sensitivity analysis of coincident critical loads with respect to minor imperfection abstract a new formulation is presented for sensitivity analysis of a coincident critical load factor only symmetric elastic structures subjected to symmetric loads are considered and sensitivity coefficients are found for a symmetric design modification which corresponds to a minor imperfection it is shown that the formulation for sensitivity analysis of multiple linear buckling load factor can be successfully combined with that of nonlinear buckling to develop a formulation for coincident nonlinear buckling load factor the proposed formulation is verified by analytical examples of simple spring bar systems

shape optimization of truss stiffened shell structures with variable thickness this paper presents an effective approach to shape optimal design of statically loaded elastic shell like structures the shape parametrization is based on a design element technique the chosen design element is a rational bezier body enhanced with a smoothly varying scalar field a body like design element makes possible to unify the shape optimization of both pure shells and truss stiffened shell structures the scalar field of the design element is obtained by attaching to each control point a scalar quantity which is an add on to the position and weight of the control point this scalar field is linked to the shell thickness distribution which can be optimized simultaneously with the shape of the shell for linear and non linear analysis of shell structures a reliable 4 node shell finite element formulation is utilized the presented optimization approach assumes the employment of a gradient based optimization algorithm and the use of the discrete method of direct differentiation to perform the sensitivity analysis four numerical examples of shell and truss stiffened shell optimization are presented in detail to illustrate the performance of the proposed approach

distortion correction in fetal epi using non rigid registration with a laplacian constraint geometric distortion induced by the main b0 field disrupts the consistency of fetal echo planar imaging epi data on which diffusion and functional magnetic resonance imaging is based in this paper we present a novel data driven method for simultaneous motion and distortion correction of fetal epi a motion corrected and reconstructed t2 weighted single shot fast spin echo ssfse volume is used as a model of undistorted fetal brain anatomy our algorithm interleaves two registration steps estimation of fetal motion parameters by aligning epi slices to the model and deformable registration of epi slices to slices simulated from the undistorted model to estimate the distortion field the deformable registration is regularized by a physically inspired laplacian constraint to model distortion induced by a source free background b0 field our experiments show that distortion correction significantly improves consistency of reconstructed epi volumes with ssfse volumes in addition the estimated distortion fields are consistent with fields calculated from acquired field maps and the laplacian constraint is essential for estimation of plausible distortion fields the epi volumes reconstructed from different scans of the same subject were more consistent when the proposed method was used in comparison with epi volumes reconstructed from data distortion corrected using a separately acquired b0 field map

maximum loads of imperfect systems corresponding to stable bifurcation abstract a simple and computationally inexpensive approach is presented for obtaining the maximum load factor of an elastic structure considering reduction of load carrying capacity due to inevitable initial imperfections the structure has a stable bifurcation point if no initial imperfection exists an antioptimization problem is formulated for minimizing the maximum loads reduced by the most sensitive imperfection within the convex bounds on the imperfections of nodal locations and nodal loads the maximum loads may be defined by bifurcation points or deformation constraints a problem of simultaneous analysis and design with energy method is formulated to avoid laborious nonlinear path following analysis the stable bifurcation point is located by minimizing the load factor under constraint on the lowest eigenvalue of the stability matrix it is shown in the examples that a minor imperfection that is usually dismissed is very important in evaluating the maximum load of a flexible structure

unwarping of unidirectionally distorted epi images echo planar imaging epi is a fast nuclear magnetic resonance imaging mri method unfortunately local magnetic field inhomogeneities induced mainly by the subject s presence cause significant geometrical distortion predominantly along the phase encoding direction which must be undone to allow for meaningful further processing so far this aspect has been too often neglected in this paper the authors suggest a new approach using an algorithm specifically developed for the automatic registration of distorted epi images with corresponding anatomically correct mri images they model the deformation field with splines which gives us a great deal of flexibility while comprising the affine transform as a special case the registration criterion is least squares interestingly the complexity of its evaluation does not depend on the resolution of the control grid the spline model gives the authors good accuracy thanks to its high approximation order the short support of splines leads to a fast algorithm a multiresolution approach yields robustness and additional speedup the algorithm was tested on real as well as synthetic data and the results were compared with a manual method a wavelet based sobolev type random deformation generator was developed for testing purposes a blind test indicates that the proposed automatic method is faster more reliable and more precise than the manual one

