shape optimization of piezoelectric devices using an enriched meshfree method we present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two dimensional electromechanical domains this meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries we use cubic splines for delineating the geometry of internal external domain boundaries and the nodal coordinates and slopes of these splines at their control points become the design parameters this approach enables smooth manipulations of bi material interfaces and external boundaries during the optimization process it also enables the calculation of displacement and electric potential field sensitivities with respect to the design parameters through direct differentiation for which we adopt the classical material derivative approach we verify this implementation of sensitivity calculations against an exact solution to a variant of lame s problem and also finite difference approximations we follow a sequential quadratic programming approach to minimize the cost function and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan copyright 2008 john wiley sons ltd

the concavity of p renyi entropy power for doubly nonlinear diffusion equations and lp gagliardo nirenberg sobolev inequalities abstract we prove the concavity of p renyi entropy power for positive solutions to the doubly nonlinear diffusion equations on r n or compact riemannian manifolds with nonnegative ricci curvature as applications we give new proofs of the sharp l p sobolev inequality and l p gagliardo nirenberg inequalities on r n moreover two improvements of l p gagliardo nirenberg inequalities are derived

design sensitivity analysis of hyperelastic structures using a meshless method a continuum based design sensitivity analysis method for hyperelastic structures is presented analysis is performed using a meshless method called the reproducing kernel particle method yeoh s energy density function is used to describe thehyperelastic structural behavior the meshless method eliminates mesh distortion orentanglement encountered in using e nite element analysis for large deformation structural analysis and structural shape design optimization both the adjoint variable and direct differentiation methods are developed for material and shape design variables an ine nitely long rubber tube a two dimensional rubber band and an engine mount are examples used to demonstrate the feasibility and accuracy of the method

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

saint venant end effects in multilayered piezoelectric laminates the saint venant end effects and stress decay in multilayered laminates of piezoelectric materials are studied a state space approach is developed in the context of generalized plane strain by means of matrix algebra and transfer matrix the characteristics of the stress decay in 2 d piezoelectric strips and laminates are examined their elastic counterparts are included as special cases evaluation of the characteristic decay length for typical materials shows that the saint venant end effects are significant it also indicates that the analysis based on the plane strain assumption is misleading

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

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

enriched reproducing kernel particle method for piezoelectric structures with arbitrary interfaces a formulation based on enriched reproducing kernel particle method is proposed for analysing non homogenous piezoelectric structures with arbitrarily shaped material interfaces the interfaces are represented using a set of cubic spline segments each of which is defined by the co ordinates and the slopes of its two end nodes special enrichment functions are introduced within the reproducing kernel particle method in order to capture discontinuities of strain and electric fields at the material interfaces several validation examples are provided to demonstrate the veracity and the utility of the proposed numerical method copyright 2006 john wiley sons ltd

vibration of plate with curvilinear stiffeners using mesh free method the element free galerkin method which is based on the moving least squares approximation is developed for vibration analysis of unitized structures e g a plate with curvilinear stiffeners the plate and stiffeners are modeled using the first order shear deformation theory and timoshenko beam theory respectively the moving least squares approximation does not satisfy the delta function property consequently an approximation method e g the well known penalty method must be used for imposing essential boundary conditions a key benefit of using element free galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes numerical results for different stiffeners configurations and boundary conditions are presented all results are verified using the commercial finite element software ansys excellent agreement is seen in all cases a comparison of the present formulations with other available results for stiffened plates is also made the mesh free approach yields highly accurate results for the plates with curvilinear stiffeners

numerical analysis of end effects in laminated piezoelectric circular cylinders abstract a method to quantify saint venant s principle for laminated piezoelectric circular cylinders is described an algebraic eigensystem is constructed based on homogeneous equations of equilibrium with displacement and electric potential voltage fields stated in exponential form the end effects for displacements and voltages as well as stresses and electric displacements of self equilibrated states are represented by the eigendata extracted from the eigensystem the real parts of the eigenvalues convey information on the inverse decay lengths and their corresponding eigenvectors are displacement and voltage distributions of the self equilibrated states stress and electric displacement eigenvectors are formed by appropriate differentiation of the eigenvectors for the displacement and voltage fields and through the coupled electromechanical constitutive laws the right and left eigenvectors which are obtained from the eigensystem and its adjoint are related through bi orthogonality relationships the end effects due to arbitrary displacements voltages tractions or electric displacements prescribed at the cylinder s ends are obtained by means of an expansion theorem based on these bi orthogonality relationships or by a least squares method a number of verification examples are provided to demonstrate that the present results compare well with known analytical solutions and numerical results obtained via three dimensional finite element analyses

