on improved predictions for structural equilibrium path evaluations the paper describes how several procedures for higher order predictions have been introduced in order to improve the convergence speed in a general finite element program for non linear structural

tracing the equilibrium path beyond compound critical points a unified presentation of some popular continuation procedures used in the non linear finite element analysis of structural mechanics is introduced an extension of the elliptical constraint equation proposed by crisfield is given it is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur for bifurcation points a modification of rheinboldt s branching procedure is presented post critical response after limit and bifurcation points is determined in some numerical examples

variational bounds on energy dissipation in incompressible flows ii channel flow a variational principle for lower bounds on the time averaged mass flux for newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible navier stokes equations when supplied with appropriate test background flow fields the variational formulation produces explicit estimates for the friction coefficient these rigorous bounds are compared with the predictions of conventional turbulence theory

on finite strain micromorphic elastoplasticity abstract in the micromorphic continuum theory of eringen it was proposed that microstructure of materials could be represented in a continuum framework using a micro deformation tensor governing micro element deformation in addition to the deformation gradient governing macro element deformation the paper formulates finite strain micromorphic elastoplasticity based on micromorphic continuum mechanics in the sense of eringen multiplicative decomposition into elastic and plastic parts of the deformation gradient and micro deformation are assumed and the clausius duhem inequality is formulated in the intermediate configuration b to analyze what stresses elastic deformation measures and plastic deformation rates are used defined in the constitutive equations the resulting forms of plastic and internal state variable evolution equations can be viewed as phenomenological at their various scales i e micro continuum and macro continuum the phenomenology of inelastic mechanical material response at the various scales can be different but for demonstration purposes j2 flow plasticity is assumed for each of three levels of plastic evolution equations identified with different stress internal state variables and material parameters all evolution equations and a semi implicit time integration scheme are formulated in the intermediate configuration for future coupled lagrangian finite element implementation a simpler two dimensional model for anti plane shear kinematics is formulated to demonstrate more clearly how such model equations simplify for future finite element implementation

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

upper bounds on the heat transport in a porous layer abstract numerical and asymptotic analytical upper bounds on the convective heat transport in a fluid saturated porous layer of infinite darcy prandtl number are obtained by the howard busse variational method of the optimum theory of turbulence the nonlinear euler lagrange equations of the variational problem possess different numerical solutions as well as different approximate analytical solutions in the region of high rayleigh numbers we use symmetric fields for the numerical investigation and obtain slightly different numerical bounds on the heat transport in comparison to the numerical bounds obtained by gupta and joseph j fluid mech 57 1973 491 514 as well as different numerical values of the wave numbers connected to the optimum fields for the analytical investigation we use new approximate solution of the euler lagrange equations for the intermediate layers of the optimum fields this solution leads to different thickness of the boundary layers of the optimum fields as well as to a lower analytical upper bounds on the heat transport in comparison to the boundary layer thicknesses and analytical upper bounds obtained by gupta and joseph

some computational aspects of the stability analysis of nonlinear structures abstract the perturbation method and the continuation method are the two most popular techniques for the solution of finite element equations that describe instability phenomena this paper presents a summary of the principles involved and describes some trends in the development of these techniques

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

a morphological affine and galilean invariant scale space for movies we study a model of multiscale analysis or scale space applied to movies this model comes from a thorough formalization that has been done in the theory of scale space of static image this formulation has led one to associate with each multiscale analysis a partial differential equation pde we examine the case of movies and insist on the motion aspects more precisely it has been proved by alvarez guichard lions and morel 1993 that there exists a unique affine and morphological and galilean invariant scale space for movies the amg model this model is described by a partial differential equation we focus on terms appearing in that equation we show that this model provides a reliable definition of an optical multiscale acceleration at the practical level scale is interpreted as a way of characterizing reliable trajectories as we prove by experiments the amg model is a riddle for decimating spurious trajectories due to any kinds of nonadditive impurities and noise simple discrete formulae are given to implement the model

multilevel approach for brick masonry walls part i a numerical strategy for the nonlinear analysis a numerical strategy based on a multilevel approach is presented for the nonlinear analysis of brick masonry walls as in plane prototypes of large masonry structures the strategy is based on an iterative scheme which uses two different local and global modelings of the masonry mechanics contemporarily the former is the reference mechanical model and is defined at the fine scale of the bricks and mortar joints and describes their nonlinear mechanical interaction including damage evolution and friction toughness phenomena the latter is a linearized finite element approximation of the previous model defined at the rough scale of the wall and used to accelerate the iteration the proposed iterative scheme proves to be efficient and robust in both linear and nonlinear contexts

