to assess stability of the original two time scale switched system even if the singular perturbation parameter tends to zero therefore we propose lmi based conditions that guarantee the asymptotic stability of the two time scale switched system using switched quadratic lyapunov functions these conditions express the fact that the coupling between fast and slow subsystems has to be taken into account in addition to stability properties of the two subsystems when the switching rule is arbitrary the presented conditions are extended to state feedback control design a numerical example illustrates the features of the proposed approach

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

variational principles in dissipative electro magneto mechanics a framework for the macro modeling of functional materials summary this paper presents a general framework for the macroscopic continuum based formulation and numerical implementation of dissipative functional materials with electro magneto mechanical couplings based on incremental variational principles we focus on quasi static problems where mechanical inertia effects and time dependent electro magnetic couplings are a priori neglected and a time dependence enters the formulation only through a possible rate dependent dissipative material response the underlying variational structure of non reversible coupled processes is related to a canonical constitutive modeling approach often addressed to so called standard dissipative materials it is shown to have enormous consequences with respect to all aspects of the continuum based modeling in macroscopic electro magnetomechanics at first the local constitutive modeling of the coupled dissipative response i e stress electric and magnetic fields versus strain electric displacement and magnetic induction is shown to be variational based governed by incremental minimization and saddle point principles next the implications on the formulation of boundary value problems are addressed which appear in energy based formulations as minimization principles and in enthalpy based formulations in the form of saddle point principles furthermore the material stability of dissipative electro magneto mechanics on the macroscopic level is defined based on the convexity concavity of incremental potentials we provide a comprehensive outline of alternative variational structures and discuss details of their computational implementation such as formulation of constitutive update algorithms and finite element solvers from the viewpoint of constitutive modeling including the understanding of the stability in coupled electro magneto mechanics an energy based formulation is shown to be the canonical setting from the viewpoint of the computational convenience an enthalpy based formulation is the most convenient setting a numerical investigation of a multiferroic composite demonstrates perspectives of the proposed framework with regard to the future design of new functional materials copyright 2011 john wiley sons ltd received 1 october 2010 revised 15 december 2010 accepted 15 december 2010

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

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

dual methods for optimizing finite element flexural systems abstract modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of thin walled elastic structures modeled by finite elements however this is not yet true for structures whose components are subject simultaneously to bending and extension loads in this paper the idea of generalized optimality criterion goc set forth in previous papers for bar membrane and pure bending elements is extended to deal with general beam and flat shell elements the modifications brought to the goc result in explicit approximations for the behavior constraints that are correct up to the first order but that exhibit a more complex algebraic form indeed these explicit expressions are no longer merely linear in the reciprocal design variables however they continue to be additively separable and therefore dual methods remain fully applicable just as in the original statement of the goc approach numerical examples will be offered to demonstrate the efficiency of the method presented

a goal oriented hp adaptive finite element method with electromagnetic applications part i electrostatics we describe the development and application of a finite element fe self adaptive hp goal oriented algorithm for elliptic problems the algorithm delivers without any user interaction a sequence of optimal hp grids this sequence of grids minimizes the error of a prescribed quantity of interest with respect to the problem size the refinement strategy is an extension of a fully automatic energy norm based hp adaptive algorithm we illustrate the efficiency of the method with 2d numerical results among other problems we apply the goal oriented hp adaptive strategy to simulate direct current dc resistivity logging instruments including through casing resistivity tools in a borehole environment and for the assessment of rock formation properties copyright 2005 john wiley sons ltd

higher order exponential time differencing scheme for system of coupled nonlinear schrodinger equations the coupled nonlinear schrodinger equations are highly used in modeling the various phenomena in nonlinear fiber optics like propagation of pulses efficient and reliable numerical schemes are required for analysis of these models and for improvement of the fiber communication system in this paper we introduce a new version of the cox and matthews third order exponential time differencing runge kutta etd3rk scheme based on the 1 2 pade approximation to the exponential function in addition we present its local extrapolation form to improve temporal accuracy to the fourth order the developed scheme and its extrapolation are seen to be strongly stable which have ability to damp spurious oscillations caused by high frequency components in the solution a computationally efficient algorithm of the new scheme based on a partial fraction splitting technique is presented in order to investigate the performance of the novel scheme we considered the system of two and four coupled nonlinear schrodinger equations and performed several numerical experiments on them the numerical experiments showed that the developed numerical scheme provide an efficient and reliable way for computing long range solitary solutions given by coupled nonlinear schrodinger equations and conserved the conserved quantities mass and energy exactly to at least five decimal places

