a simplified finite element method for large deformation post buckling analyses of large frame structures using explicitly derived tangent stiffness matrices in this paper a simplified economical and highly accurate method for large deformation post buckling analyses of frame type structures is presented using the concepts of polar decomposition of deformation an explicit expression for the tangent stiffness matrix of a member element of the frame that accounts for the nonlinear bending stretching coupling is derived in closed form at any point in the load deformation path the ranges of validity of the present simplified approach are discussed several example problems to demonstrate the feasibility of the present approach over ranges of deformation that are well beyond those likely to occur in practical large frame structures are included

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

a robust riks like path following method for strain actuated snap through phenomena in soft solids abstract in this paper a practical and robust riks like path following method is developed to automatically trace the nonlinear equilibrium path for initial finite strain induced snap through phenomena in soft solids the deformation gradient is decomposed into an elastic part and an initial strain part where the initial strain is characterized through a prescribed pattern tensor and an unknown strain factor describing the magnitude in the non linear finite element fe solution scheme an equivalent body force proportional to the increment of the strain factor is derived which varies in each iteration step due to its dependence on deformed configuration and stress both the displacement and the strain factor increments are introduced as unknowns in the linearized equation which permits to predict the critical equilibrium states before and after the snap through several examples with various configurations and strain histories are constructed including multilayer beams and film substrate systems which demonstrate the effectiveness and robustness of the algorithm to capture the strain induced snap through phenomena

work increment control method for non linear analysis to perform non linear structural analysis including large displacements and rotations requires evaluation of the non linear equilibrium equations a quadratically converging fixed point iteration scheme referred to as the work increment control solution method is presented to iteratively evaluate the non linear algebraic equations the work increment control method is superior in many respects to other published solution strategies

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

a space time finite element method for the wave equation a numerical method is introduced which uses finite elements in time and space simultaneously to solve the wave equation an error analysis for this scheme is presented and the results of several computations this scheme is accurate for time slabs of arbitrary thickness without introducing extra least squares or stabilization terms

a unified set of single step algorithms part 2 theory part 1 of this paper1 presents a very general single step algorithm sspj for the numerical integration of first and second order time dependent differential equations in part 2 we present and discuss results of the accuracy and stability analysis for ss11 ss21 ss31 ss22 and ss32 there is also a detailed comparison of ss22 and the newmark algorithm

analysis of first order errors in shock calculations in two space dimensions numerical computations show that solutions of hyperbolic conservation laws obtained by second or higher order shock capturing methods in many cases are only first order accurate downstream of shocks see e g m h carpenter and j h casper aiaa j 37 1999 pp 1072 1079 we use matched asymptotic expansions to analyze the degeneration in order of accuracy for stationary solutions of hyperbolic conservation laws in two space dimensions

the inverse mean curvature flow in warped cylinders of non positive radial curvature abstract we consider the inverse mean curvature flow in smooth riemannian manifolds of the form r 0 s n g with metric g d r 2 2 r and non positive radial sectional curvature we prove that for initial mean convex graphs over s n the flow exists for all times and remains a graph over s n under weak further assumptions on the ambient manifold we prove optimal decay of the gradient and that the flow leaves become umbilic exponentially fast we prove optimal c 2 estimates in case that the ambient pinching improves

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

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

a hybrid method for efficient solution of geometrically nonlinear structures abstract we propose a novel hybrid method for calculating accurate responses of geometrically nonlinear structures exhibiting complex snap through and snap back behaviours the proposed method employs a hybrid evolutionary algebraic method to obtain each point of the equilibrium path where the equilibrium is formulated generally as a minimisation problem genetic algorithm and nelder mead simplex methods are used together as the hybrid optimiser to obtain any arbitrary point of the equilibrium path we only need a series of sparse matrix to vector multiplications and do not require information about previous equilibrium states the assembly of tangent stiffness matrix the solution of a set of system of linear equations or factorisation processes both primary and secondary paths can be followed in addition utilising the tangent stiffness matrix this method can effectively find both the limit and bifurcation points directly the state of non proportional loading can also be considered successfully additionally we show how to generate the solution of a structure whose geometrical and mechanical properties vary slightly starting from the original solution finally to demonstrate the efficiency and capabilities of the present approach three examples that are well known for their complex snap through snap back load deflection curves are comprehensively studied and the results obtained are compared with those reported in the literature

an orthogonal residual procedure for non linear finite element equations a general and robust solution procedure for non linear finite element equations with limit points is developed at each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state the method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector the orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters passage of load and displacement limit points is discussed as well as the relation to line search minimum residual and arc length methods the method is illustrated by two examples

stability boundaries of two parameter non linear elastic structures abstract the load bearing capacity of structures can be influenced by variations in parameters such as initial geometric defects multi parameter loadings material specifications and temperature this paper aims to introduce a new formulation to trace the stability boundaries of two parameter elastic structures the proposed procedure can find a set of critical points both limit and bifurcation ones via a modified newton s method in the authors formulation the residual force is set to zero and a critically constraint is satisfied simultaneously numerical examples presented in this paper demonstrate the efficiency of the suggested method