a multiscale strategy for structural optimization this paper presents a multiscale strategy dedicated to structural optimization the applications concern the study of geometric details such as holes surface profiles etc within the structures with frictional contacts the first characteristic of the method is that it uses a micro macro approach this approach is based on a domain decomposition into substructures and interfaces which involves the resolution of independent micro problems in each substructure and transfers macro information only through the interfaces the second characteristic is the use of a multiresolution strategy in order to reduce the computation cost for problems with evolving design parameters the last characteristic is the capability to model the geometry of details without remeshing thanks to two features the use of a local enrichment method and the use of level set functions to easily modify the boundary of the detail during the optimization process

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

first and second order sensitivity analysis of linear and nonlinear structures this paper employs the principle of virtual work to derive sensitivity derivatives of structural response with respect to stiffness parameters using both direct and adjoint approaches the computations required are based on additional load conditions characterized by imposed initial strains body forces or surface tractions as such they are equally applicable to numerical or analytical solution techniques the relative efficiency of various approaches for calculating first and second derivatives is assessed it is shown that for the evaluation of second derivatives the most efficient approach is one that makes use of both the first order sensitivities and adjoint vectors two example problems are used for demonstrating the various approaches

are the optimum problems in structural design well posed from the examples considered above it can be seen that the area of the cross section minimizing the total weight of a simple rod under a given load is in general not unique only under particular assumptions on the constraints and the distribution of axial loads is the optimal solution uniquely determined by the principle of minimum weight another feature of the optimal solutions is that their properties of regularity number and location of discontinuities of the solutions and its derivatives are in general not at all obvious from the beginning

saint venant end effects for plane deformations of linear piezoelectric solids the recent developments in smart structures technology have stimulated renewed interest in the fundamental theory and applications of linear piezoelectricity in this paper we investigate the decay of saint venant end effects for plane deformations of a piezoelectric semi infinite strip first of all we develop the theory of plane deformations for a general anisotropic linear piezoelectric solid just as in the mechanical case not all linear homogeneous anisotropic piezoelectric cylindrical solids will sustain a non trivial state of plane deformation the governing system of four second order partial differential equations for the two in plane displacements and electric potential are overdetermined in general sufficient conditions on the elastic and piezoelectric constants are established that do allow for a state of plane deformation the resulting traction boundary value problem with prescribed surface charge is an oblique derivative boundary value problem for a coupled elliptic system of three second order partial differential equations the special case of a piezoelectric material transversely isotropic about the poling axis is then considered thus the results are valid for the hexagonal crystal class 6mm the geometry is then specialized to be a two dimensional semi infinite strip and the poling axis is the axis transverse to the longitudinal direction we consider such a strip with sides traction free subject to zero surface charge and self equilibrated conditions at the end and with tractions and surface charge assumed to decay to zero as the axial variable tends to infinity a formulation of the problem in terms of an airy type stress function and an induction function is adopted the governing partial differential equations are a coupled system of a fourth and third order equation for these two functions on seeking solutions that exponentially decay in the axial direction one obtains an eigenvalue problem for a coupled system of fourth and second order ordinary differential equations this problem is the piezoelectric analog of the well known eigenvalue problem arising in the case of an anisotropic elastic strip it is shown that the problem can be uncoupled to an eigenvalue problem for a single sixth order ordinary differential equation with complex eigenvalues characterized as roots of transcendental equations governing symmetric and anti symmetric deformations and electric fields assuming completeness of the eigenfunctions the rate of decay of end effects is then given by the real part of the eigenvalue with smallest positive real part numerical results are given for pzt 5h pzt 5 pzt 4 and ceramic b it is shown that end effects for plane deformations of these piezoceramics penetrate further into the strip than their counterparts for purely elastic isotropic materials

