complete electrode model of electrical impedance tomography approximation properties and characterization of inclusions in electrical impedance tomography one tries to recover the spatial admittance distribution inside a body from boundary measurements in theoretical considerations it is usually assumed that the boundary data consists of the neumann to dirichlet map when conducting real world measurements the obtainable data is a linear finite dimensional operator mapping electrode currents onto electrode potentials in this paper it is shown that when using the complete electrode model to handle electrode measurements the corresponding current to voltage map can be seen as a discrete approximation of the traditional neumann to dirichlet operator this approximating link is utilized further in the special case of constant background conductivity with inhomogeneities it is demonstrated how inclusions with strictly higher or lower conductivities can be characterized by the limit behavior of the range of a boundary operator determined through electrode measurements when the electrodes get infinitely small and cover all

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

a finite element method for stability problems in finite elasticity in this paper a finite element method is developed to treat stability problems in finite elasticity for this purpose the constitutive equations are formulated in principal stretches which allows a general representation of the derivatives of the strain energy function with respect to the principal stretches these results can then be used to derive an efficient numerical scheme for the computation of singular points

stress resultant geometrically nonlinear shell theory with drilling rotations part ii computational aspects abstract in this work we discuss some details of the numerical implementation of the geometrically nonlinear shell theory presented in part i two possibilities to represent finite rotations with an orthogonal matrix and with a rotation vector are examined in detail along with their mutual relationship in both spatial and material description the issues pertinent to the consistent linearization procedure corresponding to these rotation parameterizations are also carefully considered the geometrically nonlinear method of incompatible modes is extended to the nonlinear shell theory under consideration and used to provide a 4 node shell element with enhanced performance a rather extensive set of numerical examples in nonlinear elastostatics is solved in order to corroborate the non locking performance of the incompatible mode based shell elements the examples include not only analyses of simple shell structures undergoing very large displacements and rotations but also cases of strong practical interest such as non smooth shell structures and shell structures with stiffeners

on a stress resultant geometrically exact shell model part vii shell intersections with dof finite element formulations abstract if the mid surface of a shell is smooth the classical theory describes the orientation of the director field attached to the mid surface by two independent rotational degrees of freedom at a shell intersection where this smoothness assumption no longer holds it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom this added degree of freedom however is totally unrelated to the so called drill rotation widely used as a means of tackling the shell intersection problem a computational procedure involving a trivial modification of the global singularity free update procedure described in part iii of this work is described which completely resolves the shell intersection problem without introducing drill springs or related ad hoc devices the proposed approach leaves unchanged standard finite element formulations in terms of 5 dof node affects only the global update formulae and exhibits excellent performance as illustrated by representative numerical simulations

detecting inclusions in electrical impedance tomography without reference measurements we develop a new variant of the factorization method that can be used to detect inclusions in electrical impedance tomography from either absolute current to voltage measurements at a single nonzero frequency or from frequency difference measurements this eliminates the need for numerically simulated reference measurements at an inclusion free body and thus greatly improves the method s robustness against forward modeling errors e g in the assumed body s shape

a reduced integration solid shell finite element based on the eas and the ans concept large deformation problems in this paper we address the extension of a recently proposed reduced integration eight node solid shell finite element to large deformations the element requires only one integration point within the shell plane and at least two integration points over the thickness the possibility to choose arbitrarily many gauss points over the shell thickness enables a realistic and efficient modeling of the non linear material behavior only one enhanced degree of freedom is needed to avoid volumetric and poisson thickness locking one key point of the formulation is the taylor expansion of the inverse jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes the transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept further crucial points are the taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the taylor expansion of the second piola kirchhoff stress tensor with respect to the normal through the center of the element copyright 2010 john wiley sons ltd

reconstructing discontinuities using complex geometrical optics solutions in this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the laplacian as the leading order term we apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary measurements computational results demonstrate the versatility of these solutions to determine electrical inclusions