an efficient mixed variational reduced order model formulation for nonlinear analyses of elastic shells summary the koiter newton method had recently demonstrated a superior performance for non linear analyses of structures compared to traditional path following strategies the method follows a predictor corrector scheme to trace the entire equilibrium path during a predictor step a reduced order model is constructed based on koiter s asymptotic post buckling theory which is followed by a newton iteration in the corrector phase to regain the equilibrium of forces in this manuscript we introduce a robust mixed solid shell formulation to further enhance the efficiency of stability analyses in various aspects we show that a hellinger reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy we demonstrate that extremely large step sizes with a reasonable out of balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path more importantly the numerical effort of the corrector phase involving a newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation we study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems this article is protected by copyright all rights reserved

multilevel approach for brick masonry walls part ii on the use of equivalent continua abstract this work investigates the possibility of using equivalent continua within a multilevel strategy for the analysis of brick masonry walls as prototypes for the in plane behavior of masonry buildings this strategy proposed and discussed in detail in part i of the same paper lies in an iterative solution scheme which uses two levels local and global of description the former accounts for the interaction between the single bricks the latter modeled as a coarse finite element discretization accounts for global interactions within the same finite element format and strategy the paper compares the performances of schemes implementing the identification procedures based on equivalent continua with those implementing the algebraic re parametrization of the local model proposed in part i the former while suitable for a synthetic representation of masonry behavior does not prove to be convenient for a multilevel solution strategy

a numerical analysis of infinitesimal mechanisms the paper presents a numerical algorithm based on koiter s theory of the elastic stability for detecting the order of infinitesimal mechanisms i e kinematically indeterminate systems of pin jointed bars in cases of one degree of indeterminacy the algorithm improves in terms of computational simplicity and efficiency an analogous algorithm proposed by salerno in 1992 this is shown to be due to the vanishing of the terms higher than the third order of the asymptotic expressions of the energy owing to the use of the green strain measure and a mixed displacement and stress formulation of the problem moreover the proposed algorithm is able to provide a correct definition of mechanism in cases of several degrees of indeterminacy mainly for structures like those first studied by connelly and servatius in 1994 which the paper will treat in depth

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

a high performance element for the analysis of 2d elastoplastic continua abstract the paper presents a four node element for the analysis of 2d continua described by elastic perfectly plastic von mises laws its formulation is based on the assumed stress approach which has been widely tested in the elastic field the elastoplastic formulation of the element is obtained by enriching its variational basis with the weak enforcement of the plastic loading unloading conditions in this way the elastoplastic problem is formulated with respect to the stress parameters of the element consistently with the weak statement of the compatibility condition

a nonlinear beam finite element for the post buckling analysis of plane frames by koiter s perturbation approach abstract a nonlinear finite element of plane beam oriented to koiter s perturbation analysis of frames is presented the locking problem arising in the calculation of the post critical curvature is thoroughly examined and solved at the continuum level by means of a suitable definition of the kinematic settings the proposed strain measures are lagrangian and rationally founded geometrically exact the exact solutions of the critical problem have been chosen as shape functions of the finite element so obtaining an immediately convergent finite element in the calculation of the critical load and of the post critical slope

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a mixed solution strategy for the nonlinear analysis of brick masonry walls the paper presents a discrete mechanical model for masonry walls based on a lagrangean description where each brick is described as a rigid body and each mortar joint as an interface element constitutive assumptions characterized by elasticity damage and friction are associated to the joints only a numerical solution strategy based on a mixed path following approach in terms of stresses strains displacements damage and load parameters is proposed for avoiding convergence problems related to the joint softening behaviour some numerical results are also presented showing the robustness and effectiveness of this proposal