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

inverse curvature flows in riemannian warped products abstract the long time existence and umbilicity estimates for compact graphical solutions to expanding curvature flows are deduced in riemannian warped products of a real interval with a compact fibre notably we do not assume the ambient manifold to be rotationally symmetric nor the radial curvature to converge nor a lower bound on the ambient sectional curvature the inverse speeds are given by powers 0 p 1 of a curvature function satisfying few common properties

stability of long transversely isotropic elastic cylindrical shells under bending abstract the present paper investigates buckling of cylindrical shells of transversely isotropic elastic material subjected to bending considering the nonlinear prebuckling ovalized configuration a large strain hypoelastic model is developed to simulate the anisotropic material behavior the model is incorporated in a finite element formulation that uses a special purpose tube element for comparison purposes a hyperelastic model is also employed using an eigenvalue analysis bifurcation on the prebuckling ovalization path to a uniform wrinkling state is detected subsequently the postbuckling equilibrium path is traced through a continuation arc length algorithm the effects of anisotropy on the bifurcation moment the corresponding curvature and the critical wavelength are examined for a wide range of radius to thickness ratio values the calculated values of bifurcation moment and curvature are also compared with analytical predictions based on a heuristic argument finally numerical results for the imperfection sensitivity of bent cylinders are obtained which show good comparison with previously reported asymptotic expressions

the l 1 global decay to discrete shocks for scalar monotone schemes given a family of discrete shocks of a monotone scheme we prove that the discrete shock profile with rational shock speed is asymptotically stable with respect to the l1 topology 1 if u0 l1 then un n 1 0 as n under no restriction conditions of the initial data to the interval inf sup the asymptotic wave profile is uniquely identified from the above family by a mass parameter

finite elements in space and time for the analysis of generalised visco elastic materials numerical analysis of linear visco elastic materials requires robust and stable methods to integrate partial differential equations in both space and time in this paper symmetric space time finite element operators are derived for the first time for elementary linear elastic spring and linear viscous dashpot these can thereafter be assembled in parallel and in series to simulate an arbitrarily complex linear visco elastic behaviour the flexibility of the proposed method allows the formulation of the behaviour which closely reflects physical processes an efficient algorithm is proposed to use the generated elementary matrices in a way that is comparable with finite difference schemes in terms of both processor and memory costs this unconditionally stable and convergent procedure is equally valid for space domains in which geometry or material properties evolve with time copyright c 2013 john wiley sons ltd

post buckling analysis of shallow shells by the field boundary element method the non linear field boundary element technique is applied to the analysis of snap through phenomena in thin shallow shells the equilibrium path is traced by using the arc length method and the solution strategy is discussed in detail the results show that as compared to the approaches based on the popular symmetric variational galerkin finite element formulation the current approach based on an unsymmetric variational petrov galerkin field boundary element formulation gives a faster convergence while using fewer degrees of freedom the illustrative numerical examples deal with post buckling responses of several shallow shells with different geometries

structural stability of multi folding structures with contact problem this paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability of a folding multi layered truss both analyses are based on bifurcation theory and include geometrical nonlinearity the dynamic analysis includes an allowance for contact between nodes comparisons are made between published experimental folding patterns and the patterns obtained from both numerical methods in which bifurcations are demonstrated as elastic unstable snap through behaviour several folding patterns are identified during the elastic instability where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading the authors suggest that the understanding of the behaviour will be very useful for the development of light weight structures subject to dynamic loading based on the bifurcation static analysis and dynamic analysis using both the displacement control method and the load control method