variational approach by means of adjoint systems to structural optimization and sensitivity analysis ii structure shape variation abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems the application to optimal design is next presented and the relevant optimally conditions are derived from general expressions the path independent integrals used in fracture mechanics are rederived as a particular case of general expressions

optimal topological design through insertion and configuration of finite sized heterogeneities in this paper we develop a procedure for optimal topological design by sequentially inserting finite sized non spherical inclusions or holes within a homogeneous domain we propose a new criterion for topology change that results in a trade off problem to achieve the greatest least change in the objective for the least greatest change in the size of the inclusion hole respectively we derive the material derivative of the proposed objective termed as the configurational derivative that describes sensitivity of arbitrary functionals to arbitrary motions of the inclusion hole as well as the domain boundaries we specifically utilize the sensitivity to position orientation and scaling of finite sized heterogeneities to effect topological design we simplify the configurational derivative to the special case of infinitesimally small spherical inclusions or holes and show that the developed derivative is a generalization of the classical topological derivative the computational implementation relies on b spline isogeometric approximations we demonstrate through a series of examples optimal topology achieved through sequential insertion of a heterogeneity of fixed shape and optimization of its configuration location orientation and scale

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

influence of the exits configuration on evacuation process in a room without obstacle abstract the floor field model is the most popular cellular automata ca model which is used to simulate the pedestrian s behaviors in the floor field model the interaction between pedestrians is expressed by the dynamical field in this paper we proposed an improved and simple method to calculate the floor field in our method the pedestrians are treated as the movable obstacles which will increase the value of the floor field the additional value is interpreted as the blocking effect of preceding pedestrians and then the influence of the exits configuration on evacuation process in a room without obstacle is simulated the evacuation time for different widths and positions of the exits is investigated in the case of single exit there is a power law relationship between the evacuation time t and the exit width d w with a negative exponent when d w 6 mean flow rates and the using efficiency of each exit cell obtained by our model are higher than other models the simulation results indicate that pedestrians do not choose the shortest path but a faster path in our model for the case of two exits the relationships between the location of the exits and evacuation time are discussed when the total width of two exits is small i e d w 2 the main factor affecting the total evacuation time t is the exits capacity if the total width of two exits is large i e d w 12 the moving distance of pedestrians to exits is the main factor affecting the evacuation time and the corresponding phase diagrams are given

a new entropy power inequality a strengthened version of shannon s entropy power inequality for the case where one of the random vectors involved is gaussian is proved in particular it is shown that if independent gaussian noise is added to an arbitrary multivariate random variable the entropy power of the resulting random variable is a concave function of the variance power of the added noise the strengthened inequality is shown to hold for the class of stable distributions

modeling and identification of an arbitrarily shaped scatterer using dynamic xfem with cubic splines abstract localization and shape identification of an arbitrarily shaped scatterer embedded in elastic heterogeneous media is investigated using the dynamic extended finite element method xfem the scatterer s geometry is represented using cubic splines whose parameters are adaptively updated in a gradient based minimization framework that is used to solve the inverse identification problem the dynamic xfem is employed to solve the forward wave propagation problem because it enables direct parametric modeling of the moving boundary of the scatterer over a stationary background mesh the use of open close cubic splines combined with xfem enables the effective construction of the complicated scatterer geometry by minimizing the number of unknown shape parameters a two phase divide and conquer approach is adopted to alleviate complications due to the potential manifestation of multiple solutions to the inverse problem and for increased computational efficiency in first phase the scatterer is localized using a simple geometric representation and the search is carried out using multiple independent inversions starting from different initial estimates incidentally this strategy is perfectly scalable in parallel computation in the second phase the geometric representation is adaptively refined using cubic splines to obtain an accurate estimate of the scatterer s shape several numerical experiments are provided which clearly show that the proposed approach is robust and can yield highly accurate results