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

three dimensional shape optimization using fully automatic mesh generation introduction t he technique for associating design variables with mesh data is the most crucial factor in three dimensional shape optimization previously work in three dimensional shape optimization involved specifying design variables by associating parameters directly with grid points on an existing mesh for realistic problems this can be a very tedious and errorprone process in the past shape optimization capabilities have been developed based on a variety of design analysis capabilities ranging from associating parameters with a mesh created manually to associating parameters with control points of a mapped mesh generator special techniques have also been developed to properly move internal grid points during sensitivity calculations more recently a capability based on constructive solid geometry csg has been developed but csg representations are not particularly suitable for design optimization a new optimization approach is demonstrated in this note that uses a new fully automatic mesh generation capability the design model is developed based on design oriented geometric primitives that represent recognizable features of a part and can be assembled into complete solid models that are defined in terms of a small set of design parameters

a unified framework for input to state stability in systems with two time scales this paper develops a unified framework for studying robustness of the input to state stability iss property and presents new results on robustness of iss to slowly varying parameters to rapidly varying signals and to generalized singular perturbations the common feature in these problems is a time scale separation between slow and fast variables which permits the definition of a boundary layer system like in classical singular perturbation theory to address various robustness problems simultaneously the asymptotic behavior of the boundary layer is allowed to be complex and it generates an average for the derivative of the slow state variables the main results establish that if the boundary layer and averaged systems are iss then the iss bounds also hold for the actual system with an offset that converges to zero with the parameter that characterizes the separation of time scales the generality of the framework is illustrated by making connection to various classical two time scale problems and suggesting extensions

displacement minimization of thermoelastic structures by evolutionary thickness design structural optimization aims at finding an appropriate material distribution to achieve the best structural performance in this paper the evolutionary structural optimization method is further developed to deal with thermoelastic optimization where structural material is progressively redistributed so as to minimize the displacement under thermal and mechanical loading to evaluate the effects of material removal or addition on the displacement of thermoelastic structures a sensitivity number is proposed on the basis of the thickness variation of an element the method proves to be very simple in its mathematical operations and suitable for computer implementation the numerical examples are compared against those by the homogenization method to verify and validate this method of solving thermoelastic optimizations in addition the effect of various temperature distributions on the final optimum structures is investigated in detail

wavelet transformation induced multi time scaling watmus model for coupled transient electro magnetic and structural dynamics finite element analysis abstract multi functional devices that integrate electromagnetic and mechanical fields are gaining importance in a wide variety of applications the combined mechanical and electromagnetic regimes encompassed in these structures make it necessary to develop effective multi physics analysis tools at a range of temporal scales an important consideration is that the different fields governing multi physics response may have large frequency discrepancies e g the ultra high electromagnetic frequencies and moderate vibration frequencies computational analyses of these discrepant frequency problems using conventional time integration schemes can become intractable this paper develops a framework for coupling transient electromagnetic and dynamic fields to predict the evolution of electric and magnetic fields and their fluxes in a vibrating substrate undergoing finite deformation it addresses the issue of time integration with large frequency ratios by introducing a novel wavelet transformation induced multi time scaling watmus method in the finite element framework the method significantly enhances the computational efficiency in comparison with conventional single time scale integration methods an adaptive enhancement of watmus scheme allows for the optimal wavelet bases in the transformation and integration step sizes the accuracy and efficiency of the proposed watmus scheme is verified by comparing the results with the single time scale simulations of the coupled transient electromagnetic nonlinear vibration problems

a 2 d coupled bem fem simulation of electro elastostatics at large strain the numerical simulation of nonlinear electro elastostatics is considered in this work using the coupled boundary and finite element method the objective of the work is to properly simulate the deformation of an electroelastic body undergoing large deformation subjected to electric stimulations in the case where the surrounding space has significant influence on the electric field inside the body finite elements are used to model the nonlinear electroelastic body in which both mechanical nonlinearity and electrical nonlinearity are taken into account boundary elements are used to model the surrounding space and account for the large deformation of the boundary of the body