optimization of imperfection sensitive symmetric systems for specified maximum load factor a method is presented for optimum design of a symmetric structure which reaches an unstable bifurcation point as the load factor is increased reduction of the maximum load level due to the antisymmetric imperfection is considered and a straightforward algorithm is proposed for calculating the magnitude of reduction of the load factor corresponding to the most critical mode of antisymmetric imperfection the sensitivity coefficients of the bifurcation load factor are calculated by using the interpolation method developed by the authors and an approximate formulation is presented for sensitivity analysis of the maximum load factor it is shown in the examples that the errors in the sensitivity coefficients do not lead to any significant difference in the optimum design

an approach to optimal design of structures with non linear response a commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems where each of these is obtained as an approximation of the original problem considering structures with linear response this procedure works very well and can be implemented quite straightforwardly however considering structures with non linear response the situation is more sophisticated since structural stability properties have to be taken into account the paper presents an approach to optimal design of statically loaded structures with non linear response it is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained these similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level which is lower or at most equal to the critical load level by this approach the structural stability requirements are taken into account in an effective manner the efficiency is illustrated with several examples involving kinematic as well as material non linear effects

optimum design of flexible structures under constraints on strain energy and asymptotic stability a new concept and optimization method are presented for designing a flexible structure that allows large deformation constraint is given for the minimum strain energy that can be stored for specified norm of displacement as well as asymptotic stability of the undeformed state within the region defined by the specified displacement norm the optimal solution is obtained by solving a two level optimization problem examples are given for 2 bar and 24 bar trusses asymptotic stability of the optimized truss is verified by carrying out dynamic analysis for given random initial velocity that is equivalent to the specified strain energy

an evaluation of the use of magnetic field maps to undistort echo planar images when a head is placed in an mri scanner differences between the magnetic susceptibility of tissue bone and air distort the magnetic field while some of the resulting inhomogeneity can be corrected by the shimming process much of it cannot and this causes distortion sometimes referred to as geometric distortion of echo planar images epis one strategy for the correction of distortion is to acquire a map of the magnetic field achieved in each subject and then to use this to undistort their epis after reconstruction jezzard and balaban 1995 here we present five experiments to evaluate the application of such a strategy on data from a 3 t scanner we show that after undistortion the shape of epis is more similar to the true shape of the brain and we investigate the effect of head movement on the efficacy of undistortion if undistortion was applied first it was found that less nonlinear warping was required to transform epis into a standard space particularly in the phaseencode direction we show that if spm 99 normalization is used to perform a nonlinear warp to standard space the prior application of undistortion increases the statistical power of group studies with motor and auditory tasks we show that this increase in power is due to an increase in the overlap of activation of different subjects finally we evaluate where in the brain undistorting epis might be expected to have the greatest effect in terms both of mislocalization of activation and of a reduction in power overall undistorting epis using field maps has proved extremely successful improving the anatomical localization of activation and increasing statistical power 2002 elsevier science usa

an efficient total variation algorithm for super resolution in fetal brain mri with adaptive regularization although fetal anatomy can be adequately viewed in new multi slice mr images many critical limitations remain for quantitative data analysis to this end several research groups have recently developed advanced image processing methods often denoted by super resolution sr techniques to reconstruct from a set of clinical low resolution lr images a high resolution hr motion free volume it is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality literature has been quite attracted by total variation energies because of their ability in edge preserving but only standard explicit steepest gradient techniques have been applied for optimization in a preliminary work it has been shown that novel fast convex optimization techniques could be successfully applied to design an efficient total variation optimization algorithm for the super resolution problem in this work two major contributions are presented firstly we will briefly review the bayesian and variational dual formulations of current state of the art methods dedicated to fetal mri reconstruction secondly we present an extensive quantitative evaluation of our sr algorithm previously introduced on both simulated fetal and real clinical data with both normal and pathological subjects specifically we study the robustness of regularization terms in front of residual registration errors and we also present a novel strategy for automatically select the weight of the regularization as regards the data fidelity term our results show that our tv implementation is highly robust in front of motion artifacts and that it offers the best trade off between speed and accuracy for fetal mri recovery as in comparison with state of the art methods