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

a fully non linear axisymmetrical quasi kirchhoff type shell element for rubber like materials an axisymmetrical shell element for large deformations is developed by using ogden s non linear elastic material law this constitutive equation however demands the neglect of transverse shear deformations in order to yield a consistent theory therefore the theory can be applied to thin shells only eventually a quasi kirchhoff type theory emerges within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non linear bending behaviour furthermore special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within newton s method finally the finite element formulation for a conical two node element is given several examples show the applicability and performance of the proposed formulation

hyperbolic geometry and local dirichlet neumann map abstract we show in three dimensions that if we know the dirichlet to neumann dn map associated to the schrodinger equation with a potential around the intersection of a sphere centered outside the convex hull of a bounded domain with smooth boundary we can determine uniquely the corresponding spherical mean of the potential with an appropriate measure this allows one to determine the potential near the boundary where the dn map is measured similar results are valid for electrical impedance tomography

bisector and zero macrospin co rotational systems for shell elements a principal issue in any co rotational approach for large displacement analysis of plates and shells is associated with the specific choice of the local reference system in relation to the current deformed element configuration previous approaches utilised local co rotational systems which are invariant to nodal ordering a characteristic that is deemed desirable on several fronts however the associated definitions of the local reference system suffered from a range of shortcomings including undue complexity dependence on the local element formulation and possibly an asymmetric tangent stiffness matrix in this paper new definitions of the local co rotational system are proposed for quadrilateral and triangular shell elements which achieve the invariance characteristic to the nodal ordering in a relatively simple manner and address the aforementioned shortcomings the proposed definitions utilise only the nodal coordinates in the deformed configuration where two alternative definitions namely bisector and zero macrospin definitions are presented for each of quadrilateral and triangular finite elements in each case the co rotational transformations linking the local and global element entities are presented highlighting the simplicity of the proposed approach several numerical examples are finally presented to demonstrate the effectiveness and relative accuracy of the alternative definitions proposed for the local co rotational system

four node semi eas element in six field nonlinear theory of shells we propose a new four node c finite element for shell structures undergoing unlimited translations and rotations the considerations concern the general six field theory of shells with asymmetric strain measures in geometrically nonlinear static problems the shell kinematics is of the two dimensional cosserat continuum type and is described by two independent fields the vector field for translations and the proper orthogonal tensor field for rotations all three rotational parameters are treated here as independent hence as a consequence of the shell theory the proposed element has naturally six engineering degrees of freedom at each node with the so called drilling rotation this property makes the element suitable for analysis of shell structures containing folds branches or intersections to avoid locking phenomena we use the enhanced assumed strain eas concept we derive and linearize the modified hu washizu principle for six field theory of shells what makes the present approach original is the combination of eas method with asymmetric membrane strain measures based on literature we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry to gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches

a four node corotational quadrilateral elastoplastic shell element using vectorial rotational variables four node corotational quadrilateral elastoplastic shell element summary a four node corotational quadrilateral elastoplastic shell element is presented the local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product this local coordinate system rotates rigidly with the element but does not deform with the element as a result the element rigid body rotations are excluded in calculating the local nodal variables from the global nodal variables the two smallest components of each nodal orientation vector are defined as rotational variables leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure different from other existing corotational finite element formulations the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables for elastoplastic analyses the maxwell huber hencky von mises yield criterion is employed together with the backward euler return mapping method for the evaluation of the elastoplastic stress state the consistent tangent modulus matrix is derived to eliminate locking problems we use the assumed strain method several elastic patch tests and elastoplastic plate shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation copyright 2013 john wiley sons ltd

genuinely resultant shell finite elements accounting for geometric and material non linearity the underlying theory is statically and geometrically exact and it naturally includes small strain and finite strain problems of thin as well as thick shells this paper examines the development of computational procedures employing the newton kantorovich linearization process and the galerkin type discretization method the treatment of finite rotations through an arbitrary parametrization of the rotation group the interpolation procedure of so 3 valued functions underlying the construction of finite element basis

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

on uniqueness of recovery of a discontinuous conductivity coefficient on considere le probleme de retrouver le coefficient a de l equation elliptique div a u 0 dans un domaine avec la condition aux limites u sur quand u n est donnee pour tout regulier on demontre l unicite pour a a 0 b discontinu ou est la fonction indicateur d un ensemble ouvert a o est une fonction c 2 donnee et b est une fonction c 2 inconnue