shape optimization with p adaptivity the p method of analysis when used with shape optimization has certain advantages over the h method the method of h adaptivity results in fine meshes with small elements in areas of stress concentration the presence of these small elements prevents the shape from changing significantly during optimization due to mesh distortion the p adaptive method uses relatively large sized elements and adaptivity is achieved by increasing the polynomial order of the shape functions rather than by introducing small elements as in the h method thus the p adaptive method allows for greater shape changes without sacrificing the accuracy of the analysis a methodology is developed in this paper to integrate p adaptive analysis with shape optimization for general velocity fields the key contributions lie in an easily implementable shape update strategy and an adaptive scheme to locally increase the polynomial order based on error indicators numerical results show that significant shape change is achievable prior to serious mesh distortion in addition need for an h p adaptive strategy rather than a pure p adaptive strategy is also highlighted

singular perturbation in piecewise linear systems a singular perturbation technique is developed that allows for a decoupling of a continuous piecewise linear system into slow and fast subsystems under the assumption of asymptotic stability the fast variable is found to decay in the boundary layer to its quasi steady state solution which is given by a continuous implicit function of the slow variable the solution is found using a finite step algorithm sufficient conditions for the approximation to be accurate to an order of o mu where mu is a parameter of the system are given the technique is illustrated by a numerical example

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

shape optimization of 2d structures using simulated annealing the goal of this study is to obtain globally optimum shapes for two dimensional structures subject to quasi static loads and restraints for this purpose a technique is proposed using which the volume or weight of a structure can be minimized the emphasis is on how one can define the shape precisely and find a shape that accurately reflects the globally optimum shape as design constraints stresses developed in the structure should not exceed the maximum allowable stress and connectivity of the structure should not be lost during shape changes optimization is achieved by a stochastic search algorithm called direct simulated annealing dsa which seeks the global minimum through randomly generated configurations in order to obtain random configurations a boundary variation technique is used in this technique a set of key points is chosen and connected by cubic splines to describe the boundary of the structure whenever the positions of the key points are changed in random directions a new shape is obtained thus coordinates of the key points serve as design variables in order to apply the optimization procedure a general computer code was developed using ansys parametric design language a number of cases were examined to test its effectiveness the results show that this technique can be applied to two dimensional shape optimization problems with high reliability even for cases where the entire free boundary is allowed to vary 2007 elsevier b v all rights reserved

stability of planar switched systems the linear single input case we study the stability of the origin for the dynamical system dot x t u t ax t 1 u t bx t where a and b are two 2 2 real matrices with eigenvalues having strictly negative real part x in mbox bf r 2 and u 0 infty to 0 1 is a completely random measurable function more precisely we find a coordinates invariant necessary and sufficient condition on a and b for the origin to be asymptotically stable for each function u the result is obtained without looking for a common lyapunov function but studying the locus in which the two vector fields ax and bx are collinear there are only three relevant parameters the first depends only on the eigenvalues of a the second depends only on the eigenvalues of b and the third contains the interrelation among the two systems and it is the cross ratio of the four eigenvectors of a and b in the projective line cp1 in the space of these parameters the shape and the convexity of the region in which there is stability are studied this bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation

analysis of a time domain finite element method for 3 d maxwell s equations in dispersive media abstract we consider the time dependent maxwell s equations in dispersive media on a bounded domain in three dimensional space a fully discrete finite element scheme is developed to approximate the electric field equation derived from the maxwell s equations optimal energy norm error estimates are proved for nedelec curl conforming edge elements this is the first finite element error analysis for maxwell s equations in dispersive media

structural optimization based on preconditioned conjugate gradient analysis methods an efficient method for structural optimization is presented instead of classical direct decomposition methods preconditioned conjugate gradient pcg methods in conjunction with two proposed starting vector generation schemes are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems these inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization this technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints the effectiveness of the pcg methods of analysis in structural optimization is demonstrated comparison among different preconditioners is made the effect of the proposed starting vector generation schemes is shown the comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis when using pcg methods of analysis are assessed the parallel computation potential of pcg methods is discussed because of the iterative nature of pcg analysis methods and the prospects they offer for parallel computation it is found that pcg analysis methods show promise in the context of structural optimization

isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization an important feature that drives the auxetic behaviour of the star shaped auxetic structures is the hinge functional connection at the vertex connections this feature poses a great challenge for manufacturing and may lead to significant stress concentrations to overcome these problems we introduced smoothed petal shaped auxetic structures where the hinges are replaced by smoothed connections to accommodate the curved features of the petal shaped auxetics a parametrisation modelling scheme using multiple nurbs patches is proposed next an integrated shape design frame work using isogeometric analysis is adopted to improve the structural performance to ensure a minimum thickness for each member a geometry sizing constraint is imposed via piece wise bounding polynomials this geometry sizing constraint in the context of isogeometric shape optimization is particularly interesting due to the non interpolatory nature of nurbs basis the effective poisson ratio is used directly as the objective function and an adjoint sensitivity analysis is carried out the optimized designs smoothed petal auxetic structures are shown to achieve low negative poisson s ratios while the difficulties of manufacturing the hinges are avoided for the case with six petals an in plane isotropy is achieved

stability analysis of singularly perturbed switched linear systems this note is concerned with the stability of planar linear singularly perturbed switched systems we propose a characterization of the stability properties of such multiple time scale switched systems as the perturbation parameter goes to zero we also study transitions as this parameter varies and we restrict their number and nature finally we compare the results obtained in this way with the tikhonov type results for differential inclusions available in the literature

nice reachability for planar bilinear control systems with applications to planar linear switched systems corrected we consider planar bilinear control systems with measurable controls we show that any point in the reachable set can be reached by a ldquonicerdquo control specifically a control that is a concatenation of a bang arc with either 1 a bang bang control that is periodic after the third switch or 2 a piecewise constant control with no more than two discontinuities under the additional assumption that the bilinear system is positive or invariant for any proper cone we show that the reachable set is spanned by a concatenation of a bang arc with either 1 a bang bang control with no more than two discontinuities or 2 a piecewise constant control with no more than two discontinuities in particular any point in the reachable set can be reached using a piecewise constant control with no more than three discontinuities several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result we demonstrate this with an example

cad inspired hierarchical partition of unity constructions for nurbs based meshless design analysis and optimization in this paper we develop a unified representational paradigm for design and analysis that is inspired by the set theoretic boolean operations of the constructive solid geometry csg procedure of computer aided design cad we develop the notion of a primitive design state corresponding to a csg primitive region which is characterized by a description of the geometrical shape of the primitive and by a description of the material distribution within the primitive we analogously define a primitive behaviour state that is associated with a primitive design state and that is determined through a global analysis problem we define a global multi level design problem to determine the primitive design states we define boolean operations on the fields belonging to primitive design and behaviour spaces and show that the compositions of these fields amount to a hierarchical partition of unity construction we propose to use non uniform rational b splines nurbs to discretize the geometry material and behavioural fields local approximations defined on the primitive regions we show that this leads to recursive partition of unity constructions on the knot spaces sub local approximations due to the partition of unity property of nurbs basis functions since the primitive shapes are parametrically defined using nurbs the numerical quadrature is carried out on the parametric sub regions of the nurbs entities this eliminates the need for either a background mesh or a pseudo mesh for quadrature the developed methodology is implemented in a symbolic meshless computational framework written using the java language jnurbs and was demonstrated on two classes of problems the first class is the simultaneous optimal design of shape and multi material distributions the procedure is argued as being a generalization of classical topology optimization to designing objects made of functionally graded materials with pre defined geometrical constraints such as holes or fixed boundary shape the second class of problems demonstrated in the paper is optimal design to mitigate the effects of cracks here we identify the optimal locations of holes introduced to reduce the stress intensity factor of an edge crack copyright 2007 john wiley sons ltd