extended voronoi cell finite element model for multiple cohesive crack propagation in brittle materials this paper introduces an extended voronoi cell finite element model x vcfem for modelling cohesive crack propagation in brittle materials with multiple cracks the cracks are modelled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip extension to vcfem is achieved through enhancements in stress functions in the assumed stress hybrid formulation in addition to polynomial terms the stress functions include branch functions in conjunction with level set methods and multi resolution wavelet functions in the vicinity of crack tips the wavelet basis functions are adaptively enriched to accurately capture crack tip stress concentrations conditions and methods of stability are enforced in x vcfem for improved convergence with propagating cracks two classes of problems are solved and compared with existing solutions in the literature for validation of the x vcfem algorithms the first set corresponds to results for static cracks while in the latter set the propagation of cohesive cracks are considered comparison of x vcfem simulation results with results in literature for several fracture mechanics problems validates the effectiveness of x vcfem copyright 2005 john wiley sons ltd

a multiscale finite element method with embedded strong discontinuity model for the simulation of cohesive cracks in solids abstract a multiscale finite element method with the embedded strong discontinuity model is proposed to simulate the cohesive cracks in solids in the proposed method the kinematic descriptions of the strong discontinuity and space discretization are considered based on the fine scale with the strong discontinuity approach then in order to correctly and conveniently deliver the discontinuous information between the coarse scale and fine scale an enhanced coarse element strategy is proposed to construct the multiscale base functions that can well capture the discontinuous characteristics and preserve an adequate accuracy for the unit cells exhibiting a strong discontinuity the main idea is that the coarse nodes of the enhanced coarse element can be dynamically added according to the identification of the intersection between the crack path and the boundaries of the unit cell during the computational procedure the strategy overcomes the deficiency that the traditional coarse elements in the multiscale finite element method cannot well characterize the displacement jump property on the boundary of the unit cell moreover to accurately obtain the microscopic displacement the displacement decomposition technique is adopted to modify the downscale computations by adding the perturbation solutions numerical examples of normal tension and bending tests are presented to validate the proposed method by comparing the results with the analytical or fine finite element solutions finally the three point bending and four point bending benchmarks are performed to further demonstrate the effectiveness and high efficiency of the method

supersonic flow onto a solid wedge we consider the problem of two dimensional supersonicflow onto a solid wedge or equivalently in a concave corner formed by two solid walls for mild corners there are two possible steady state solutions one with a strong and one with a weak shock emanating from the corner the weak shock is observed in supersonic flights a longstanding natural conjecture is that the strong shock is unstable in some sense we resolve this issue by showing that a sharp wedge will eventually produce weak shocks at the tip when accelerated to a supersonic speed more precisely we prove that for upstream state as initial data in the entire domain the timedependent solution is self similar with a weak shock at the tip of the wedge we construct analytic solutions for self similar potential flow both isothermal and isentropic with arbitrary 1 in the process of constructing the self similar solution we develop a large number of theoretical tools for these elliptic regions these tools allow us to establish large data results rather than a small perturbation we show that the wave pattern persists as long as the weak shock is supersonic supersonic when this is no longer true numerics show a physical change of behavior in addition we obtain rather detailed information about the elliptic region including analyticity as well as bounds for velocity components and shock tangents c 2007 wiley periodicals inc

an asymptotic numerical method to compute the postbuckling behaviour of elastic plates and shells in this paper we apply an asymptotic numerical method for computing the postbuckling behaviour of plate and shell structures the bifurcating branch is sought in the form of polynomial expansions and it is determined by solving numerically fem several linear problems with a single stiffness matrix a large number of terms of the series can easily be computed by using recurrent formulas in comparison with a more classical step by step procedure the method is rapid and automatic however the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point in the present form the method should be viewed as a cheap and automatic way of completing a linear buckling analysis it is illustrated in two examples a square plate under in plane compression and a cylindrical shell under pressure

finite element modelling of spatially chaotic structures a simple non linear mechanical system comprising a pin jointed string of finite length links supported by elastic springs at the pins and compressed by an axial load is viewed from two perspectives when seen as an initial value problem equilibrium equations provide an iterative non linear mapping when seen as a boundary value problem it becomes a simple finite element model at loads less than the critical buckling load a preferred buckling configuration is found that is localized along the length in the limit of infinite length this is described as a homoclinic connection in phase space joining the flat equilibrium state to itself the infinite sequence of homoclinic points thus defined embeds within the complex topological structure of a homoclinic tangle within which also appear periodic quasi periodic and chaotic spatial solutions implications in the finite element setting are discussed 1997 john wiley sons ltd

insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds we construct a solution to inverse mean curvature flow on an asymptotically hyperbolic 3 manifold which does not have the convergence properties needed in order to prove a penrose type inequality this contrasts sharply with the asymptotically flat case the main idea consists in combining inverse mean curvature flow with work done by shi tam regarding boundary behavior of compact manifolds assuming the penrose inequality holds we also derive a nontrivial inequality for functions on s