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

shape sensitivity analysis of sequential structural acoustic problems using fem and bem abstract a shape design sensitivity formulation for structural acoustic problems using sequential finite element and boundary element methods is presented frequency response analysis is used to obtain the dynamic behavior of the structure while boundary element analysis is used to solve for the pressure response of the acoustic domain it is shown that the adjoint method which takes the reverse direction to response analysis provides a very efficient way of sensitivity calculation in addition it has been shown that the adjoint equation for the shape design problem is the same as that of the sizing design problem the only difference is the numerical integration that evaluates the sensitivity coefficient the combination of the semi analytical method for the structure and the analytical differentiation method for the acoustic cavity yields a very practical approach for the shape design sensitivity formulation the accuracy of the sensitivity information is compared with the analytical sensitivity as well as the sensitivity calculated using the finite difference method

a continuous lagrangian sensitivity equation method for incompressible flow a continuous lagrangian sensitivity equation method clsem is presented as a cost effective alternative to the continuous eulerian sensitivity equation method cesem in the case of shape parameters boundary conditions for the clsem are simpler than those of the cesem however a mapping must be introduced to relate the undeformed and deformed configurations thus making the pdes more complicated we propose the use of pseudo elasticity equations to provide a general framework to generate this mapping for unstructured meshes on complex geometries the methodology is presented in details for the incompressible navier stokes and sensitivity equations in variational form the pdes are solved with an adaptive fem sensitivity data obtained with both approaches for a flow around a naca 4512 are used to obtain estimates of flows around nearby geometries results indicate that the clsem produces significant improvements in terms of both accuracy and cpu time

nonlinear structural design sensivitity analysis for path dependent problems part 1 general theory abstract two procedures direct differentiation and adjoint structure for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper continuum formulation is used and both geometric and material nonlinearities are included in the derivations incremental nonlinear analysis based on the total lagrangian concept is adopted the reference volume concept is used to unify the shape and nonshape design problems to show the generality of the theory the derived expressions are reduced to some special cases that have been treated previously in the literature in part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory the theory has also beendiscretized elsewhere using finite element approximations for implementation into structural analysis programs these developments offer a firm foundation for design optimization of complex structural systems

higher order extended fem for weak discontinuities level set representation quadrature and application to magneto mechanical problems in this article we present the application of bilinear and biquadratic extended fem xfem formulations to model weak discontinuities in magnetic and coupled magneto mechanical boundary value problems for properly resolving the location of curved interfaces and the discontinuous physical behaviour the major part of the contribution is devoted to review and develop methods for level set representation of curved interfaces and numerical integration of the weak form in higher order xfem formulations in order to reduce the complexity of the representation of curved interfaces an element local approach that allows for an automated computation of the level set values and also improves the compatibility between the level set representation and the integration subdomains is proposed integration rules for polygons and strain smoothing are applied in conjunction with biquadratic elements and compared with curved integration subdomains eventually a coupled magneto mechanical demonstration problem is modelled and solved by xfem for demonstration purposes a magneto mechanical coupling due to magnetic stresses is considered errors and convergence rates are analysed for the different level set representations and numerical integration procedures as well as their dependence on the ratio of material parameters at an interface copyright c 2012 john wiley sons ltd

treatment of material discontinuity in the element free galerkin method abstract a method is presented for application of the element free galerkin method efg to solid mechanics problems containing material discontinuities by using the efg method the trial and test functions for the weak form are constructed with moving least square interpolants in each material domain additional constraints are imposed at the variational level to ensure satisfaction of interface conditions as a result only nodal data no elemental connectivity is needed given c 1 continuity of the interpolant weighting function the dependent variable and its gradient are continuous in each material domain two linear elastic bi material examples are presented to illustrate the effectiveness of the method

the concavity of p entropy power and applications in functional inequalities abstract in this paper we prove the concavity of p entropy power of probability densities solving the p heat equation on closed riemannian manifold with nonnegative ricci curvature as applications we give new proofs of l p euclidean nash inequality and l p euclidean logarithmic sobolev inequality moreover an improvement of l p logarithmic sobolev inequality is derived

shape sensitivity analysis in linear elastic fracture mechanics shape sensitivity analysis of an elastic solid in equilibrium with a known load system applied over its boundary is presented in this work the domain and boundary integral expressions of the first and second order shape derivatives of the total potential energy are established by using an arbitrary change of the domain characterized by a velocity field defined over the initial body configuration in these expressions we recognize free divergence tensors that are denoted in this paper as energy shape change tensors next shape sensitivity analysis is applied to cracked bodies for that purpose a suitable velocity distribution field is adopted to simulate the crack advance of a unit length in a two dimensional body finally the corresponding domain and the equivalent path independent integral expressions of the first and second order potential energy release rate of fracture mechanics are also derived