a fourier transformation based method for gradient enhanced modeling of fatigue a key limitation of the most constitutive models that reproduce a degradation of quasi brittle materials is that they generally do not address issues related to fatigue one reason is the huge computational costs to resolve each load cycle on the structural level the goal of this paper is the development of a temporal integration scheme which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations the essential constituent of the fatigue model is an implicit gradient enhanced formulation of the damage rate the evolution of the field variables is computed as amultiscale fourier series in time on a microchronological scale attributed to single cycles the initial boundary value problem is approximated by linear bvps with respect to the fourier coefficients using the adaptive cycle jump concept the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration the performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs

a geometric comparison of aerofoil shape parameterisation methods a comprehensive review of aerofoil shape parameterization methods that can be used for aerodynamic shape optimization is presented seven parameterization methods are considered for a range of desi

a physics based parameterization method for shape optimization a physical approach is presented to provide shape modification of nurbs curve the movement of the control polygon of nurbs is simulated by a physical frame structure and the curve deformation is then carried out through changes of the mode coordinates which are derived from the eigenvectors of the finite element equations of the physical frame system the shape of the design boundaries is described by a linear combination of the mode shape vectors based on the presented design variable representation and p version finite element analysis an integrated approach to structural shape optimization is discussed a method is developed that enables the description of the shape to be adaptively refined during the shape optimization process numerical examples are used to demonstrate the applicability of this approach to structural shape optimization

computational method for optimization of structural shapes in the direct method of shape optimum design mesh regridding is a necessary step in avoiding the distortion of finite element grids the effect of internal nodal movements on the shape design sensitivity associated with the regridding process has been carefully examined in this paper it shows that to maintain computational accuracy the effects of internal nodal movement should be considered in shape design sensitivity analysis to take the internal nodal movement into account the numerical accuracy of the speed method is investigated a new approach which constructs the velocity field over the element domain is presented although it takes more computational time the new approach does improve the accuracy of shape design sensitivity

a new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes in this paper a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes our approach consists of three main steps 1 surface partitioning of polygonal meshes 2 generation of shape design variables on the basis of partitioned surface patches and 3 gradient based shape optimization of the structures by reducing a weighted compliance among all load cases the main contributions of this paper include i that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times compared to the conventional design variable scheme of using each mesh node ii our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch except on its boundary and iii overall our approach can be used to automate time consuming shape optimization of polygonal meshes to a greater extent numerical experiments have been conducted and the results indicate the effectiveness of the approach copyright 2003 john wiley sons ltd

a unified parametric design approach to structural shape optimization this paper presents a general parametric design approach for 2 d shape optimization problems this approach has been achieved by integrating practical design methodologies into numerical procedures it is characterized by three features i automatic selection of a minimum number of shape design variables based on the cad geometric model ii integration of sequential convex programming algorithms to solve equality constrained optimization problems iii efficient sensitivity analysis by means of the improved semi analytical method it is shown that shape design variables can be either manually or systematically identified with the help of equality constraints describing the relationship between geometric entities numerical solutions are performed to demonstrate the applicability of the proposed approach a discussion of the results is also given

optimization of geometrically nonlinear thin shells subject to displacement and stability constraints a methodology is developed for shape optimization of thin plate and shell structures undergoing large deflections subject to displacement and system stability constraints the optimization method considers shape parameters and overall thickness of the structure as the design variables and aims to minimize the total mass of the structure subject to stability or displacement constraint two optimality criteria based on karush kuhn tucker conditions are developed for mass minimization problems optimality criteria are combined with nonlinear corotational analysis to optimize structures with geometric nonlinearity the method is applied to plate and shallow shell structures the efficiency of the developed design optimization methodology is compared with that of the gradient based method of optimization sequential quadratic programming

solution techniques for the p version of the adaptive finite element method this paper investigates the performance of a class of methods based on the preconditioned conjugate gradient pcg method for the solution of large and sparse systems of linear equations which arise from the p version of the adaptive finite element method the hierarchical type of preconditioning used in the past is extended to the ssor and incomplete factorization type preconditioning and applied with a global handling of the stiffness matrix the paper also presents some new ideas on domain decomposition dd matrix handling techniques whereby the explicit formulation of the resulting schur complement is avoided by utilizing the pcg method with efficient preconditioners and by processing separately on the coarse and the fine mesh the suitability of the methods to the p version of the adaptive finite element method is demonstrated through extensive numerical tests in two dimensions

a note on stability conditions for planar switched systems this article is concerned with the stability problem for the planar linear switched system where the real matrices a 1 a 2 2 2 are hurwitz and u 0 0 1 is a measurable function we give coordinate invariant necessary and sufficient conditions on a 1 and a 2 under which the system is asymptotically stable for arbitrary switching functions u the new conditions unify those given in previous papers and are simpler to be verified since we reduced to study 4 cases instead of 20 most of the cases are analysed in terms of the function

