shape optimization of three dimensional continuum structures via force approximation techniques the existing need to develop methods whereby the shape design efficiency can be improved through the use of high quality approximation methods is addressed an efficient approximation method for stress constraints in three dimensional shape design problems is proposed based on expanding the nodal forces in taylor series with respect to shape variations the significance of this new method is shown through elementary beam theory calculations and via numerical computations using three dimensional solid finite elements numerical examples including the classical cantilever beam structure and realistic automotive parts like the engine connecting rod are designed for optimum shape using the proposed method the numerical results obtained from these methods are compared with other published results to assess the efficiency and the convergence rate of the proposed method it is concluded that by taking advantage of this high quality approximation the total number of finite element analyses required for structural shape optimization can be reduced significantly resulting in the same level of efficiency achieved previously in sizing problems

the cavity of the optimal shape under the shear stresses the problem of optimal shape of a single cavity in an infinite 2 d elastic domain is analyzed an elastic plane is subjected to a uniform load at infinity the cavity of the fixed area is said to be optimal if it provides the minimal energy change between the homogeneous plane and the plane with the cavity we show that for the case of shear loading the contour of the optimal cavity is not smooth but is shaped as a curved quadrilateral the shape is specified in terms of conformal mapping coefficients and explicit analytical representations for components of the dipole tensor associated with the cavity are employed we also find the exact values of angles at the corners of the optimal contour the applications include the problems of optimal design for dilute composites

survey paper transfer functions of distributed parameter systems a tutorial in this tutorial article the rich variety of transfer functions for systems described by partial differential equations is illustrated by means of several examples under various boundary conditions an important feature is the strong influence of the choice of boundary conditions on the dynamics and on system theoretic properties such as pole and zero locations properness relative degree and minimum phase it is sometimes possible to design a controller using the irrational transfer function and several such techniques are outlined more often the irrational transfer function is approximated by a rational one for the purpose of controller design various approximation techniques and their underlying theory are briefly discussed

structural optimization a new dual method using mixed variables a new and powerful mathematical programming method is described which is capable of solving a broad class of structural optimization problems the method employs mixed direct reciprocal design variables in order to get conservative first order approximations to the objective function and to the constraints by this approach the primary optimization problem is replaced with a sequence of explicit subproblems each subproblem being convex and separable it can be efficiently solved by using a dual formulation an attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs examples of application to real life aerospace structures are offered to demonstrate the power and generality of the approach presented

modal analysis and shape optimization of rotating cantilever beams when a cantilever beam rotates about an axis perpendicular to its neutral axis its modal characteristics often vary significantly if the geometric shape and the material property of the beam are given the modal characteristic variations can be accurately estimated following a well established analysis procedure employing assumed mode method or finite element method in many practical design situations however some modal characteristics are usually specified as design requirements and the geometric shape that satisfies the requirements needs to be found in the present study certain modal characteristic requirements such as maximum or minimum slope natural frequency loci are specified and the geometric shapes that satisfy the requirements are obtained through an optimization procedure

shape optimization in contact problems with coulomb friction the paper deals with a discretized problem of the shape optimization of elastic bodies in unilateral contact the aim is to extend existing results to the case of contact problems following the coulomb friction law mathematical modelling of the coulomb friction problem leads to a quasi variational inequality it is shown that for small coefficients of friction the discretized problem with coulomb friction has a unique solution and that this solution is lipschitzian as a function of a control variable describing the shape of the elastic body the shape optimization problem belongs to a class of so called mathematical programs with equilibrium constraints mpecs the uniqueness of the equilibria for fixed controls enables us to apply the so called implicit programming approach its main idea consists of minimizing a nonsmooth composite function generated by the objective and the single valued control state mapping in this paper the control state mapping is much more complicated than in most mpecs solved in the literature so far and the generalization of the relevant results is by no means straightforward numerical examples illustrate the efficiency and reliability of the suggested approach