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

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

exit dynamics of occupant evacuation in an emergency abstract a two dimensional cellular automata model is proposed to simulate the exit dynamics of occupant evacuation concerning the exit width and the door separation we put forward some useful standpoints 1 exit width should be bigger than a critical value and the door separation should be neither too small nor too big 2 for single exit door with the increase of exit width the flux per unit width will decrease but the total flux will always increase 3 the total flux of the exit is an increasing nonlinear function of the exit width 4 the optimal value of the door separation does not vary with the value of exit width 5 the layout of exits should be symmetry those results are helpful in performance based design of building

a spline based enrichment function for arbitrary inclusions in extended finite element method with applications to finite deformations summary a novel enrichment function which can model arbitrarily shaped inclusions within the framework of the extended finite element method is proposed the internal boundary of an arbitrary shaped inclusion is first discretized and a numerical enrichment function is constructed on the fly using spline interpolation we consider a piecewise cubic spline which is constructed from seven localized discrete boundary points the enrichment function is then determined by solving numerically a nonlinear equation which determines the distance from any point to the spline curve parametric convergence studies are carried out to show the accuracy of this approach compared with pointwise and linear segmentation of points for the construction of the enrichment function in the case of simple inclusions and arbitrarily shaped inclusions in linear elasticity moreover the viability of this approach is illustrated on a neo hookean hyperelastic material with a hole undergoing large deformation in this case the enrichment is able to adapt to the deformation and effectively capture the correct response without remeshing copyright 2013 john wiley sons ltd

the concavity of renyi entropy power we associate to the pth renyi entropy a definition of entropy power which is the natural extension of shannon s entropy power and exhibits a nice behavior along solutions to the p nonlinear heat equation in rn we show that the renyi entropy power of general probability densities solving such equations is always a concave function of time whereas it has a linear behavior in correspondence to the barenblatt source type solutions this result extends costa s concavity inequality for shannon s entropy power to renyi entropies

bem first order regularisation method in linear elasticity for boundary identification in this paper we study the identification of an unknown portion of the boundary of a two dimensional domain occupied by an isotropic linear elastic material from additional cauchy data on the remaining known portion of the boundary this inverse problem is approached using the boundary element method bem in conjunction with the tikhonov first order regularisation procedure the choice of the regularisation parameter is based on the l curve criterion the numerical results obtained show that the proposed method produces a convergent and stable solution

efg approximation with discontinuous derivatives a technique for incorporating discontinuities in derivatives into meshless methods is presented the technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives the special shape functions have compact support which results in banded matrix equations the technique is described in element free galerkin context but is easily applicable to other meshless methods and projections numerical results for problems in one and two dimensions are reported 1998 john wiley sons ltd

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

variational principle for shape design sensitivity analysis in this paper the adjoint method of design sensitivity analysis is stated as a general variational principle that is applicable to a wide range of problems the principle gives a very simple and straightforward method of obtaining the design sensitivity expression for a functional dependent on the state fields the sensitivity expression involves certain adjoint fields and explicit design variations of the functional and the governing equations for the primary state fields the principle is stated in terms of an augmented functional that is defined by adding to the response functional whose sensitivity is desired the equilibrium equation of the primary problem then explicit design variation of the augmented functional gives the total design variation of the response functional stationarity of the augmented functional with respect to the state fields defines the adjoint problem for the response functional the principle is proved and applied to several classes of linear and nonlinear problems such as field problems structural problems and dynamic response problems it is shown that the design sensitivity expressions derived in the literature using long procedures are obtained quite routinely by use of the principle

grid optimization for the boundary element method the quality of solution obtained using the boundary element method bem is dependent on how the boundary is discretized this is particularly true in domains of complex geometry a rule for grid optimization for the bem is derived on the bases of an asymptotic measure of the boundary element error that preserves the number of elements degrees of freedom three example problems are provided to show the advantages of grid optimization in terms of accuracy and cost