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

on the discrete variant of the traction method in parameter free shape optimization abstract one of the major challenges in the parameter free approach to computational shape optimization is the avoidance of oscillating i e non smooth boundaries in the optimal design trials in order to achieve this we investigate a method for regularization that corresponds to the discrete variant of the so called traction method in this approach the design updates are generated in terms of a displacement field which is obtained as the solution to an auxiliary boundary value problem that is defined on the actual design domain the main idea herein is to apply fictitious nodal forces corresponding to the discrete sensitivity of the objective function we propose an algorithm in which constraint functions will be taken into account by using an augmented lagrangian formulation and a step length control ensures a sufficient decrease condition in terms of the objective function within each iteration we examine the benefits of the proposed regularization method on the basis of some numerical examples in comparison to an unregularized steepest descent algorithm

shape optimal design using fictitious loads implementation aspects of the natural velocity field approach for shape optimal design are discussed the problem of concern is to find the optimum shape of an elastic body that requires minimizing an objective function subject to stress displacement frequency and manufacturing constraints in this paper fictitious loads are applied at certain control nodes on an auxiliary structure and the deformation produced by these loads is used to update the shape the use of beam stiffeners in the auxiliary structure leads to smoother shapes furthermore softer material properties in the auxiliary structure result in faster convergence when iterating through the feasibile region the method is applied in conjunction with both discrete and continuum methods of design sensitivity analysis

return mapping algorithms and consistent tangent operators in ferroelectroelasticity return mapping algorithms for a rather general class of phenomenological rate independent models for ferroelectroelastic materials are presented the fully coupled thermodynamically consistent three dimensional constitutive model with two internal variables remanent polarization vector and remanent strain tensor proposed by c m landis in 2002 is used for the simulation of electromechanical hysteresis effects in polycrystalline ferroelectric ceramics based on the operator splitting methodology the return mapping algorithm employs the closest point projection scheme to obtain an efficient and robust integration of the constitutive model the consistent tangent operator is obtained in closed form by linearizing the return mapping algorithm and is found to be non symmetric in the general case due to the dependence of the switching criterion on internal variables conditions that provide the symmetry of the consistent tangent matrix are analyzed the compactness and generality of the received relations are achieved by means of using the thermodynamically based compact notations combining mechanical and electrical values both the cases scalar potential finite element fe formulation primary variables strain and electric field and vector potential fe formulation primary variables strain and electric displacement are considered the accuracy and robustness of the algorithms are assessed through numerical examples copyright 2009 john wiley sons ltd

on singular perturbations due to fast actuators in hybrid control systems a stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators if a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted or equivalently are infinitely fast then the same compact set is semiglobally practically asymptotically stable in the finite speed of the actuator dynamics this result which generalizes classical results for differential equations justifies using a simplified plant model that ignores fast but continuous actuator dynamics even when using a hybrid feedback control algorithm

a meshless compositional approach to shape optimal design meshless computational strategies for shape optimal design through the composition of behavioral fields are developed in this paper the composition of behavioral fields is carried out in a manner that is procedurally similar to composition of primitive geometrical entities through set theoretic boolean operations in constructive solid geometry the methodology is shown to lead to a tighter integration between design and analysis and is termed constructive solid analysis a meshless approximation using non uniform rational b spline basis functions is used to discretize the behavioral fields defined over the geometrical primitives remeshing which is a critical bottleneck in shape optimization using conventional finite element analysis is either eliminated or limited to those primitives that are modified further it is demonstrated that the reconstruction of stiffness matrices is required only for those geometrical primitives that are affected by the design changes design sensitivity analysis techniques are developed for the discretized solution system arising out of the compositional analysis an adaptive numerical integration scheme is developed and shown to be necessary to accurately compute the effect of small domain perturbations on the problem functions some of the common challenges in conventional shape optimization problems such as difficulty in creating and merging multiple holes are naturally resolved using the developed compositional approach several representative problems are solved to validate and to demonstrate the methodology