a quadratically convergent algorithm for the computation of stability points the application of the determinant of the tangent stiffness matrix abstract this paper presents a quadratically convergent algorithm for the computation of stability points limit and bifurcation points in the finite element formulation of the problems of the nonlinear structural mechanics one such approach was given by wriggers and coworkers comput methods appl mech engrg 70 1988 329 347 and int j numer methods engrg 30 1990 155 176 their approach employs the eigenvector equation k t 0 as the characterization of the stability point in the present paper an alternative approach is proposed which uses the equation det k t 0 as the stability point condition in combination with newton s iteration scheme this condition has so far been considered unsuitable for the implementation in the finite element analysis because it has been believed that it requires the full assembly of the derivative of the global tangent stiffness matrix which is a very costly operation objectives of our paper are i to derive a new quadratically convergent algorithm for the computation of stability points which uses the condition det k t 0 for the characterization of the stability point ii to show that the full assembly of the global tangent stiffness matrix derivative is not required and that the linearization of the determinant of the global tangent stiffness matrix can be done in an element by element fashion and iii to indicate that in terms of the number of algebraic operations memory requirements and the computer programming effort our algorithm practically equals the one based on an eigenvector equation but has the advantage of a larger radius of convergence an additional benefit of the proposed algorithm is that it can also be used without any modification as a comprehensive path following procedure to calculate regular and singular stability points the effectiveness of our algorithm is illustrated by numerical examples its convergence characteristics are compared with those of the algorithm based on the eigenvector equation we show stability analyses of elastic plastic planar frames the algorithm is of course valid generally and is not limited to this particular kind of structures

a general procedure for the direct computation of turning and bifurcation points we address the formulation and numerical implementation of general purpose algorithme suitable for the direct computation of stability points in non linear solid mechanics the effectiveness of the resulting algorithm is illustrated by numerical simulation that include bifurcation and loss of stability in elastoplasticity non linear rods and non linear three dimensional shells

design of frames against buckling using a rayleigh quotient approximation a rayleigh quotient approximation is applied to the design of structures while guarding against elastic instability it approximates buckling eigenvalues by separately estimating the modal strain energy due to the linear and geometric stiffness of the structure previously used during structural optimization for the fundamental natural eigenvalue the rayleigh quotient approximation is derived for the buckling design problem for the first time the critical buckling load is found by solving the eigenvalue problem that arises by considering the geometric nonlinearity of the deforming structure rayleigh s principle is used to justify the choice of intermediate design variables for approximating terms in the rayleigh quotient a truss model illustrates the importance of the design space chosen for approximating the modal strain energy a beamtcolumn two plane frames and a space frame are used to verify the formulation special attention is paid to difficult bimodal optima

design sensitivity analysis and optimization for nonlinear buckling of finite dimensional elastic conservative structures the purpose of this review paper is to summarize the existing methods of design sensitivity analysis and optimization of elastic conservative finite dimensional systems with respect to nonlinear buckling behavior difficulties related to geometrical nonlinear singular behaviors are discussed in detail characteristics of optimized structures are demonstrated in reference to snapthrough behavior hill top branching and degenerate critical points a new optimization result of a flexible truss that fully utilizes the snapthrough behavior is also presented

optimization of shallow trusses against limit point instability the problem of the maximization of the critical load limit point instability of shallow space trusses of constant volume or weight is considered exact solutions being possible in simple cases a detailed investigation of the question of the uniqueness of the optimum designs for two and four bar shallow truss problems is carried out the optimized trusses satisfy the constant strain energy density criteria and the load maximization problem is verified to be the dual of the minimization of the total potential energy