discrete adjoint formulation for continuum sensitivity analysis continuum sensitivity analysis csa is an approach for calculating analytic derivatives a direct csa formulation is advantageous for computing derivatives of many state variables or performance functions an adjoint formulation of csa is beneficial for computing derivatives with respect to many design variables although adjoint csa boundary conditions are often problematic for the proposed continuum discrete hybrid adjoint approach the adjoint variable is introduced after discretization which simplifies boundary conditions the sensitivity boundary conditions for the hybrid csa are posed in terms of the continuum state variables thus the hybrid adjoint formulation of csa results in design derivatives that are as accurate as those obtained from direct csa in addition to making the analysis efficient for the case of large number of design variables two test cases first of an axial bar and second of a cantilever beam modeled with solid elements illustrate how the hybrid adjoint formulation inherits the benefits of the direct and adjoint csa formulations this is also the first application of csa to obtain design derivatives nonintrusively using three dimensional 3 d spatial gradient reconstruction sgr method for 3 d solid elements

sensitivity analysis of linear elastic systems using domain parameterization and a mixed mutual energy principle abstract a unified approach for explicit structural design sensitivity analysis of linear elastic systems is presented first order sensitivity expression involving the complete set of design variable including shape design parameters are derived for general response functional both direct differentiation and adjoint variable methods are developed in a general variational context a domain parameterization method related to the mixed eulerian lagrangian kinematic description is introduced for the treatment of shape variation problems this approach is an alternative to the material derivative methods presented elsewhere in the literature the adjoint variable derivation is based on a mixed energy principle the mutual hu washizu energy principle which is formally stated and proved the design sensitivity derivation based on this principle unifies and extends several of the adjoint variable methods found in the literature the derivations presented here are extended to nonlinear systems in a subsequent paper the sensitivity expressions are valid for use with force displacement or mixed approximate solutions of the elasticity equations other formulations are generally only consistent with displacement solution methods numerical implementation of the design sensitivity methods is discussed and illustrative examples are included

variational approach to first and second order sensitivity analysis of elastic structures for a linear elastic structure the first variations of arbitrary stress strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain in references 1 and 2 by using the solutions for primary and adjoint systems in this paper explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters these expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems furthermore the variation of local stress strain or displacement is considered several illustrative examples are provided for the first and second order sensitivity analysis of beams

a meshless integral method based on regularized boundary integral equation a meshless integral method based on the regularized boundary integral equation is developed and applied to two dimensional linear elasticity the governing integral equation is obtained from the weak form of elasticity over a local sub domain and the moving least squares approximation is used for meshless function approximation the method is built on the lbie method proposed by atluri and co workers and several key improvements are introduced in this work that significantly enhance the accuracy and robustness of the method the most critical improvement is the use of the subtraction technique to remove the strong singularity that results in a regularized governing integral equation the technique is straightforward and efficient and is much simpler and easier compared to other singularity removal techniques a special numerical integration is employed for the calculation of integrals with weak singularity which further improves accuracy the collocation method is employed to enforce the essential boundary conditions exactly which is simple and computationally efficient the natural boundary conditions are incorporated in the system governing equation and require no special handling numerical tests show that the meshless integral method is accurate and robust the effects of weight function support domain sub domain and monomial basis are investigated and discussed

analytical solution for rectangular thick laminated plates subjected to arbitrary boundary conditions three dimensional deformations of a multilayered linear elastic anisotropic rectangular plate subjected to arbitrary boundary conditions at its edges are analyzed by the generalized eshelby stroh formalism the rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses perfect bonding is assumed between the adjoining laminae in the sense that both surface tractions and displacements are assumed to be continuous across their interfaces the analytical solution is in terms of infinite series and the effect of truncating the series on the accuracy of the solution is scrutinized the method is also applicable to rectangular laminated plates with edges of each lamina subjected to different boundary conditions results are presented for thick plates with different sets of edge boundary conditions e g two opposite edges simply supported and the other two subjected to eight different conditions or all four edges clamped