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

reconstruction of penetrable inclusions in elastic waves by boundary measurements abstract we use ikehata s enclosure method to reconstruct penetrable unknown inclusions in a plane elastic body in time harmonic waves complex geometrical optics solutions with complex polynomial phases are adopted as the probing utility in a situation similar to ours due to the presence of a zeroth order term in the equation some technical assumptions need to be assumed in early researches in a recent work of sini and yoshida they succeeded in abandoning these assumptions by using a different idea to obtain a crucial estimate in particular the boundaries of the inclusions need only to be lipschitz in this work we apply the same idea to our model it s interesting that with more careful treatment we find the boundaries of the inclusions can in fact be assumed to be only continuous

isogeometric kirchhoff love shell formulation for elasto plasticity abstract an isogeometric thin shell formulation allowing for large strain plastic deformation is presented a stress based approach is adopted which means that the constitutive equations are evaluated at different integration points through the thickness allowing the use of general 3d material models the plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points the deformation of the shell structure is completely described by the deformation of its midsurface and furthermore the formulation is rotation free which means that the discrete shell model involves only three degrees of freedom several numerical benchmark examples with comparison to fully 3d solid simulations confirm the accuracy and efficiency of the proposed formulation

a real time algorithm for the location search of discontinuous conductivities with one measurement we consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current voltage observation we develop a real time algorithm for determining the location of the anomaly this new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage combined with the size estimation result this algorithm gives a good initial guess for newton type schemes we give the rigorous proof for the location search algorithm both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast stable and efficient 2001 john wiley sons inc

reconstructing acoustic obstacles by planar and cylindrical waves in this paper we develop a novel method of reconstructing acoustic obstacles in r2 which follows a similar spirit of the linear sampling method originated by colton and kirsch the reconstruction scheme makes use of the near field measurements encoded into the boundary dirichlet to neumann map or the neumann to dirichlet map both the plane waves and cylindrical waves are shown to meet the reconstruction purpose rigorous mathematical justification of the reconstruction scheme is established the mapping properties of the newly introduced function operators involved in the reconstruction scheme are established these results are of significant mathematical interests for their own sake moreover due to the distinct properties of the function operators the indictor function in the proposed reconstruction scheme exhibits completely different behaviors from those having been established for the indictor function in the original linear sampling method for inverse scattering problems numerical experiments

probing for electrical inclusions with complex spherical waves let a physical body in 2 or 3 be given assume that the electric conductivity distribution inside consists of conductive inclusions in a known smooth background further assume that a subset is available for boundary measurements it is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on more precisely given a ball b with center outside the convex hull of and satisfying b boundary measurements on with explicitly given dirichlet data are enough to determine whether b intersects the inclusion an approximate detection algorithm is introduced based on the theory numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion free domain near and is robust against measurement noise 2007 wiley periodicals inc

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

a direct impedance tomography algorithm for locating small inhomogeneities impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface in its most general form impedance tomography is quite ill posed but when additional a priori information is admitted the situation changes dramatically in this paper we consider the case where the goal is to find a number of small objects inhomogeneities inside an otherwise known conductor taking advantage of the smallness of the inhomogeneities we can use asymptotic analysis to design a direct i e non iterative reconstruction algorithm for the determination of their locations the viability of this direct approach is documented by numerical examples

a mixed shell formulation accounting for thickness strains and finite strain 3d material models a non linear quadrilateral shell element for the analysis of thin structures is presented the reissner mindlin theory with inextensible director vector is used to develop a three field variational formulation with independent displacements stress resultants and shell strains the interpolation of the independent shell strains consists of two parts the first part corresponds to the interpolation of the stress resultants within the second part independent thickness strains are considered this allows incorporation of arbitrary non linear 3d constitutive equations without further modifications the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison with other element formulations we present results for finite strain elasticity inelasticity bifurcation and post buckling problems copyright 2007 john wiley sons ltd

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

finite elastoplastic deformations of space curved membranes abstract under restriction of an isotropic elastic response of deformed lattice a covariant theory of finite elastoplasticity is developed in principal axes of a pair of deformation tensors in material description the tensor pair consists of the plastic deformation tensor and the total deformation cauchy green tensor the proposed theory is applied to elastoplastic membranes whose reference and current configurations can be arbitrary space curved surfaces pressure insensitive von mises yield criterion and isotropic hardening are considered as a model problem with a particular form of the strain energy function given in terms of elastic principal stretches through an explicit enforcement of the plane stress condition we arrive at a reduced two dimensional problem representation which is set in the membrane tangent plane numerical implementation details are given to show an important role of the operator split methodology in simplifying the state update computation and the computation of the consistent tangent modulus a set of numerical examples illustrates the performance of the presented theory and indicates some of the possible areas of application