minimum weight design of truss structures with geometric nonlinear behavior the paper presents an optimization method based on optimality criterion for minimum weight design of structures with geometric nonlinear behavior the nonlinear critical load is determined by finding the load level at which the hessian of the potential energy ceases to be positive definite a recurrence relation based on the criterion that at optimum the nonlinear strain energy density be equal in all the members is used to develop an algorithm sample problems are given to illustrate the application of the method to truss type structures with a large number of design variables number of algorithms based on the optimality criterion approach have been developed to design a minimum weight structure with specified constraints on nodal displacements element stresses system stability etc 1 2 the optimization algorithm consisted of analyzing the structure by the finite element method and using a recurrence relation derived from the appropriate optimality criterion to modify the design variables the optimality criterion was derived by differentiating the lagrangian with respect to the design variables the displacements were assumed to be small and in the finite element analysis linear equilibrium equations were solved to determine the response of the structure to the ap plied loads in the case of system stability the constraints were defined see refs 3 6 by the associated linear eigenvalue problem this definition of system stability for some structures may not be valid because of the nonlinear behavior of the structure which may be due to the geometry of the structure or the presence of geometric imperfections the correct procedure for these structures would be to analyze the structure by using nonlinear equilibrium equations this will be particularly true for large space structures lss in this paper an optimization method based on the optimality criterion approach is presented for structures with geometric nonlinear behavior in the case of a structure optimized with constraints on linear stability the optimum structure can have more than one critical buckling mode this design tends to become im perfection sensitive and a small deviation in the geometry of the structure can reduce its load carrying capacity sub stantially the imperfection sensitivity of the optimized structure can be reduced by designing the structure so that buckling loads associated with the critical buckling modes are not equal see ref 7 a real structure has geometric im perfections and these structures tend to have nonlinear

parameter sensitivity of inelastic buckling and post buckling response this paper is concerned with recent sensitivity results for buckling and post buckling problems the article starts with an overview of the fem based approach to inelastic structural mechanics systems with singular points along the equilibrium path the existing sensitivity techniques are reviewed their inherent drawbacks are indicated and a new methodology is suggested the discretized formalism is mainly employed throughout but a continuum formulation appropriate for this class of problems is also given numerical studies illustrate the presentation

the fiber of the secondary suspension map there are several different choices for the indexing this one works nicely for both odd primes and the prime 2 in this paper we will only consider the prime 2 the groups ek are an associated graded group to lrk qs0 filtered by the sphere of origin the ehp sequence from a quite general point of view is discussed in 13 the chain complex to calculate the e2 term is given by dl elknkn ek 1 n 1 if we invert the prime 2 then d1 is an isomorphism if k n 1 and n is odd the spectral sequence collapses at e2 this gives serre s theorem that rationally s2nis just k q 2n1

design sensitivity analysis of elastoplastic structures an iterative and incremental algorithm is presented for the design sensitivity analysis dsa of elastoplastic structures geometrical non linearity is included in the formulation and the structure may be subjected to a cyclic loading the key concept is discussed using an elastoplastic truss it is shown that the design sensitivity coefficients dscs are path dependent and discontinuous at the time at which yielding takes place in a member yield time in the proposed algorithm the yield time is considered to be a function of the design variables in this way the discontinuity in the dscs at the material transition points can be overcome in a simple and routine way incremental response analysis and dsa are carried out simultaneously using the newton raphson type iterative procedure since the proposed algorithm is completely consistent with the analysis procedure it can be implemented into an existing code for structural analysis application to distributed parameter structures with kinematic and or isotropic hardening is discussed using the von mises yield condition and the elastic predictor radial return method dsa is carried out for a ten bar truss with a piecewise linear constitutive relation it is shown that the dscs found using the proposed method agree quite well with those calculated by the central difference method finally an alternate method without any iteration for dsa is proposed and the results from the two methods are compared

imperfection sensitivity analysis of hill top branching with many symmetric bifurcation points imperfection sensitivity properties are derived for finite dimensional elastic conservative systems exhibiting hill top branching at which arbitrary many bifurcation points coincide with a limit point the critical load at a hill top branching point is demonstrated to be insensitive to initial imperfections when all the bifurcation points are individually symmetric therefore it is not dangerous to design a frame or truss so that many members buckle simultaneously at the limit point although the notion of the danger of optimization by compound bifurcation is widespread