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

saint venant end effects in piezoceramic materials the stress decay rate and characteristic decay length for anisotropic materials and fiber composites have been intensively investigated however those for piezoelectric materials have not been studied in this paper we examine the saint venant end effects of piezoceramic materials by considering the problem of a semi infinite piezoceramic strip polarized in the thickness direction and with applied voltages on the upper and lower surfaces it is assumed that the gradient of electric potential in the axial direction is much smaller than that in the thickness direction thus the governing equations in terms of the airy stress function and electric potential function can be uncoupled the governing equation in terms of the airy stress function involves only two non dimensional parameters after non dimensionalization finally the stress decay rates and characteristic decay lengths for a variety of piezoceramic materials are computed numerically and their variation with the two non dimensional parameters is presented

a systematic approach to shape sensitivity analysis abstract a fully detailed development of the domain parameterization method is presented for shape sensitivity analysis it is shown that equivalent results are obtained from the material derivative method in fact the material derivative method may be viewed as a special case of the domain parameterization method which occurs when the reference configuration coincides with the body configuration the method is illustrated for the laplace problem in which explicit shape sensitivities are derived by the adjoint and direct differentiation methods both finite element and boundary element applications are discussed the similarities between this approach and the isoparametric finite boundary element method are transparent in the finite element approach it is shown that the sensitivity integrals may be transformed to the boundary as is commonly done in the material derivative method for the adjoint method however this does not seem possible for the direct differentiation method finally in the boundary element approach the sensitivities do not require the differentiation of the fundamental solutions

an exposition of the material derivative approach for structural shape sensitivity analysis abstract the material derivative approach for structural shape design sensitivity analysis is described in a unified manner using the continuum formulation both the direct differentiation and adjoint methods are derived and computer implementation aspects are discussed the basic purpose of the paper is to present the shape design sensitivity analysis as an application of the material derivative concept of continuum mechanics and the calculus of variation procedures for taking variations of integrals over the variable domains it is also shown that the use of a recently developed variational principle for design sensitivity analysis greatly simplifies derivation of the adjoint method the indicial notation is used and expressions derived by different authors are related to each other a basic understanding of the material derivative approach of shape sensitivity analysis has been gained which can lead to insights for computer implementations of the method

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

a semi analytic meshfree method for almansi michell problems of piezoelectric cylinders abstract saint venant s problem almansi michell problems meshfree methods piezoelectricity we present a semi analytical method for analyzing prismatic nonhomogeneous piezoelectric cylinders with arbitrary cross sectional geometry the prescribed loads considered in this study include axial forces torques moments and voltage resultants prescribed at the cylinder s ends as well as body forces lateral surface shears voltages and pressures as long as they can be represented by a power series in the axial coordinate this problem can be considered as an extension of saint venant and almansi michell problems for elastic bodies to piezoelectric bodies in this computationally efficient method the cross sectional plane is discretized with a meshfree approach and the solution is obtained analytically with respect to the axial coordinate a number of examples are provided to demonstrate the veracity and utility of the proposed method

the meshless standard and hypersingular boundary node methods applications to error estimation and adaptivity in three dimensional problems the standard singular boundary node method bnm and the novel hypersingular boundary node method hbnm are employed for the usual and adaptive solutions of three dimensional potential and elasticity problems these methods couple boundary integral equations with moving least squares interpolants while retaining the dimensionality advantage of the former and the meshless attribute of the latter the hypersingular residuals developed for error estimation in the mesh based collocation boundary element method bem and symmetric galerkin bem by paulino et al are extended to the meshless bnm setting a simple a posteriori error estimation and an effective adaptive refinement procedure are presented the implementation of all the techniques involved in this work are discussed which includes aspects regarding parallel implementation of the bnm and hbnm codes several numerical examples are given and discussed in detail conclusions are inferred and relevant extensions of the methodology introduced in this work are provided copyright 2001 john wiley sons ltd