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects

a continuum based shell theory for non linear applications the paper introduces a non linear shell theory which provides a complete three dimensional state of stress since the theory is derived from simple three dimensional continuum mechanics it is very easy to understand as an example the theory is applied to quadrilateral shell elements which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface it is proposed to eliminate this degree of freedom on element level so that the elements have the same layout as the equivalent brick elements but have a better behaviour in bending have stress resultants and are cheaper with respect to computational effort the advantages with respect to implementation in a finite element program as well as in special applications are obvious however well known conditioning problems in thin shell applications must be expected therefore emphasis is put on this issue in the example problems it is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non linear applications which will be considered in a forthcoming paper

an efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach for geometrically and physically nonlinear analyses of shell structures a computational model employing a reissner mindlin type kinematic assumption a layered finite element approach and a closest point projection return mapping algorithm completely formulated in tensor notation is presented as a result of a consistent linearization a tangent modulus is derived expressed also in tensor components the applied constitutive model includes a von mises yield criterion and linear isotropic as well as kinematic hardening all stress deviator components are employed in the formulation the material model is implemented into a four noded isoparametric assumed strain finite element which permits the simulation of geometric nonlinear responses considering finite rotations the proposed numerical concept is unconditionally stable and allows large time steps as the numerical examples illustrate further the numerical simulations demonstrate the expected quadratic convergence in a global iterative technique

an investigation of a finite rotation four node assumed strain shell element the paper presents a shell formulation based on the degenerated solid approach the theory employs covariant strains and performs explicit integration through the shell thickness the rigid body motion is exactly represented the consistent tangent stiffness matrix is evaluated for the four node quadrilateral it is shown in the final part that this type of element which distinguishes itself by a very simple and easily understandable theory gives good answers for linear as well as non linear applications

computationally efficient explicit nonlinear analyses using reduced integration based solid shell finite elements abstract solid shell formulations based on reduced integration with hourglass stabilization have several advantages among these are the smaller number of gauss points and the direct modelling of the thickness stretch a feature which is usually not present in standard degenerated shell elements the latter issue is especially important for applications where contact is involved e g for almost all relevant systems in production technology obviously this makes solid shell formulations very attractive for their use in industrial design a major disadvantage in the context of explicit analyses is however the fact that the critical time step is determined by the thickness of the solid shell element which is usually smaller than the smallest in plane dimension therefore four node shells where the critical time step is determined by the in plane dimensions are still often preferred for explicit analysis in the present paper we suggest several techniques to overcome this difficulty also in the case of problems dominated by nonlinearities such as finite deformations elastoplasticity and contact reference is made to an 8 node hexahedron solid shell element recently proposed by schwarze and reese 2011 32 in an implicit context first of all the time steps in explicit analyses are so small that it may be not necessary to update the hourglass stabilization and the implicit computation of the internal element degrees of freedom in every time step performing the update in only every hundredth step or computing an explicit rather than implicit update can reduce the computational effort up to about 50 another important issue is selective mass scaling which means to modify the mass matrix in such a way that the speed of sound in thickness direction is reduced this enables the choice of a larger time step the cpu effort can be finally noticeably decreased without changing the structural response significantly this makes the presently used solid shell formulation competitive to four node shells also for explicit analysis

a note on enhanced strain methods for large deformations abstract enhanced strain elements have been applied to simulate geometrically and materially non linear problems their main advantage is due to the fact that they perform very good in the incompressible limit as well as in bending situations however in compressive deformation states these elements depict stability modes which are associated with hour glass forms and thus denote a rank deficiency for such deformations in this paper the appearance of these modes will be investigated analytically by means of a simple representative example