brief paper output regulation for linear distributed parameter systems using finite dimensional dual observers in this article the solution of the output regulation problem is considered for linear infinite dimensional systems where the outputs to be controlled cannot be measured it is shown that this problem can be solved by a finite dimensional dual observer that is directly implementable so that the separation principle can be applied for the stabilization as in finite dimensions a parametric design of these dual observers is proposed for riesz spectral systems that allows to achieve a low controller order and a desired control performance for the closed loop system the presented results are illustrated by determining a finite dimensional regulator for an euler bernoulli beam with kelvin voigt damping that achieves tracking for steplike reference inputs and that asymptotically rejects sinusoidal disturbances

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

a backstepping approach to the output regulation of boundary controlled parabolic pdes in this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach thereby the outputs to be controlled are not required to be measurable and can be pointwise distributed or boundary quantities whereas the measurement is located at the boundary by solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result so that their analysis and solution is facilitated the output feedback regulator design is completed by determining a finite dimensional reference observer and an infinite dimensional disturbance observer for the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates this allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer it is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed loop system with a prescribed stability margin the output regulation results of the article are illustrated by means of a parabolic system with an in domain pointwise controlled output

dynamical analysis of distributed parameter tubular reactors this paper is dedicated to the dynamical analysis of tubular reactor models namely plug flow and axial dispersion reactors involving sequential reactions for which the kinetics only depends on the concentrations of the reactants involved in the reaction this analysis is performed by describing these models as infinite dimensional state space systems with bounded observation and control operators it is shown that these systems are exponentially stable and that a the plug flow reactor model is observable when the component concentrations are measured at the reactor output and observable with respect to its physical domain when only the product concentration is measured and it is reachable with respect to its physical domain when it is controlled at the reactor input and b any finite set of dominant modes of the axial dispersion reactor model is observable when either all the component concentrations or only the product concentration are measured and reachable by using appropriate sensors and actuators the dynamical properties of related finite dimensional models are also discussed

constructive solid geometry approach to three dimensional structuralshape optimization this paper presents a constructive solid geometry approach to generic three dimensional shape optimization the problem definition and shape control are based on constructive solid geometry whereas the assets of boundary representation are exploited to specify the physics of the problem and for meshing the object this approach is strongly coupled to an automatic mesh generator and uses to its advantage the explicit association of the finite element data with the model geometry for performing shape sensitivity analysis hybrid approximation methods are used to minimize the number of finite element analyses a classical example of a cantilevered plate with a hole and a realistic aircraft turbine disk problem are solved for optimum shape using this new approach

a note on the epstein hubbell generalized elliptic type integral abstract the main object of this note is to present a remarkably simple derivation of the explicit representation of the epstein hubbell generalized elliptic type integral as a gauss hypergeometric function of argument k4 the method applied here is based upon rather elementary formulas and unlike the earlier derivations it does not make use of complex integration with or without residues it is also pointed out how this method can be applied mutatis mutandis in substantially more general cases

boundary feedback control in networks of open channels this article deals with the regulation of water flow in open channels modelled by saint venant equations by means of a riemann invariants approach we deduce stabilizing control laws for a single horizontal reach without friction the stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies a control law design based on this condition is illustrated with a simple case study two reaches in cascade the proof of the main stability theorem is based on a previous result from li ta tsien concerning the existence and decay of classical solutions of hyperbolic systems

the state feedback regulator problem for regular linear systems this paper is about the state feedback regulator problem for infinite dimensional linear systems the plant assumed to be an exponentially stable regular linear system is driven by a linear possibly infinite dimensional exosystem via a disturbance signal the exosystem has its spectrum in the closed right half plane and also generates the reference signal for the plant output the regulator problem is to design a controller that while guaranteeing the stability of the closed loop system without the exosystem drives the tracking error to zero a particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller under suitable assumptions we show that the latter problem is solvable if and only if a pair of algebraic equations called the regulator equations is solvable we derive conditions in terms of the transfer function of the plant and eigenvalues of the exosystem for the solvability of the regulator equations three examples illustrating the theory are presented