an approximation concepts approach to shape optimal design abstract in the past much of the work done in structural optimization consisted in resizing the members of fixed configuration models in that case a powerful design procedure has now emerged which is based on the coordinate use of explicit high quality approximations of the behavior constraints and dual methods of mathematical programming there is however a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself the main objectives of this paper are to recall briefly a convenient geometric representation in which the boundaries of the structure are represented by bezier or b spline curves and then to discuss the choice of optimization algorithm it is shown that cost efficient methods for structural sizing may be advantageously extended to shape optimal design problems different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods many large scale applications are treated to demonstrate the generality and the efficiency of the new formulation finally considerations are given about an integrated approach including cad computer codes and finite element optimization software

a new class of time discretization schemes for the solution of nonlinear pdes we consider issues of stability of time discretization schemes withexacttreatment of thelinear part elp schemes for solving nonlinear pdes a distinctive feature of elp schemes is the exact evaluation of the contribution of the linear term that is if the nonlinear term of the equation is zero then the scheme reduces to the evaluation of the exponential function of the operator representing the linear term computing and applying the exponential or other functions of operators with variable coefficients in the usual manner requires evaluating dense matrices and is highly inefficient it turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices for a finite but arbitrary accuracy this observation makes our approach practical in a number of applications in particular we consider applications of elp schemes to advection diffusion equations we study the stability of these schemes and show that both explicit and implicit elp schemes have distinctly different stability properties if compared with known implicit explicit schemes for example we describe explicit schemes with stability regions similar to those of typical implicit schemes used for solving advection diffusion equations

a variational finite deformation constitutive model for piezoelectric materials we present a constitutive model for piezoelectric materials the model is fully variational and supports finite kinematics the postulated free energy depends on the deformation mapping and an electric vector potential from which the strain and the electric displacement are derived respectively the divergence free condition of the electric vector potential is enforced by means of a penalty method which leads to a positive definite tangent for the system of equations that represent the problem the performance of the formulation is demonstrated by several examples published in 2010 by john wiley sons ltd

on singular perturbations for differential inclusions on the infinite interval abstract we consider a differential inclusion subject to a singular perturbation i e part of the derivatives are multiplied by a small parameter 0 we show that under some stability and structural assumptions every solution of the singularly perturbed inclusion comes close to a solution of the degenerate inclusion obtained for 0 when tends to 0 the goal of the present paper is to provide a new result of tikhonov type on the time interval 0

computational homogenization in dissipative electro mechanics of functional materials abstract the homogenization of the complex microscopic response of functional materials with electro mechanical coupling is a highly demanding research topic and of utmost importance for technological design smart materials are characterized by microstructural properties which can be changed by external stress and electric field stimuli and hence find use as the active components in sensors and actuators in this context an important challenge is to combine phase field descriptions of microscopic electric domain evolution with homogenization techniques in order to define the macroscopic overall response this paper offers a new approach to computational homogenization in dissipative electro mechanics based on a rigorous exploitation of rate type and incremental variational principles governing the scale bridging between micro and macroscales it provides a canonical insight in the structure of the coupled electro mechanical problems where all field equations appear as the euler lagrange equations of variational principles a challenge is to link the gradient type continuum description of the microstructure governed by a phase field of micro electric polarization to a local electro mechanical macro continuum this is achieved by the definition of boundary conditions on the surface of the microstructure which include the phase field to this end dirichlet neumann type and periodic boundary constraints are derived from a generalization of the hill mandel macro homogeneity condition towards the coupled electro mechanical problem we outline in detail techniques for the numerical implementation of these boundary conditions by means of lagrange multiplier and penalty methods two and three dimensional numerical simulations treat electric domain wall motions in microstructures and their hysteretic homogenized overall response for macroscopic strain and electric field driven volume elements