finite rotation elements for the non linear analysis of thin shell structures abstract for the numerical analysis of shells undergoing finite rotations doubly curved finite shell elements are developed via the displacement formulation the derivation starts from a consistent finite rotation shell theory which is transformed by a variational procedure into an incremental formulation thus the non linearity can be treated by an incremental iterative technique the non linear element matrices are obtained by a tensor oriented procedure permitting a direct transformation of the initial equations into efficient numerical models unlike in the usual procedure the kirchhoff love assumption is treated as a subsidiary condition at the element level this computer oriented approach permits the elimination of the dependent rotational degrees of freedom without loss of accuracy finally some examples are presented to demonstrate the ability of the resulting finite elements to deal with finite rotation problems

a large deformation solid shell concept based on reduced integration with hourglass stabilization in this paper a new eight node brick solid shell finite element formulation based on the concept of reduced integration with hourglass stabilization is presented the work focuses on static problems the starting point of the derivation is the three field variational functional upon which meanwhile established 3d enhanced strain concepts are based important additional assumptions are made to transfer the approach into a powerful solid shell first of all a taylor expansion of the first piola kirchhoff stress tensor with respect to the normal through the centre of the element is carried out in this way the stress becomes a linear function of the shell surface co ordinates whereas the dependence on the thickness co ordinate remains non linear secondly the jacobian matrix is replaced by its value in the centre of the element these two assumptions lead to a computationally efficient shell element which requires only two gauss points in the thickness direction and one gauss point in the plane of the shell element additionally three internal element degrees of freedom have to be determined to avoid thickness locking one important advantage of the element is the fact that a fully three dimensional stress state can be modelled without any modification of the constitutive law the formulation has only displacement degrees of freedom and the geometry in the thickness direction is correctly displayed copyright 2006 john wiley sons ltd

on a physically stabilized one point finite element formulation for three dimensional finite elasto plasticity abstract in the case of linear elasticity a direct connection between the concept of reduced integration with hourglass stabilization and a mixed method can usually be established in the non linear case this is in general not possible to overcome this difficulty we suggest in this paper a new concept based on a taylor expansion of the constitutively dependent quantities with respect to the centre of the element the push forward of the second linear term of the taylor series for the first piola kirchhoff stress tensor to the current configuration determines the so called hourglass stabilization part of the residual force vector due to the fact that the element uses only one gauss point and the hourglass stabilization part is computed by means of a simple functional evaluation the present element technology is very efficient from the computational point of view in contrast to the 2d case the computation of the jacobi determinant only in the centre of the 3d element does not yield the correct volume if the element shape deviates from being a parallelipiped it is shown in the paper that the error becomes negligibly small for a relatively coarse discretization the formulation is free of volumetric locking and can compete with shell formulations up to an aspect ratio of about hundred for bending dominated problems at least two elements over the thickness are needed in order to compute the onset of plastification correctly the element behaves very robustly in finite elasticity and inelasticity also when large element distortions occur

elasto plastic analysis of shells with the triangular element tric tric is a simple but sophisticated three node shear deformable isotropic and composite facet shell element suitable for large scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures in the present work an elasto plastic constitutive model based on the von mises yield criterion with isotropic hardening is incorporated into the element the characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element this is achieved by transforming quantities such as equivalent plastic strain equivalent stress the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system these transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities

reconstruction of a penetrable obstacle by complex spherical waves we consider an inverse acoustic scattering problem for identifying a non convex penetrable obstacle in three dimensions in a homogeneous medium we apply the complex geometrical optics solutions with logarithmic phase which is called complex spherical waves to reconstruction problem the reconstruction schemes will be demonstrated in the last section

an efficient higher order family of root finders a one parameter family of iterative methods for the simultaneous approximation of simple complex zeros of a polynomial based on a cubically convergent hansen patrick s family is studied we show that the convergence of the basic family of the fourth order can be increased to five and six using newton s and halley s corrections respectively since these corrections use the already calculated values the computational efficiency of the accelerated methods is significantly increased further acceleration is achieved by applying the gauss seidel approach single step mode one of the most important problems in solving nonlinear equations the construction of initial conditions which provide both the guaranteed and fast convergence is considered for the proposed accelerated family these conditions are computationally verifiable they depend only on the polynomial coefficients its degree and initial approximations which is of practical importance some modifications of the considered family providing the computation of multiple zeros of polynomials and simple zeros of a wide class of analytic functions are also studied numerical examples demonstrate the convergence properties of the presented family of root finding methods