a modular approach for three dimensional shape optimization of structures an approach for shape optimization of three dimensional solid structures is described a major consideration in the development of this capability was the desire to use a commercially available finite element program such as nastran for analysis since nastran cannot be called a subroutine a system architecture of independently executable modules was developed in which sequential execution is controlled by job control language also sensitivities are not commonly available in commercial programs a material derivative approach was developed to obtain shape sensitivities by postprocessing finite element boundary stresses stored on files a parameterized surface description and mesh generation are provided using isoparametric mapping patches the feasible directions algorithm conmin is used for optimization several automotive related examples are used to evaluate the program s effectiveness

control of continuum models of production systems a production system which produces a large number of items in many steps can be modelled as a continuous flow problem the resulting hyperbolic partial differential equation pde typically is nonlinear and nonlocal modeling a factory whose cycle time depends nonlinearly on the work in progress one of the few ways to influence the output of such a factory is by adjusting the start rate in a time dependent manner we study two prototypical control problems for this case i demand tracking where we determine the start rate that generates an output rate which optimally tracks a given time dependent demand rate and ii backlog tracking which optimally tracks the cumulative demand the method is based on the formal adjoint method for constrained optimization incorporating the hyperbolic pde as a constraint of a nonlinear optimization problem we show numerical results on optimal start rate profiles for steps in the demand rate and for periodically varying demand rates and discuss the influence of the nonlinearity of the cycle time on the limits of the reactivity of the production system differences between perishable and non perishable demand demand versus backlog tracking are highlighted

comparison between the variational and implicit differentiation approaches to shape design sensitivities the most commonly used approach to the shape design sensitivity problem results from the implicit differentiation of the discretized equilibrium equations the most general implementation of this technique requires that finite differences be used to differentiate the element stiffness matrices proper choice of the step size is necessary to obtain high levels of accuracy and to avoid round off errors furthermore since it is necessary to operate on the element matrices this method is difficult to implement into a general purpose finite element program a more recent shape design sensitivity formulation based upon variational calculus avoids having to differentiate the discretized equations and results in an analytical expression for the derivative the approach is based upon the total derivative of the variational state equation and uses an adjoint variable technique for design sensitivity analysis only structural response data on the boundary of the structure is necessary thereby making implementation into a general purpose program less difficult this paper attempts to compare the two different techniques and point out the similarities two test problems are shown to demonstrate the accuracy of the variational approach

three dimensional shape optimization using the boundary element method a practical design sensitivity calculation technique of displacements and stresses for three dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method the shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod

epstein hubbell elliptictype integral and its generalizations abstract a survey of the evaluation series expansions properties and approximation of the epstein hubbell elliptictype integral is considered we review different generalizations of this integral r k k k m s k v etc and examine some of their important properties including asymptotic expansions in the neighborhood of k 2 1 we express j k and its generalizations in terms of hypergeometric series of argument k 4 furthermore we show that a new infinite series of epstein hubbell integral obtained recently by some authors using the residue theory of complex variables can be easily deduced from known transformations it is shown that the elliptictype integrals can be expressed as the differintegral of elementary functions

robust regulation of distributed parameter systems with infinite dimensional exosystems in this paper a robust regulation problem for infinite dimensional systems with infinite dimensional exosystems is discussed the input and output spaces are also allowed to be infinite dimensional a new definition of internal model in terms of the controller parameters is given it is shown that there exists a feedback controller containing an internal model of the exosystem which robustly regulates the class of signals generated by the exosystem and strongly or weakly stabilizes the closed loop system as far as the authors know the results are new even for finite dimensional systems with infinite dimensional exosystems

a computational methodology for shape optimization of structures in frictionless contact this paper presents a computational methodology for shape optimization of structures in frictionless contact which provides a basis for developing user friendly and efficient shape optimization software for evaluation it has been implemented as a subsystem of a general finite element software the overall design and main principles of operation of this software are outlined the parts connected to shape optimization are described in more detail the key building blocks are analytic sensitivity analysis an adaptive finite element method an accurate contact solver and a sequential convex programing optimization algorithm results for three model application examples are presented in which the contact pressure and the effective stress are optimized