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

jamming transition in pedestrian counter flow a lattice gas model with biased random walkers is presented to mimic the pedestrian counter flow in a channel under the open boundary condition of constant density there are two types of walkers without the back step the one is the random walker going to the right and the other is the random walker going to the left it is found that a dynamical jamming transition from the freely moving state at low density to the stopped state at high density occurs at the critical density the transition point is given by pc 0 45 0 01 not depending on the system size the transition point depends on the strength of drift and decreases with increasing drift also we present the extended model to take into account the traffic rule in which a pedestrian walks preferably on the right hand side of the channel

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

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

variational method for design sensitivity analysis in nonlinear structural mechanics this paper describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape nonshape and material selection problems the concepts of reference volume and adjoint structure are used to develop the unified viewpoint a general formula for design sensitivity analysis is derived several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use such analytical examples give insight into the application of the general formula to more complex problems that must be treated numerically adjoint state fields are also interpreted as sensitivities for the functional related to the primary structure

structural shape sensitivity analysis relationship between material derivative and control volume approaches the material derivative and control volume approaches for structural shape design sensitivity analysis are presented analyzed and compared starting with a continuum formulation and a general response functional needing sensitivity analysis the two approaches are derived it is shown that the final design sensitivity expression for one approach can be obtained from the final expression for the other thus the two approaches are theoretically equivalent discretizations of the continuum expressions are presented and it is shown that the two approaches can lead to different implementations for numerical calculations a unified interpretation is developed in which the explicit design variations partial derivatives with respect to the design variables of the internal and external forces are the major calculations needed to implement the design sensitivity analysis the discretized forms of the continuum sensitivity expressions are also compared with the ones obtained by starting with the discretized model ab initio this comparison shows that these two approaches lead to similar expressions for numerical calculations therefore the exact same procedures can be used for computer implementations for both of the approaches the presented analyses give insights for implementation of the design sensitivity analysis theory with the finite element analysis programs

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

identification of a scatterer embedded in elastic heterogeneous media using dynamic xfem abstract a numerical approach for identifying a scatterer embedded in elastic heterogeneous media is described this scatterer may be a crack a void or an inclusion with properties that have detectable contrasts from those of the host medium the forward wave propagation problem is solved using the dynamic extended finite element method xfem which allows the boundary of the scatterer to be easily relocated over a stationary background mesh the inverse problem is cast as a minimization problem whereby the unknown shape parameters of the scatterer e g a line crack s center coordinates size and orientation are the updating parameters a gradient based method is utilized to solve the minimization problem in order to alleviate the potential manifestation of multiple solutions to the inverse problem various deployment patterns for multiple sensors are investigated and also a divide and conquer approach is adopted wherein a set of independent inversions using multiple initial guesses are carried out

isogeometric shape optimization for quasi static processes summary a framework to solve shape optimization problems for quasi static processes is developed and implemented numerically within the context of isogeometric analysis iga recent contributions in shape optimization within iga have been limited to static or steady state loading conditions in the present contribution the formulation of shape optimization is extended to include time dependent loads and responses a general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems an adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of iga the methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi axial tension and pure shear under quasi static loading conditions the method is validated using a passive control approach with an a priori known solution several applications of time dependent mechanical problems are shown to illustrate the capabilities of this approach in particular a problem is considered where an external load is allowed to move along the surface of a structure the shape of the structure is modified in order to control the time dependent displacement of the point where the load is applied according to a pre specified target copyright 2015 john wiley sons ltd

adaptivity in linear elastic fracture mechanics based on shape sensitivity analysis abstract if crack growth of an elastic body is viewed as a shape change we can use the well known concept of shape sensitivity analysis to compute the energy release rate to do this we adopt as cost function the total potential energy and as state equation the equilibrium equation the shape derivative of the total potential energy stored in the cracked body depends on the displacement field u and on the shape change velocity field v which characterize the crack growth following this procedure the present paper deals with the derivation of a novel a posteriori error estimator which is an upper bound of the global error h this error estimator has been specifically designed to evaluate the energy release rate in mesh refinement or re meshing procedures so as to obtain improved meshes for which the optimal rate of convergence is recovered even in a case of singularities this novel estimator is capable to capture all source of errors for the energy release rate the ones from stress concentration and the errors from the sensitivity of the solution to shape changes due to crack growth finally well known three dimensional examples of un cracked and cracked body are considered in order to illustrate the potentiality of the proposed methodology