v1 and v2 periodicity in stable homotopy theory this paper we construct some self maps related to the elements v1 e 7r2 bp and v2 e 76 bp and use them to obtain families in the 2 primary stable homotopy of spheres in particular we obtain nonzero elements in the 48k 10 stem for all k 0 here bp denotes the brown peterson spectrum associated to p 2 although our results have convenient interpretations in the bp adamsnovikov spectral sequence 251 we make hardly any use of this spectral sequence except in the final step of one argument the only knowledge of bp required here is its homotopy ring our methods are those of the classical k z2 adams spectral sequence ass as we shall be working entirely in the stable category we will denote by x y the abelian group of stable homotopy classes of maps x to y when x is a finite cw complex and y a spectrum we will identify x y with eix y for any integer i and we will not distinguish between a map and its stable homotopy class if v e e x x vk denotes

the image of j in the ehp sequence the ehp sequence is based on a result of james j who showed that there is h a map h such that s q sn s2n 1 is a fibration when localized at 2 the map sn sn is usually labeled e the boundary homomorphism in the homotopy sequence is usually labeled p for our purposes it will be most convenient to combine all the ehp sequences into one system this gives the following filtration of o201 s q s

design sensitivity analysis and optimization of nonlinear structuralresponse using incremental procedure this paper describes procedures for design sensitivity analysis of nonlinear structural response using the incremental solution scheme the total and updated lagrangian approaches are discussed sensitivity analyses for the stress strain and displacement constraints are developed in the optimization process the buckling load constraint is also imposed numerical aspects of design sensitivity analysis are discussed three numerical examples are solved to illustrate the design sensitivity analysis and optimization process the numerical procedures are stable and work well they can be applied to more complex structures to optimize them

sensitivity analysis of bifurcation load of finite dimensional symmetric systems three methods are presented for sensitivity analysis of bifurcation load factor of finite dimensional conservative symmetric systems subjected to a set of symmetric proportional loads in the first method a conventional method with diagonalization is utilized to derive an explicit formula of sensitivity coefficients corresponding to a minor imperfection next a new concept is introduced to find the sensitivity coefficients of the load factor displacements and the eigenmodes under fixed lowest eigenvalue of the tangent stiffness matrix based on this concept a method is presented for finding approximate sensitivity coefficients of the buckling load factor finally a direct method is presented to find the accurate sensitivity coefficients of the bifurcation load factor displacements at buckling and the buckling mode of a symmetric system note that different formula should be used for sensitivity analysis of a limit point load factor in the examples the proposed three methods are compared in view of accuracy of the results and simplicity in coding

how to correct susceptibility distortions in spin echo echo planar images application to diffusion tensor imaging diffusion tensor imaging is often performed by acquiring a series of diffusion weighted spin echo echo planar images with different direction diffusion gradients a problem of echo planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility this results in distorted diffusion tensor maps to resolve this we suggest acquiring two images for each diffusion gradient one with bottom up and one with top down traversal of k space in the phase encode direction this achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas the resulting dt maps exhibit considerably higher geometric fidelity as assessed by comparison to an image volume acquired using a conventional 3d mr technique

bifurcation hierarchy of symmetric structures abstract a group theoretic method for the analysis of bifurcation behavior of regular polygonal symmetric structures is described possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups which express the symmetry in particular we offer a complete description of those double bifurcation points which occur due to group symmetry the type the number and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations the existence of a potential function plays a substantial role for the existence of bifurcation paths as a result of these all possible bifurcation process can be known a priori as a natural consequence of bifurcation hierarchy before actual numerical analysis an implementation of this method in numerical analysis shows its validity and usability

nonlinear analysis of optimized structure with constraints on systemstability an optimization algorithm based on an optimality criterion was used to design a minimum weight space truss with different constraint requirements on system stability the constraints were specified so that the eigenvalues associated with all the critical buckling modes are either equal or separated by a specified factor for the second case the critical buckling mode was preselected from all the possible critical modes the designs obtained for the various constraint conditions were analyzed with and without specified geometric imperfections using a nonlinear finite element program which accounts for geometric nonlinearity the results obtained for various designs were compared for their imperfection sensitivity