exponential stability of a mono tubular heat exchanger equation with output feedback abstract this paper is concerned with stability analysis of a mono tubular heat exchanger equation with static output feedback the mono tubular heat exchanger equation is exponentially stable when the input variable is identically zero in this paper it is shown that the c 0 semigroup generated by the closed loop operator consisting of the mono tubular heat exchanger equation and the output feedback law satisfies the spectrum determined growth assumption

internal model theory for distributed parameter systems in this paper we consider robust output regulation of distributed parameter systems and the internal model principle the main purpose is to generalize the internal model principle by francis and wonham for infinite dimensional systems and clarify the relationships between different generalizations of the internal model we also construct a signal generator capable of generating infinite dimensional polynomially increasing signals

a direct approach to compensator design for distributed parameter systems we present a direct approach to finite order compensator design for distributed parameter systems i e one that is not based on reduced order modelling instead we use a parametrization around an initial compensator which displays both controller order and closed loop stability in a convenient way the main result is an existence theorem which holds for a wide class of linear time invariant systems parabolic delay damped hyperbolic the most important assumptions are bounded inputs and outputs finitely many unstable modes completeness of eigenvectors an example is included to illustrate the feasibility of our method for purposes of design

on boundary feedback stabilization of non uniform linear 2 2 hyperbolic systems over a bounded interval conditions for boundary feedback stabilizability of non uniform linear 2 2 hyperbolic systems over a bounded interval are investigated the main result is to show that the existence of a basic quadratic control lyapunov function requires that the solution of an associated ode is defined on the considered interval this result is used to give explicit conditions for the existence of stabilizing linear boundary feedback control laws the analysis is illustrated with an application to the boundary feedback stabilization of open channels represented by linearized saint venant equations with non uniform steady states

finite dimensional regulators for a class of regular hyperbolic pde systems abstractin this paper the output regulation problem is addressed for a class of linear hyperbolic infinite dimensional systems with spatially varying coefficients modelling a large class of convection dominated transport reaction systems in particular distributed parameter systems with bounded input and unbounded output operators are considered first we demonstrate a general conclusion about the exponential stability of the considered system by relating the stability to the solution of an associated differential equation based on the assumption that the hyperbolic system satisfies the exponential stability conditions the main manuscript contribution is the development of two novel finite dimensional regulators output and error feedback regulators such that the controlled output of the plant tracks a reference signal generated by a known signal process exosystem in order to guarantee the feasibility of the proposed regulators the solvability of the corresponding sylvester equations is discusse

optimal lq feedback regulation of a nonisothermal plug flow reactor model by spectral factorization the linear quadratic lq optimal temperature and reactant concentration regulation problem is studied for a partial differential equation model of a nonisothermal plug flow tubular reactor by using a nonlinear infinite dimensional hilbert state space description first the dynamical properties of the linearized model around a constant temperature equilibrium profile along the reactor are studied it is shown that it is exponentially stable and approximately reachable next the general concept of lq feedback is introduced it turns out that any lq feedback is optimal from the input output viewpoint and stabilizing for the plug flow reactor linearized model a state lq feedback operator is computed via the solution of a matrix riccati differential equation mrde in the space variable thanks to the reachability property the computed lq feedback is actually the optimal one then the latter is applied to the nonlinear model and the resulting closed loop system dynamical performances are analyzed a criterion is given which guarantees that the constant temperature equilibrium profile is an asymptotically stable equilibrium of the closed loop system moreover under the same criterion it is shown that the control law designed previously is optimal along the nonlinear closed loop model with respect to some cost criterion the results are illustrated by some numerical simulations