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

convective heat transport in a rotating fluid layer of infinite prandtl number optimum fields and upper bounds on nusselt number by means of the howard busse method of the optimum theory of turbulence we investigate numerically upper bounds on convective heat transport for the case of infinite fluid layer with stress free vertical boundaries rotating about a vertical axis we discuss the case of infinite prandtl number 1 ensuremath ensuremath alpha solution of the obtained variational problem and optimum fields possessing internal intermediate and boundary layers we investigate regions of rayleigh and taylor numbers r and ta where no analytical bounds can be derived and compare the analytical and numerical bounds for these regions of r and ta where such comparison is possible the increasing rotation has a different influence on the rescaled optimum fields of velocity w 1 temperature ensuremath theta 1 and the vertical component of the vorticity f 1 the increasing ta for fixed r leads to vanishing of the boundary layers of w 1 and ensuremath theta 1 opposite to this the increasing ta leads first to a formation of boundary layers of the field f 1 but further increasing the rotation causes vanishing of these boundary layers we obtain optimum profiles of the horizontal averaged total temperature field which could be used as hints for construction of the background fields when applying doering constantin method to the problems of rotating convection the wave number ensuremath alpha 1 corresponding to the optimum fields follows the asymptotic relationship ensuremath alpha 1 r 5 1 4 for intermediate rayleigh numbers however when r becomes large with respect to ta after a transition region the power law for ensuremath alpha 1 becomes close to the power law for the case without rotation the nusselt number nu is close to the nonrotational bound 0 32r 1 3 for the case of large r and small ta nu decreases with increasing taylor number thus the upper bounds reflect the tendency of inhibiting thermal convection by increasing rotation for a fixed rayleigh number for the regions of rayleigh and taylor numbers where the numerical and asymptotic bounds on nu can be compared the numerical bounds are about 70 lower than the asymptotic bounds

on steplength algorithms for a class of continuation methods the continuation methods considered here are algorithms for the computational analysis of the regular parts of the solution field of equations of the form fx b f d subset r n 1 to r n for given b in r n while these methods are similar in structure to those used for ode solvers their errors are independent of the history of the process and are solely determined by the termination criterion of the corrector at the current step this suggests the use of a posteriors estimates of the convergence radii of the corrector it is proved here that such estimates cannot be obtained from the sequence of corrector iterates alone but that they require some global information about f however it is shown that a finite sequence of corrector iterates does allow for the computation of effective estimates of the convergence quality of certain types of correctors this is used for the design of various step algorithms for continuation processes two of them are based on a newton corrector while the third o

an isostatic assumed stress triangular element for the reissner mindlin plate bending problem the paper describes a new assumed stress triangular element for reissner mindlin plates called tip3 with three nodes and three degrees of freedom per node the kinematics is constructed by means of the so called linked interpolation ruled by technically significant degrees of freedom i e one transversal displacement and two rotations per node without using additional bubble modes the static representation starts from a moment shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number the resulting element is locking free presents correct rank and passes the bending patch test even for very thin plates the good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature copyright 2007 john wiley sons ltd

finite element asymptotic analysis of slender elastic structures a simple approach an asymptotic method directly derived from koiter s theory and suitable for the solution of elastic buckling problems and its natural adaptation to a numerical solution by means of a finite element technique are presented here the order of the extrapolation of the equilibrium equations has been intentionally kept very low because attention has been entirely devoted to all those features theoretical definitions eigenproblem numerical techniques suitable fem implementation which make such an approach competitive with respect to the classic step by step methods for plane frames and 3d pin jointed trusses the performances of the algorithm numerical accuracy and computational cost are compared with those of riks are length method

a study of incremental iterative strategies for non linear analyses the paper describes a study of incremental iterative solution techniques for geometrically non linear analyses the solution methods documented are based on a modified newton raphson approach meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations a consistent mathematical notation is employed in the description of the iterative and load incrementation strategies enabling the simple inclusion of several solution options in a computer program the iterative strategies investigated are iteration at constant load iteration at constant displacement iteration at constant arc length iteration at constant external work iteration at minimum unbalanced displacement norm iteration at minimum unbalanced force norm and iteration at constant weighted response the load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step strategies based on the current stiffness parameter and a strategy based on a parabolic approximation to the load deflection response criteria for detecting when the applied external load increment should reverse sign are described a challenging example of a circular arch exhibiting snap through load limit point behaviour and snap back displacement limit point behaviour is solved using several different iterative and load incrementation strategies the performance of the solution schemes is evaluated and conclusions are drawn

an arc length method including line searches and accelerations this paper describes a method for introducing line searches into the arc length solution procedure such line searches may be used at each iteration to calculate an optimum scalar step length which scales the normal iterative vector in practice a loose tolerance is provided so that on many iterations the line searches are avoided however on difficult iterations the line searches are shown to lead to a substantial improvement in the convergence characteristics a simple single parameter acceleration is also developed using line search concepts the new arc length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs significant improvements are demonstrated in relation to the standard arc length method