algorithmically imposed thermodynamic compliance for material models in mechanical simulations using the aim method thermodynamic irreversibility can be imposed on empirical material behaviour by using an appropriate algorithm which takes the path dependence of the degradation process into account this new algorithm algorithmically imposed mechanics aim for algorithmically irreversible mechanics is described and the convergence and unicity of the solutions obtained are proven aim is applicable to a range of mechanical behaviour and is demonstrated to work in conjunction with non local damage with rotating cracks as well as a mixed plastic and damage behaviour copyright c 2015 john wiley sons ltd

isoperimetric type problems and alexandrov fenchel type inequalities in the hyperbolic space abstract in this paper we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space h n by using quermassintegral preserving curvature flows as a byproduct we obtain hyperbolic alexandrov fenchel inequalities

a three dimensional finite element formulation for thermoviscoelastic orthotropic media summary this paper is concerned with the development of a numerical algorithm for the solution of the uncoupled quasistatic initial boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and or mechanical deformation the constitutive equations expressed in integral form involving the relaxation moduli are transformed into an incremental algebraic form prior to development of the nite element formulation this incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the nite element solution use is made of a dirichlet prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory three illustrative example problems are included to demonstrate the method 1997 by john wiley sons ltd

numerical null controllability of the 1d linear schrodinger equation abstract this paper deals with the numerical approximation to boundary controls that drive the solution to the 1 d linear schrodinger equation to a prescribed state at a final time using ideas from fursikov and imanuvilov we consider the control that minimizes over the class of admissible controls a functional that involves weighted integrals with weights that blow up at t we will see that this extremal problem is equivalent to a differential problem that is fourth order in space and second order in time adapting some numerical techniques applied by the first author and munch to the heat equation we approximate the variational formulation by introducing appropriate space time finite elements that are c 1 in space and c 0 in time we present two approaches the second one relies on a change of variable which leads to a lower condition number for the stiffness matrix the results of some experiments show the efficiency of these methods

solution method for nonlinear problems with multiple critical points a generalized displacement control method has been proposed for geometrically nonlinear analysis and has been proven to be bery effective by several problems with multiple limit points and snap back points this method can be implemented easily in a general purpose finite element program

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

a semi analytical approach to the non linear dynamic response problem of beams at large vibration amplitudes part ii multimode approach to the steady state forced periodic response abstract the semi analytical approach to the non linear dynamic response of beams based on multimode analysis has been presented in part i of this series of papers azrar et al 1999 journal of sound and vibration 224 183 207 1 the mathematical formulation of the problem and single mode analysis have been studied the objective of this paper is to take advantage of applying this semi analytical approach to the large amplitude forced vibrations of beams various types of excitation forces such as harmonic distributed and concentrated loads are considered the governing equation of motion is obtained and can be considered as a multi dimensional form of the duffing equation using the harmonic balance method the equation of motion is converted into non linear algebraic form techniques of solution based on iterative incremental procedures are presented the non linear frequency and the non linear modes are determined at large amplitudes of vibration the basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated the percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution also the percentage contributions of the higher modes to the bending moment near to the clamps are given in order to determine accurately the error introduced in the non linear bending stress estimated by different approximations solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency the non linear deflection shapes in various regions of the solution the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes the numerical results obtained here for the non linear forced response are compared with those from the linear theory with available non linear results based on various approaches and with the single mode analysis

a new mass for asymptotically flat manifolds abstract in this paper we introduce a mass for asymptotically flat manifolds by using the gauss bonnet curvature we first prove that the mass is well defined and is a geometric invariant if the gauss bonnet curvature is integrable and the decay order satisfies n 4 3 motivated by an elegant idea of lam 35 we then show a positive mass theorem for this new mass for asymptotically flat graphs over r n moreover we obtain various penrose type inequalities in this case in these penrose type inequalities we establish relationship between the new mass and various geometric integrals

an arc length control procedure to solve parabolic problems abstract an arc length method is applied as a time step selector for a class of stiff parabolic problems related to heat conduction and radiation the resulting system of nonlinear equations is solved by iteration not only on the temperature vector but also on the current time step the procedure is linked with an a posteriori estimate of the time integration error used as input to the arc length selection algorithm in addition a quasi newton method us used to obtain approximate factorizations of the jacobian matrix during the iterative process