robust multivariable pi controller for infinite dimensional systems a robust multivariable controller is introduced for a class of distributed parameter systems the system to be controlled is given as dot x ax bu y cx in a banach space the purpose of the control which is based on the measurement y is to stabilize and regulate the system so that y t rightarrow y r as t rightarrow infty where y r is a constant reference vector under the assumptions that operator a generates a holomorphic stable semigroup b is linear and bounded c is linear and a bounded and the input and output spaces are of the same dimension a necessary and sufficient condition is found for the existence of a robust multivariable controller this controller appears to be a multivariable pi controller also a simple necessary criterion for the existence of a decentralized controller is derived the tuning of the controller is discussed and it is shown that the i part of the controller can be tuned on the basis of step responses without exact knowledge of the system s parameters the presented theory is then used as an example to control the temperature profile of a bar with the dirichlet boundary conditions

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

a finite dimensional robust controller for systems in the cd algebra robust multivariable controllers for stable infinite dimensional systems in the callier desoer cd algebra are discussed in particular the following robust regulation problem is solved given reference and disturbance signals which are linear combinations of signals of the form t sup j sin spl omega sub k t spl phi sub k j spl ges 0 k 0 spl middot spl middot spl middot n find a low order finite dimensional controller so that the outputs asymptotically track the reference signals asymptotically reject the disturbance signals and the closed loop system is stable and robust with respect to a class of perturbations in the plant the proposed controller consists of a positive scalar gain spl epsi and certain polynomial matrices k sub k s for k 0 spl middot spl middot spl middot n the main result of the paper shows that the matrices k sub k s must satisfy certain stability conditions involving the values of the plant transfer function only at the reference and disturbance signal frequencies spl omega sub k for k 0 spl middot spl middot spl middot n the controller has unstable poles on the imaginary axis the behavior of these poles as a function of the scalar parameter spl epsi in the form of a puiseux series is given

output regulation for linear distributed parameter systems this work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system in particular it is shown that the full state feedback and error feedback regulator problems are solvable under the standard assumptions of stabilizability and detectability if and only if a pair of regulator equations is solvable for linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in francis 1997 and isidori and byrnes 1990 we also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function examples are given of periodic tracking set point control and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system

the internal model principle for systems with unbounded control and observation in this paper the theory of robust output regulation of distributed parameter systems with infinite dimensional exosystems is extended for plants with unbounded control and observation as the main result we present the internal model principle for linear infinite dimensional systems with unbounded input and output operators we do this for two different definitions of an internal model found in the literature namely the p copy internal model and the mathcal g conditions we also introduce a new way of defining an internal model for infinite dimensional systems the theoretic results are illustrated with an example where we consider robust output tracking for a one dimensional heat equation with boundary control and pointwise measurements

design space optimization using a numerical design continuation method summary a generalized optimization problem in which design space is also a design to be found is de9ned and a numerical implementation method is proposed in conventional optimization only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted a design space is speci9ed by the number of design variables and the layout or con9guration to solve this type of design space problems a simple initial design space is selected and gradually improved while the usual design variables are being optimized to make the design space evolve into a better one one may increase the number of design variables but in this transition there are discontinuities in the objective and constraint functions accordingly the sensitivity analysis methods based on continuity will not apply to this discontinuous stage to overcome the di culties a numerical continuation scheme is proposed based on a new concept of a pivot phase design space two new categories of structural optimization problems are formulated and concrete examples shown copyright 2001 john wiley sons ltd

series expansions for the third incomplete elliptic integral via partial fraction decompositions we find convergent double series expansions for legendre s third incomplete elliptic integral valid in overlapping subdomains of the unit square truncated expansions provide asymptotic approximations in the neighborhood of the logarithmic singularity 1 1 if one of the variables approaches this point faster than the other each approximation is accompanied by an error bound