direct evaluation of the worst imperfection shape in shell buckling abstract for the evaluation of the imperfection sensitivity of elastic and elastic plastic shells a fully nonlinear finite element method has been developed that directly gives the worst imperfection shape connected to the ultimate limit load the approach uses no approximations such as asymptotical theories or computations in the deep postcritical range the key point of the method is the description of imperfections as nodal degrees of freedom at the element level these unknown quantities are implemented by isoparametric shape functions in a finite shell element including finite rotations and thickness stretch the ultimate buckling load and the corresponding worst imperfection shape is defined by two different criteria and numerically determined by an extended system of nonlinear equations in the computation of the structurally stable collapse the deflections the imperfection shape the eigenvector and the lowest possible load level are obtained the method is illustrated by several numerical examples

efficient handling of stability problems in shell optimization by asymmetric worst case shape imperfection the paper presents an approach to shape optimization of proportionally loaded elastic shell structures under stability constraints to reduce the stability related problems a special technique is utilized by which the response analysis is always terminated before the first critical point is reached in this way the optimization is always related to a precritical structural state the necessary load carrying capability of the optimal structure is assured by extending the usual formulation of the optimization problem by a constraint on an estimated critical load factor since limit points are easier to handle the possible presence of bifurcation points is avoided by introducing imperfection parameters they are related to an asymmetric shape perturbation of the structure during the optimization the imperfection parameters are updated to get automatically the worst case pattern and amplitude of the imperfection both the imperfection parameters and the design variables are related to the structural shape via the design element technique a gradient based optimizer is employed to solve the optimization problem three examples illustrate the proposed approach copyright 2007 john wiley sons ltd

design sensitivity analysis of non linear structures in regular and critical states abstract a general design sensitivity formulation is introduced for non linear elastic structures reaching critical equilibrium states a discretized formulation is considered first and the sensitivity analysis is discussed for regular and critical states including analysis of post critical behavior next a variational approach is presented for beam and surface structures for which generalized stress and strain operator formulation is applied the formulae for sensitivity of bifurcation loads are derived in terms of adjoint fields which are shown to be equivalent to post buckling fields in the case of symmetric bifurcation

sensitivity analysis and optimization corresponding to a degenerate critical point sensitivity coefficients of a critical load factor corresponding to a degenerate critical point is shown to be unbounded even for a minor imperfection excluding very restricted case where the imperfection does not have direct effect on the lowest eigenvalue of the stability matrix this fact leads to serious difficulty in obtaining optimum design under nonlinear stability constraints the optimum design problem is alternatively formulated with constraint on the lowest eigenvalue of the stability matrix and the sensitivity formula for the lowest eigenvalue is presented the existence of a degenerate critical point and accuracy of the sensitivity coefficient are discussed through the example of a four bar truss

structural design optimization of nonlinear symmetric structures using the group theoretic approach among multidisciplinary analysis and optimization problems structural optimization of geometrically nonlinear stability problems is of great importance especially in structures used in space applications because of their long and slender configurations in this study application of the group theoretic approach gta in structural optimization of geometrical nonlinear problems under system stability constraint has been investigated according to gta the number of displacement degrees of freedom in the initial configuration can be reduced significantly by using the set of symmetry transformations of the undeformed structure to construct a projection matrix from full space to a reduced subspace spanned by the symmetry modes a structural optimization algorithm is developed for shallow structures undergoing large deflections subject to system stability constraint the method combines the nonlinear buckling analysis based on the displacement control technique using gta with the optimality criteria approach based on the potential energy of the system a shallow dome truss structure has been designed to illustrate the proposed methodology this paper demonstrates that structural optimization of nonlinear symmetric structures using gta is computationally efficient and excellent agreement exists between optimal results in full space and those in the reduced subspace also it is shown that structural design based on the generalized eigenvalue problem linear buckling highly underestimates the optimum mass which may lead to structural failure