an eulerian approach for large displacements of thin shells including geometrical non linearities abstract this paper is devoted to the problem of large displacement of shells the only non linearity being geometrical the geometry of the mid surface of the shell is determined thanks to the knowledge of nodes and normal vectors and is continuously updated stresses are also carried from one configuration to another which enables us to linearize the equilibrium equations it is then possible to build an eulerian formulation moreover some control strategies are proposed in order to find limit points and unstable solutions finally we check in some classical examples the accuracy of this technique

secant structural solution strategies under element constraint for incremental damage abstract two major difficulties in the nonlinear analysis of post peak structural behavior are the occurrence of an ill conditioned tangent stiffness matrix around critical points namely limit and bifurcation points and the selection of a suitable constrain on the solution path as an attempt to make failure prediction available in a routine manner new solution strategies are proposed in which a secant structural stiffness matrix is formulated for incremental damage models and the solution path is controlled through a suitable measure of failure at the most severely damaged point in the body numerical solutions are given for plane strain and plane stress problems to show that snap back and snap through associated with shear band formation can be inexpensively predicted

a minkowski inequality for hypersurfaces in the anti de sitter schwarzschild manifold we prove a sharp inequality for hypersurfaces in the n dimensional anti de sitter schwarzschild manifold for general n 3 this inequality generalizes the classical minkowski inequality for surfaces in the three dimensional euclidean space and has a natural interpretation in terms of the penrose inequality for collapsing null shells of dust the proof relies on a new monotonicity formula for inverse mean curvature flow and uses a geometric inequality established by the first author in 3 c 2015 wiley periodicals inc

a geometric inequality on hypersurface in hyperbolic space in this paper we use the inverse curvature flow to prove a sharp geometric inequality on star shaped and two convex hypersurface in hyperbolic space

tracing post limit point paths with reduced basis technique abstract a reduced basis technique and a problem adaptive computational algorithm are presented for predicting the post limit point paths of structures in the proposed approach the structure is discretized by using displacement finite element models the nodal displacement vector is expressed as a linear combination of a small number of vectors and a rayleigh ritz technique is used to approximate the finite element equations by a small system of nonlinear algebraic equations to circumvent the difficulties associated with the singularity of the stiffness matrix at limit points a constraint equation defining a generalized arc length in the solution space is added to the system of nonlinear algebraic equations and the rayleigh ritz approximation functions or basis vectors are chosen to consist of a nonlinear solution of the discretized structure and its various order derivatives with respect to the generalized arc length the potential of the proposed approach and its advantages over the reduced basis load control technique are outlined the effectiveness of the proposed approach is demonstrated by means of numerical examples of structural problems with snap through and snap back phenomena

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

proof of the riemannian penrose inequality using the positive mass theorem we prove the riemannian penrose conjecture an important case of a con jecture 41 made by roger penrose in 1973 by defining a new flow of metrics this flow of metrics stays inside the class of asymptotically flat riemannian 3 manifolds with nonnegative scalar curvature which contain minimal spheres in particular if we consider a riemannian 3 manifold as a totally geodesic submanifold of a space time in the context of general relativity then outermost minimal spheres with total area a correspond to apparent horizons of black holes contributing a massa 16 scalar cur vature corresponds to local energy density at each point and the rate at which the metric becomes flat at infinity corresponds to total mass also called the adm mass the riemannian penrose conjecture then states that the total mass of an asymptotically flat 3 manifold with nonnegative scalar curvature is greater than or equal to the mass contributed by the black holes the flow of metrics we define continuously evolves the original 3 metric to a schwarzschild 3 metric which represents a spherically symmetric black hole in vacuum we define the flow such that the area of the minimal spheres which flow outward and hence the mass contributed by the black holes in each of the metrics in the flow is constant and then use the positive mass theorem to show that the total mass of the metrics is nonincreasing then since the total mass equals the mass of the black hole in a schwarzschild metric the riemannian penrose conjecture follows we also refer the reader to the beautiful work of huisken and ilmanen 30 who used inverse mean curvature flows of surfaces to prove that the total mass is at least the mass contributed by the largest black hole in sections 1 and 2 we motivate the problem discuss important quantities like total mass and horizons of black holes and state the positive mass theorem and the penrose conjecture for riemannian 3 manifolds in section 3 we give the proof of the riemannian penrose