brief paper lq control design of a class of hyperbolic pde systems application to fixed bed reactor a general linear controller design method for a class of hyperbolic linear partial differential equation pdes systems is presented this is achieved by using an infinite dimensional hilbert state space description with infinite dimensional distributed input and output a state lq feedback operator is computed via the solution of a matrix riccati differential equation in the space variable the proposed method is applied to a fixed bed chemical reactor control problem where one elementary reaction takes place an optimal controller is designed for linearized fixed bed reactor model it is applied to the original nonlinear model and the resulting closed loop stability is analyzed numerical simulations are performed to show the performance of the designed controller

output tracking control of a parallel flow heat exchange process abstract in this paper we consider an output tracking problem of a parallel flow heat exchange process with distributed and boundary inputs as the distributed inputs to the system the output feedback control is first applied under zero boundary inputs it is shown that the c 0 semigroup describing the closed loop system satisfies the spectrum determined growth condition next we apply a backstepping method to the design of the boundary inputs for output tracking our main result shows that the output of the system reaches a reference signal in finite time under both the output feedback control and the boundary control law derived by the backstepping method

solutions of elliptic integrals and generalizations by means of bessel functions the elliptic integrals and its generalizations are applied to solve problems in various areas of science this study aims to demonstrate a new method for the calculation of integrals through bessel functions we present solutions for classes of elliptic integrals and generalizations the latter refers to the hyperelliptic integrals and the integral called epstein hubbell the solutions obtained are expressed in terms of power series and or trigonometric series under a particular perspective the final form of a class of hyperelliptic integrals is presented in terms of lauricella functions the proposed method allowed to obtain solutions in ways not yet found in the literature

design sensitivity analysis for shape optimization based on the lie derivative abstract the paper presents a theoretical framework for the shape sensitivity analysis of systems governed by partial differential equations the proposed approach based on geometrical concepts borrowed from differential geometry shows that sensitivity of a performance function i e any function of the solution of the problem with respect to a given design variable can be represented mathematically as a lie derivative i e the derivative of that performance function along a flow representing the continuous shape modification of the geometrical model induced by the variation of the considered design variable theoretical formulae to express sensitivity analytically are demonstrated in detail in the paper and applied to a nonlinear magnetostatic and a linear elastic problem following both the direct and the adjoint approaches following the analytical approach one linear system of which only the right hand side needs be evaluated the system matrix being known already has to be solved for each of the design variables in the direct approach or for each performance functions in the adjoint approach a substantial gain in computation time is obtained this way compared to a finite difference evaluation of sensitivity which requires solving a second nonlinear system for each design variable this is the main motivation of the analytical approach there is some freedom in the definition of the auxiliary flow that represents the shape modification we present a method that makes benefit of this freedom to express sensitivity locally as a volume integral over a single layer of finite elements connected to both sides of the surfaces undergoing shape modification all sensitivity calculations are checked with a finite difference in order to validate the analytic approach convergence is analyzed in 2d and 3d with first and second order finite elements

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

asymptotic formulas for generalized elliptic type integrals abstract epstein hubbell 1 elliptic type integrals occur in radiation field problems the object of the present paper is to consider a unified form of different elliptic type integrals defined and developed recently by several authors we obtain asymptotic formulas for the generalized elliptic type integrals

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

regulator problem for infinite dimensional systems abstract in this paper a regulator problem is investigated for an infinite dimensional system with constant disturbances the regular problem is to determine a feedback control law which stabilizes and regulates the system a design procedure of a regulator is proposed which can be realized in finite dimensional theories and techniques for an infinite dimensional system

internal model based tracking and disturbance rejection for stable well posed systems in this paper we solve the tracking and disturbance rejection problem for infinite dimensional linear systems with reference and disturbance signals that are finite superpositions of sinusoids we explore two approaches both based on the internal model principle in the first approach we use a low gain controller and here our results are a partial extension of results by hamalainen and pohjolainen in their papers the plant is required to have an exponentially stable transfer function in the callier desoer algebra while in this paper we only require the plant to be well posed and exponentially stable these conditions are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable our second approach concerns the case when the second component of the plant transfer function from control input to tracking error is positive in this case we identify a very simple stabilizing controller which is again an internal model but which does not require low gain we apply our results to two problems involving systems modeled by partial differential equations the problem of rejecting external noise in a model for structure acoustics interactions and a similar problem for two coupled beams