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

finite element concepts for finite elastoplastic strains and isotropic stress response in shells theoretical and computational analysis this paper presents appropriate finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail in this context the importance of the deformation gradient for an efficient implementation is especially emphasized according to the parameterizations the computational plasticity algorithms are derived in general three dimensional 3 d form for thick shell structures and a restricted 2 d form satisfying the plane stress state underlying thin shells in order to describe arbitrary shell geometries the isoparametric concept is applied to all proposed finite element formulations these are based on quadrilateral 4 node mixed finite shell elements the variational approaches of the enhanced assumed strain method the assumed natural strain concept and the reduced integration technique are accurately considered by means of representative numerical examples the performance of the three different finite element concepts is demonstrated furthermore their individual properties are addressed with respect to efficiency and numerical accuracy thus crucial consequences for an optimal modelling of finite plastic strains in shells can be outlined

nonlinear fourier analysis for discontinuous conductivities computational results abstract two reconstruction methods of electrical impedance tomography eit are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics cgo solutions to d bar equations involving the global uniqueness proofs for calderon problem exposed in nachman 1996 43 and astala and paivarinta 2006 6 the astala paivarinta theory based low pass transport matrix method implemented in astala et al 2011 3 and the shortcut method which considers ingredients of both theories the latter method is formally similar to the nachman theory based regularized eit reconstruction algorithm studied in knudsen et al 2009 34 and several references from there new numerical results are presented using parallel computation with size parameters larger than ever leading mainly to two conclusions as follows first both methods can approximate piecewise constant conductivities better and better as the cutoff frequency increases and there seems to be a gibbs like phenomenon producing ringing artifacts second the transport matrix method loses accuracy away from a freely chosen pivot point located outside of the object to be studied whereas the shortcut method produces reconstructions with more uniform quality

inverse conductivity problem with one measurement uniqueness of balls in r 3 we prove that the location and size of an unknown ball d entering the conductivity equation mbox div 1 k 1 chi d nabla u 0 in a bounded domain omega subset bbb r 3 are uniquely determined by any single nonzero cauchy data u pd u nu on bo

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

on shear correction factors in the non linear theory of elastic shells abstract theoretical values of two correction factors s 5 6 and t 7 10 are established for the respective transverse shear stress resultants and stress couples within the general dynamically and kinematically exact six field theory of elastic shells these values do not depend on the shell material symmetry geometry of the base surface the shell thickness or any kind of kinematic and or dynamic constraints the analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section the appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with s and t as the respective correction factors four numerical examples of highly non linear shell structures illustrate the influence of different values of s and t on the results in particular some influence of t is noticed on the placement of bifurcation points in dynamic problem of flight of three intersecting plates analysed with newmark type temporal algorithm the value of t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure

a model adaptive hanging node concept based on a new non linear solid shell formulation in this contribution we propose an innovative approach to automatically refine shell finite element meshes in thickness direction the procedure employs a new eight node solid shell element formulation based on the concept of reduced integration with hourglass stabilization apart from the important advantages of computational efficiency and robustness this element formulation offers the possibility to work with a variable mesh density in thickness direction in the present paper we suggest an adaptive approach using the hanging node concept to avoid additional mesh distortion among different stress and strain based error criteria the warping of the cross section and the residual error in the solution of the strong form of the balance of linear momentum have been proven to be suitable error measures the former represents the deviation of the realistically non linear dependence of the characteristic strain coefficient from its corresponding linear distribution applications show that the mesh refines as expected in loading domains in the neighbourhood of bearings or regions with strongly accumulating inelastic deformation on the other hand the discretization remains rather coarse in uncritical parts of the structure which decreases the computational effort noticeably

thin shells with finite rotations formulated in biot stresses theory and finite element formulation a bending theory for thin shells undergoing finite rotations is presented and its associated finite element model is described the kinematic assumption is based on a shear elastic reissner mindlin theory the starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures the associated work conjugate stress resultants and stress couples are integrals of the biot stress tensor this tensor is invariant with respect to rigid body motions and therefore appropriate for the formulation of constitutive equations finite rotations are introduced via eulerian angles the finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration the numerical model is applied to different non linear plate and shell problems and compared with existing formulations due to a consistent linearization the step size of a load increment is only limited by the local convergence behaviour of newton s method