solution of linear elastodynamics problems with space time finite elements on structured and unstructured meshes abstract a new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space time finite elements is suggested new weak formulations are based on time continuous tcg and discontinuous tdg galerkin methods it was shown that for structured meshes the new tcg method has a higher order of accuracy by a factor of two than that of the standard tcg method at the same number of degrees of freedom the accuracy of the new tcg method is one order higher than the accuracy of the standard tdg method the introduction of new weighting functions for the weak formulations of the tcg and tdg methods allows control of the high frequency behavior without degradation of accuracy of the methods a variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space time adaptive procedure using structured or unstructured meshes numerical examples for 1 d problems demonstrate the effectiveness of the technique

nonlinear analysis based on homogeneous incremental systems abstract the performance of path following techniques depends on so called constraint equations which are used in the augmented incremental systems it is common practice in the literature that these equations are explicitly defined following the arbitrary geometrical or physical ideas in the present paper their role is discussed in order to establish a reliable method of augmentation it is shown that the explicitly defined constraint equation is not necessary the implicit formulation is proposed which is based on the rank analysis performed on the rectangular matrix of the homogeneous incremental system the proposed method allows to solve problems where the well known continuation schemes fail the theoretical considerations are illustrated by the numerical examples

an efficient model reduction method for buckling analyses of thin shells based on iga abstract an efficient reduced basis method is proposed for buckling analyses of thin shells subject to large deformations and strains the thin shells are modeled with the classical kirchhoff love kinematics under the framework of iga isogeometric analysis which makes it possible to satisfy the requirement of c 1 continuity the analytically defined geometry of thin shells can be exactly represented by the nurbs non uniform rational b splines basis functions in addition the critical buckling point can be better pin pointed due to the exact geometric description for efficient structural analyses a simplified rom reduced order model is presented by combining the koiter perturbation technique and the finite element method fem alternative perturbation forces based on nonlinear eigenvalue analyses are also proposed embedding three strategies including arc length control accompanying eigenvalue analysis and mode injection into the analysis procedure the proposed method is extended to be applicable to nonlinear buckling analyses furthermore imperfection sensitivity analyses can be conveniently performed with the proposed method finally the effectiveness and efficiency of the proposed method are validated via three benchmark problems

a penrose type inequality for graphs over reissner nordstrom anti desitter manifold in this paper we use the inverse mean curvature flow to establish an optimal minkowski type inequality a weighted alexandrov fenchel inequality for the mean convex star shaped hypersurfaces in the reissner nordstrom anti desitter manifold and a penrose type inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over the reissner nordstrom anti desitter manifold

theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage this paper presents the theory and the numerics of an isotropic gradient damage formulation within a thermodynamical background the main motivation is provided by localization computations whereby classical local continuum formulations fail to produce physically meaningful and numerically converging results we propose a formulation in terms of the helmholtz free energy incorporating the gradient of the damage field a dissipation potential and the postulate of maximum dissipation as a result the driving force conjugated to damage evolution is identified as the quasi nonlocal energy release rate which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate on the numerical side besides balance of linear momentum the algorithmic consistency condition must be solved in weak form thereby the crucial issue is the selection of active constraints which is solved by an active set search algorithm borrowed from convex nonlinear programming in the examples we compare the behavior in local damage with the performance of the gradient formulation

the gbc mass for asymptotically hyperbolic manifolds the paper consists of two parts in the first part by using the gauss bonnet curvature which is a natural generalization of the scalar curvature we introduce a higher order mass the gauss bonnet chern mass m mathbb h k for asymptotically hyperbolic manifolds and show that it is a geometric invariant moreover we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs and establish a relationship between the corresponding penrose type inequality for this mass and weighted alexandrov fenchel inequalities in the hyperbolic space mathbb h n in the second part we establish these weighted alexandrov fenchel inequalities in mathbb h n for any horospherical convex hypersurface sigma begin aligned int sigma v sigma 2k 1 d mu ge c n 1 2k 1 omega n 1 left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned where sigma j is the j th mean curvature of sigma subset mathbb h n v cosh r and sigma is the area of sigma as an application we obtain an optimal penrose type inequality for the new mass defined in the first part begin aligned m k mathbb h ge frac 1 2 k left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned for asymptotically hyperbolic graphs with a horizon type boundary sigma provided that a dominant energy type condition tilde l k ge 0 holds both inequalities are optimal