koiter s analysis of thin walled structures by a finite element approach summary this paper refers to the analysis of the postbuckling behaviour of thin walled structures by means of an asymptotic approach based on a finite element implementation of koiter s non linear theory of instability the analysis has been accomplished by using the following assumptions i the structure is described as an assemblage of flat slender rectangular panels ii a non linear kirchhoff type plate theory is used to model each panel iii hc finite elements discretization is used iv linear and quadratic extrapolations are assumed for the fundamental and the postbuckling paths respectively v multimodal buckling is considered and vi imperfection sensitivity analysis is performed in both multimodal and monomodal form based on the steepest descent path criterion several numerical results are presented and discussed comparisons with numerical solution obtained by standard incremental codes are given which show the accuracy and reliability of the proposed approach

on the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction gradient based approaches to the computation of optical flow often use a minimization technique incorporating a smoothness constraint on the optical flow field the author derives the most general form of such a smoothness constraint that is quadratic in first derivatives of the grey level image intensity function based on three simple assumptions about the smoothness constraint 1 it must be expressed in a form that is independent of the choice of cartesian coordinate system in the image 2 it must be positive definite and 3 it must not couple different component of the optical flow it is shown that there are essentially only four such constraints any smoothness constraint satisfying 1 2 or 3 must be a linear combination of these four possibly multiplied by certain quantities invariant under a change in the cartesian coordinate system beginning with the three assumptions mentioned above the author mathematically demonstrates that all best known smoothness constraints appearing in the literature are special cases of this general form and in particular that the weight matrix introduced by h h nagel is essentially modulo invariant quantities the only physically plausible such constraint

improved iteration strategy for nonlinear structures a solution strategy for the analysis of nonlinear structures is described the strategy is a simple extension of existing newton type procedures and can easily be incorporated into existing computer programs earlier work which contributed to the development of the strategy is reviewed and the theory of the procedure is presented six examples covering several different types of structural behaviour are described these examples suggest that the strategy is remarkably stable and efficient

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

mixed formulation in koiter analysis of thin walled beams abstract the paper extends the asymptotic mixed formulation proposed in g garcea g salerno sanitizing of locking in koiter perturbation analysis through mixed formulation fourth world congress on computational mechanics buenos aires argentina 1988 g garcea g salerno r casciaro comput methods appl mech engrg 180 1 2 1999 137 167 to structures composed of an assemblage of flat slender elastic panels the same type of structure has already been investigated in a d lanzo g garcea r casciaro int j numer methods engrg 38 1995 2325 2345 a d lanzo g garcea int j numer methods engrg 39 1996 3007 3031 with a compatible formulation and using the usual hypothesis of negligible precritical rotations in order to avoid the extrapolation locking see also g garcea g a trunfio r casciaro comput methods appl mech engrg 165 1 4 1998 137 167 produced by the high axial to flexural stiffness ratio of the panels the use of a mixed formulation provides a consistent way of eliminating the extrapolation locking without introducing ad hoc approximations it is thus both reliable and accurate when combined with a quadratic strain displacement relationship as presented here it gives zero fourth order energy variations further computational simplifications and a natural linearization of the eigenvalue problem required by the buckling analysis an extensive numerical testing shows the effectiveness and robustness of the proposed approach

variational bounds in dissipative systems abstract we present a general method for estimating the space time average dissipation in a large class of dissipative pdes the method leads to variational problems with spectral side conditions

asymptotic post buckling analysis of rectangular plates by hc finite elements the present paper extends the finite element perturbation approach already presented for pin jointed and framed structures15 to rectangular thin plates koiter s asymptotic strategy2 is coupled with a high continuity finite element discretization of the plate 22 the consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported it appears that use of the hc elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour it also allows the use of very fine discretization meshes at low computational cost

element behavior in post critical plane frame analysis depending on the type of uni modal cuspoid catastrophe which governs the local behavior of a structure at a simple critical point correct prediction of the post critical path requires an accurat