on the internal model structure for infinite dimensional systems two common controller types and repetitive control in this paper we shall extend and amplify the recent theory of controllers employing the so called internal model structure for exponentially stable closed loop control systems this structure has been shown in another paper to be necessary and sufficient for robust output regulation also in infinite dimensional spaces here we shall derive conditions under which two controller types occurring frequently in applications have the internal model structure under these conditions robust output regulation is achieved also in infinite dimensional spaces if the closed loop system is sufficiently stable in the case that the closed loop system is only strongly but not exponentially stable it is sometimes possible to obtain conditional robustness this means that asymptotic tracking disturbance rejection is not destroyed by small perturbations so long as closed loop stability also persists our results allow for infinite dimensional plants controllers and exogenous systems and as an application of such a general setting we shall consider generalized repetitive control for exponentially stable infinite dimensional siso systems

a study on the epstein hubbell generalized elliptic type integral using residue theory abstract in this study a new solution method for epstein hubbell generalized elliptic type integral is developed and complex variable residue theory is used to arrive at the self truncating series associated with this integral by means of this method we determined that only a closed term c j 2 2n 2n n 2n n 2 n 0 1 2 contributes to the obtained series

output regulation problem for a class of regular hyperbolic systems this paper investigates the output regulation problem for a class of regular first order hyperbolic partial differential equation pde systems a state feedback and an error feedback regulator are considered to force the output of the hyperbolic pde plant to track a periodic reference trajectory generated by a neutrally stable exosystem a new explanation is given to extend the results in the literature to solve the regulation problem associated with the first order hyperbolic pde systems moreover in order to provide the closed loop stability condition for the solvability of the regulator problems the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper this paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator riccati equation

finite time output regulation for linear 2 2 hyperbolic systems using backstepping this contribution presents the backstepping design of output feedback regulators for boundary controlled linear 2 2 hyperbolic systems that achieve regulation in finite time it is assumed that the disturbances can act in domain at both boundaries and at the output to be controlled the latter need not be available for measurement and consists of in domain pointwise distributed or boundary outputs firstly a solution of the finite time state feedback regulator problem is given on the basis of the regulator equations they are formulated in backstepping coordinates so that a solution is attainable in closed form this leads to a very straightforward regulator design for 2 2 hyperbolic systems with a general class of outputs then a finite dimensional reference observer that converges in finite time is introduced which consists of two observers and a delay this result is extended to the backstepping design of finite time disturbance observers for 2 2 hyperbolic systems with a collocated measurement in particular two backstepping disturbance observers are determined so that after introducing a delay the disturbance model and plant states can be estimated in finite time hence by combining the state feedback regulator with these observers a finite time output feedback regulator is obtained for the state feedback regulator and the disturbance observer existence conditions are derived in terms of the plant transfer behaviour a simple example with an in domain pointwise and distributed output illustrates the theoretical results

new approximation method for stress constraints in structural synthesis a new approximation method for dealing with stress constraints in structural synthesis is presented in previous methods it has been common to create an approximation of the actual constraints with respect to the design variables and then use this with optimization to produce a new candidate design in the present method the finite element nodal forces are instead approximated and these are used to create an explicit but often nonlinear approximation to the original problem the principal motivation is to create the best approximation possible in order to reduce the number of detailed finite element analyses needed to reach the optimum the method is shown to be quite simple while providing significant efficiency gains in the overall optimization task also the method produces such high quality approximations to the original problem that the need for move limits during the approximate optimization stage is greatly reduced examples are offered and compared with published results to demonstrate the efficiency and reliability of the proposed method it is concluded that there are considerable gains yet to be achieved through continued careful investigation of approximation techniques