continuous and discontinuous galerkin methods with finite elements in space and time for parallel computing of viscoelastic deformation abstract new non symmetric variational and discretized formulations with space time finite elements are proposed for viscoelastic problems based on the continuous galerkin method cgm and discontinuous galerkin method dgm viscoelastic behaviour is described by the three parameter malvern model which is represented by means of internal variables it allows to use only differential equations for the constitutive equations instead of integrodifferential ones the variational formulation reduces to two types of equations for total displacements and internal displacements internal variables namely to the equilibrium equation and the evolution equation for the internal displacements which are fulfilled in the weak form using continuous trial functions a continuous space time finite element formulation is obtained with simultaneous discretization in space and time subdividing the total observation time interval into time slabs and introducing discontinuous trial functions being continuous within time slabs and allowing jumps across interfaces a more general discontinuous finite element formulation is obtained the difference between these two formulations for one time slab consists in the satisfaction of initial conditions which are fulfilled exactly for the continuous formulation and in a weak form for the discontinuous case the proposed approach has some very attractive advantages with respect to semidiscretization methods regarding the possibility of adaptive space time refinements and parallel processing on mimd parallel computers the considered numerical examples show the effectiveness of simultaneous space time finite element calculations and a high convergence rate for adaptive refinement numerical efficiency is an advantage of dgm in comparison with cgm for discontinuously changing e g piecewise constant boundary conditions in time

the equality case of the penrose inequality for asymptotically flat graphs we prove the equality case of the penrose inequality in all dimensions for asymptotically flat hypersurfaces it was re cently proven by g lam 19 that the penrose inequality holds for asymptotically flat graphical hypersurfaces in euclidean space with non negative scalar curvature and with a minimal boundary our main theorem states that if the equality holds then the hy persurface is a schwarzschild solution as part of our proof we show that asymptotically flat graphical hypersurfaces with a min imal boundary and non negative scalar curvature must be mean convex using the argument that we developed in 15 this en ables us to obtain the ellipticity for the linearized scalar curvature operator and to establish the strong maximum principles for the scalar curvature equation

the mass of asymptotically hyperbolic manifolds motivated by certain problems in general relativity and riemannian geometry we study manifolds which are asymptotic to the hyperbolic space in a certain sense it is shown that an invariant the so called total mass can be defined unambiguously a positive mass theorem is established by using the spinor method

discrete shocks for finite difference approximations to scalar conservation laws numerical simulations often provide strong evidences for the existence and stability of discrete shocks for certain finite difference schemes approximating conservation laws this paper presents a framework for converting such numerical observations to mathematical proofs the framework is applicable to conservative schemes approximating stationary shocks of one dimensional scalar conservation laws the numerical flux function of the scheme is assumed to be twice differentiable but the scheme can be nonlinear and of any order of accuracy to prove existence and stability we show that it would suffice to verify some simple inequalities which can usually be done using computers as examples we use the framework to give an unified proof of the existence of continuous discrete shock profiles for a modified first order lax friedrichs scheme and the second order lax wendroff scheme we also show the existence and stability of discrete shocks for a third order weighted essentially nonoscillatory eno scheme

a convergence study of monolithic simulations of flow and deformation in fractured poroelastic media a consistent linearisation has been carried out for a monolithic solution procedure of a poroelastic medium with fluid transporting fractures including a comprehensive assessment of the convergence behaviour the fracture has been modelled using a sub grid scale model with a continuous pressure across the fracture the contributions to the tangential stiffness matrix of the fracture have been investigated to assess their impact on convergence simulations have been carried out for different interpolation orders and for non uniform rational b splines as interpolants vs lagrangian polynomials to increase the generality of the results newtonian as well as non newtonian power law fluids have been considered unsurprisingly a consistent linearisation invariably yields a quadratic convergence but comes at the expense of a loss of symmetry and recalculation of the contribution of the interface to the stiffness matrix at each iteration when using a linear line search however the inclusion of only those terms of the interface stiffness which result in a symmetric and constant tangential stiffness matrix is sufficient to obtain a stable and convergent iterative process

a critical comparison of nonlocal and gradient enhanced softening continua continuous models of material degradation may cease to produced meaningful results in the presence of high strain gradients these gradients may occur for instance in the propagation of waves with high wave numbers and at stress concentrators adding nonlocal or gradient terms to the constitutive modelling may enhance the ability of the models to describe such situations the effect of adding nonlocal or gradient terms and the relation between these enhancements are examined in a continuum damage setting a nonlocal damage model and two different gradient damage models are considered in one of the gradient models higher order deformation gradients enter the equilibrium equations explicitly while in the other model the gradient influence follows in a more implicit way from an additional partial differential equation the latter implicit gradient formulation can be rewritten in the integral format of the nonlocal model and can therefore be regarded as truly nonlocal this is not true for the explicit formulation in which the nonlocality is limited to an infinitesimal volume this fundamental difference between the formulations results in quite different behaviour in wave propagation localisation and at crack tips this is shown for the propagation of waves in the models their localisation properties and the behaviour at a crack tip the responses of the nonlocal model and the implicit gradient model agree remarkably well in these situations while the explicit gradient formulation shows an entirely different and sometimes nonphysical response