variational bounds on energy dissipation in incompressible flows iii convection building on a method of analysis for the navier stokes equations introduced by hopf math ann 117 764 1941 a variational principle for upper bounds on the largest possible time averaged convective heat flux is derived from the boussinesq equations of motion when supplied with appropriate test background fields satisfying a spectral constraint reminiscent of an energy stability condition the variational formulation produces rigorous upper bounds on the nusselt number nu as a function of the rayleigh number ra for the case of vertical heat convection between parallel plates in the absence of sidewalls a simplified but rigorous formulation of the optimization problem yields the large rayleigh number bound nu ensuremath le 0 167 mathrm ra 1 2 1 nonlinear euler lagrange equations for the optimal background fields are also derived which allow us to make contact with the upper bound theory of howard j fluid mech 17 405 1963 for statistically stationary flows the structure of solutions of the euler lagrange equations are elucidated from the geometry of the variational constraints which sheds light on busse s j fluid mech 37 457 1969 asymptotic analysis of general solutions to howard s euler lagrange equations the results of our analysis are discussed in the context of theory recent experiments and direct numerical simulations textcopyright 1996 the american physical society

mode jumping and attractive paths in multimode elastic buckling this paper summarizes a part of the first author s ph d thesis completely devoted to multimode elastic buckling within an fem strategy the theoretical arguments unfold among critical points on radial paths the unique post critical paths variationally defined algebraic characterizations proposition demonstrations and so on by aiming to prove that the complexity of the phenomenon of multimode buckling secondary bifurcations post critical attractive paths can be theoretically explained 1997 by john wiley sons ltd

on nonlinear beam models from the point of view of computational post buckling analysis abstract the buckling and post buckling analysis of elastic planar frames is considered and the use of geometrically exact beam models is thereby advocated it is shown that usual technical beam models fail to predict correctly the curvature of the post buckling curve at bifurcation even for standard problems of elastic stability theory it is also argued that versatile and efficient computational procedures for bifurcation analysis of general planar frames are to be based on unconstrained beam models some remarks on finite element representation of nonlinear beam models are passed in conclusion

application of the method of simplest equation for obtaining exact traveling wave solutions for the extended korteweg de vries equation and generalized camassa holm equation a version of the method of the simplest equation called modified method of simplest equation is applied to the extended korteweg de vries equation and to generalized camassa holm equation exact traveling wave solutions of these two nonlinear partial differential equations are obtained the equations of bernoulli riccati and the extended tanh equation are used as simplest equations some of the obtained solutions correspond to surface water waves

how to improve efficiency and robustness of the newton method in geometrically non linear structural problem discretized via displacement based finite elements abstract in this paper we show how to significantly improve the robustness and the efficiency of the newton method in geometrically non linear structural problems discretized via displacement based finite elements the strategy is based on the relaxation of the constitutive equations at each integration point this leads to an improved iterative scheme which requires a very low number of iterations to converge and can withstand very large steps in step by step analyses the computational cost of each iteration is the same as the original newton method the impressive performances of the proposal are shown by many numerical tests in geometrically non linear analysis the proposed strategy called mip newton seems worthy to replace the standard newton method in any finite element code based on displacement formulations its implementation in existing codes is very easy

orthogonal trajectory accession to the nonlinear equilibrium curve abstract an alternative to the riks wempner crisfield iterative correction scheme is presented that does not require an explicit displacement load accession path to the nonlinear equilibrium curve nor a known equilibrium point its symmetry with respect to the displacement and load assures success in rounding limit points as well as turning points

on linear constraints for newton raphson corrections and critical point searches in structural f e problems the paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non linear mechanical finite element f e problems an alternative to the normal two phase solution method is discussed this method is used to represent different iteration constraints and in conjunction with the search for critical solution points numerical tests are presented evaluating the efficiency of different iteration constraints for a model problem practically useful criteria for critical points are discussed the basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems

continuum modeling of periodic brickwork continuum models of periodic masonry brickwork viewed at a micro level as a discrete system are identified within the frame of linearized elasticity the accuracy of various identification schemes is investigated for standard and micropolar continua which are directly compared with the help of some numerical benchmarks for different loading conditions that induce periodic and non periodic deformation states it is shown that periodic deformation states of brickwork are exactly reproduced by both continua provided that a suitable identification scheme is adopted for non periodic states micropolar continuum is shown to better reproduce the discrete solutions due to its capability to take scale effects into account both continua are asymptotically equivalent as the characteristic length of the discrete system tends to zero while providing an upper and a lower bound of the discrete solution