a continuum model for a re entrant factory high volume multistage continuous production flow through a re entrant factory is modeled through a conservation law for a continuous density variable on a continuous production line augmented by a state equation for the speed of the production along the production line the resulting nonlinear nonlocal hyperbolic conservation law allows fast and accurate simulations little s law is built into the model it is argued that the state equation for a re entrant factory should be nonlinear comparisons of simulations of the partial differential equation pde model and discrete event simulations are presented a general analysis of the model shows that for any nonlinear state equation there exist two steady states of production below a critical start rate a high volume high throughput time state and a low volume low throughput time state the stability of the low volume state is proved output is controlled by adjusting the start rate to a changed demand rate two linear factories and a re entrant factory each one modeled by a hyperbolic conservation law are linked to provide proof of concept for efficient supply chain simulations instantaneous density and flux through the supply chain as well as work in progress wip and output as a function of time are presented extensions to include multiple product flows and preference rules for products and dispatch rules for re entrant choices are discussed

output and error feedback regulator designs for linear infinite dimensional systems abstract this manuscript addresses the output regulation problem for linear distributed parameter systems dpss with bounded input and unbounded output operators we introduce novel methods for the design of the output feedback and error feedback regulators in the output feedback regulator design the measurements available for the regulator do not belong to the set of controlled outputs the proposed output feedback regulator with the injection of the measurement y m t and reference y r t can realize both the plant and the exosystem states estimation disturbance rejection and reference signal tracking simultaneously moreover new design approach provides an alternative choice for seeking the output injection gain in a traditional error feedback regulator design the regulator parameters are easily configured to solve the output regulation problems and to ensure the stability of the closed loop systems the results are demonstrated via computer simulation in two types of representative systems the parabolic partial differential equation pde system and the first order hyperbolic pde system

approximation method for configuration optimization of trusses an efficient method for truss configuration optimization is presented elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints constraints on member stresses and euler buckling are imposed and multiple loading conditions are considered the method presented here utilizes an approximate structural analysis based on first order taylor series expansions of the member forces the force approximation succeeds in reducing the degree of coupling between the sizing and geometry design variables and thereby increases the accuracy of the approximation a numerical optimizer uses information from the approximate structural analysis as it minimizes the weight of the truss

backstepping design of robust state feedback regulators for linear 2 times 2 hyperbolic systems this technical note deals with the robust output regulation problem for boundary controlled linear 2 times 2 hyperbolic systems thereby the output to be controlled can be located at one of the boundaries or is a pointwise in domain output by utilizing the internal model principle a state feedback regulator is determined for a finite dimensional signal model describing the exogenous signals this amounts to stabilizing a hyperbolic pde ode cascade coupled at an intermediate point for this a systematic backstepping method is developed to determine the stabilizing state feedback controller the solvability of the considered output regulation problem can easily be verified on the basis of the nominal plant transfer behaviour for non destabilizing model uncertainties the robustness of the achieved output regulation is verified an uncertain hyperbolic system with an in domain output illustrates the results of the technical note

backstepping design of robust output feedback regulators for boundary controlled parabolic pdes in this article a backstepping based solution of the robust output regulation problem for boundary controlled parabolic pdes with spatially varying parameters is presented this is achieved by stabilizing the plant extended with a finite dimensional internal model of the exogenous signals for the resulting pde ode system with spatially varying parameters a systematic backstepping based compensator design method is developed the robustness of the achieved output regulation is verified for non destabilizing model uncertainties an uncertain parabolic system illustrates the results of the article

survey of shape parameterization techniques for high fidelity multidisciplinary shape optimization a survey is provided of shape parameterization techniques formultidisciplinary optimization and some emerging ideas are highlighted the survey focuses on the suitability of available techniques for multidisciplinary applications of complex cone gurations using high e delity analysis tools such as computational e uid dynamics and computational structural mechanics the suitability criteria are based on the efe ciency effectiveness ease of implementation and availability of analytical sensitivities for geometry and grids a section on sensitivity analysis grid regeneration and grid deformation techniques is also provided