asymptotic numerical methods and pade approximants for non linear elastic structures in this paper we apply asymptotic numerical methods for computing non linear equilibrium paths of elastic beam plate and shell structures the non linear branches are sought in the form of asymptotic expansions and they are determined by solving numerically fem several linear problems with a single stiffness matrix a large number of terms of the series can be easily computed by using recurrence formulas in comparison with a more classical step by step procedure the method is rapid and automatic we show with some examples that the choice of the expansion s parameter and the use of pade approximants play an important role in the determination of the size of the domain of convergence

gradient damage models toward full scale computations abstract the description of localisation and structural failure through local damage constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of damage in addition to the strain and the damage under some assumptions it is shown that these gradient laws can be cast into a variational formulation its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as newton s method and path following techniques are still available possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws finally numerical applications show the convergence with mesh refinement the compatibility with coarser approaches such as griffith s theory and cohesive crack models the robustness in case of unstable multi cracking the applicability to full scale 3d situations and the physical relevance compared to experimental data

large displacement elastoplastic analysis of semirigid steel frames a mathematical programming approach for the large displacement analysis of elastoplastic plane frames with flexible partial strength beam to column connections is proposed the incremental formulation is developed within the framework of a discrete model piecewise linear yield surfaces and large displacement theory it is based on the fundamental relations of equilibrium compatibility and constitutive laws all expressed in incremental form the irreversible plasticity laws are used in a stepwise holonomic format a feature of the final mathematical programming problem known as a non linear complementarity problem is that the governing relations exhibit symmetry as a result of the use of fictitious quantities and non linear residuals the iterative predictor corrector computational scheme adopted has the ability of tracing historically a sequence of plastic hinge activations and or unloadings well beyond any critical point numerical examples are presented to illustrate and validate the accuracy of the approach

existence and asymptotic stability of relaxation discrete shock profiles kin this paper we study the asymptotic nonlinear stability of discrete shocks of the relaxing scheme for approximating the general system of nonlinear hyperbolic conservation laws the existence of discrete shocks is established by suitable manifold construction and it is shown that weak single discrete shocks for such a scheme are nonlinearly stable in l 2 provided that the sums of the initial perturbations equal zero these results should shed light on the convergence of the numerical solution constructed by the relaxing scheme for the single shock solution of the system of hyperbolic conservation laws these results are proved by using both a weighted norm estimate and a characteristic energy method based on the internal structures of the discrete shocks

a truncated newton lanczos method for overcoming limit and bifurcation points in this study procedures for overcoming limit and bifurcation points in large scale structural analysis problems are described and evaluated the methods are based on newton s method for the outer iterations while for the linearized problem in each iteration the preconditioned truncated lanczos method is employed special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method the proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix the necessary eigenvalue information is retained in the tridiagonal matrix of the lanczos approach

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

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

bending instabilities of elastic tubes the present paper examines instabilities of long thin elastic tubes both initially straight and initially bent tubes are analyzed under in plane bending tube response a combination of ovalization instability and bifurcation instability buckling is investigated using a nonlinear finite element fe technique which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross sectional deformation it is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature the ovalization of initially bent tubes is examined in detail and in particular the case of opening moments furthermore the paper emphasizes on bifurcation instability it is shown that buckling may occur prior to or beyond the ovalization limit point depending on the value of the initial curvature using the nonlinear fe formulation the location of bifurcation on the primary path is detected post buckling equilibrium paths are traced and the corresponding wavelengths of the buckled configurations are calculated moreover results over a wide range of initial curvature values are presented extending the findings of previous works finally several analytical approaches introduced in previous research works are also employed to estimate the moments causing ovalization and bifurcation instability these approaches are based on nonlinear flexible shell theory or simplified ring analysis the efficiency and accuracy of those analytical methods with respect to the nonlinear fe formulation are examined

a new approach in non linear mechanics the large time increment method a new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non linearities and is tested on some examples in elastoplasticity the method considerably reduces the number of transfers between local and global levels hence the numerical cost of calculation is also diminished