a polar theory for vibrations of thin elastic shells abstract in relation to a polar continuum this paper presents a 2 d shear deformable theory for the high frequency vibrations of a thin elastic shell to begin with the 3 d fundamental equations of the micropolar elastic continuum are expressed as the euler lagrange equations of a unified variational principle next the kinematic variables of the shell are represented by the power series expansions in its thickness coordinate and then they are used to establish the 2 d theory by means of the variational principle the 2 d theory is derived in invariant variational and differential forms and governs all the types of vibrations of the functionally graded micropolar shell lastly the uniqueness is investigated in solutions of the initial mixed boundary value problems defined by the 2 d theory and some of special cases are indicated in the theory

smooth optimization methods for minimax problems the classical discrete minimax problem is considered it is transformed into an equivalent problem by a monotone transformation of the initial functions it was found that the classical lagrangian of the equivalent problem has a number of important properties both in primal and dual spaces in convex as well as in nonconvex cases in particular the classical lagrangian of the equivalent problem being as smooth as the initial functions has the main advantages of augmented lagrangians this makes it possible to construct a multiplier method for the minimax problem and a general method for the simultaneous solution of the primal and the dual problems these methods are based on the theory of methods of smooth optimization and preserve the main advantages of the latter for nonsmooth minimax problems

variational principles and membrane finite elements with drilling rotations for geometrically non linear elasticity reference epfl article 102735view record in web of science record created on 2007 04 23 modified on 2016 08 08

the finite deformation theory for beam plate and shell part v the shell element with drilling degree of freedom based on biot strain due to the facts that the spatial moment force is non conservative and the three components of the finite rotation pseudo vector are not independent the ordinary variational principle based on a functional achieving its stationary value is not suitable for the problem subject to non conservative loading the finite element method proposed in this paper is based on the virtual work principle rigid normal assumption polar decomposition and total lagrangian formulation

stress resultant geometrically nonlinear shell theory with drilling rotations part i a consistent formulation abstract in this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear shell theory the main feature of the present shell theory development which stands in contrast with the classical developments in the shell theory is the presence of a rotation component around the shell normal so called drilling rotation in the description of shell finite rotations the relationship of the proposed theory with a finite deformation theory of a three dimensional continuum with independent rotation field is clearly identified the latter is shown to be an important link which facilitates the proper choice of the shell constitutive model and a proper construction of the regularized form of the theory capable of supporting the drilling rotations the corresponding linearized form of the present shell theory is discussed in the closure

finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

a variational principle for the formulation of partitioned structural systems a continuum based variational principle is presented for the formulation of the discrete governing equations of partitioned structural systems this application includes coupled substructures as well as subdomains obtained by mesh decomposition the present variational principle is derived by a series of modifications of a hybrid functional originally proposed by atluri for finite element development the interface is treated by a displacement frame and a localized version of the method of lagrange multipliers interior displacements are decomposed into rigid body and deformational components to handle floating subdomains both static and dynamic versions are considered an important application of the present principle is the treatment of nonmatching meshes that arise from various sources such as separate discretization of substructures independent mesh refinement and global local analysis the present principle is compared with that of a globalized version of the multiplier method copyright 2000 john wiley sons ltd

an alternative alpha finite element method aαfem for free and forced structural vibration using triangular meshes an alternative alpha finite element method email protected using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent solution in the energy norm for the static analysis of two dimensional solid mechanics problems in the email protected the piecewise constant strain field of linear triangular fem models is enhanced by additional strain terms with an adjustable parameter a which results in an effectively softer stiffness formulation compared to a linear triangular element the element is further extended to the free and forced vibration analyses of solids several numerical examples show that the email protected achieves high reliability compared to other existing elements in the literature

an intrinsic beam model based on a helicoidal approximation part i formulation the focus of the present work is directed towards the one dimensional non linear analysis of space curved and twisted beams undergoing large displacements and finite rotations according to cosserat s model a beam is intended here as a continuum generated by the rigid motion of a cross section along a curve the novelty of the proposed methodology is implied in the assumption that the reference line of the beam both in the undeformed and in the deformed configurations is a helicoid in space this formulation radically departs from the classical beam models based on polynomial interpolations of the independent fields in fact within the framework of helicoidal geometry a powerful description of space curved beam kinematics with large displacements and finite rotations can be developed furthermore the beam model developed herein can be proved to enjoy several invariance properties that make it particularly attractive for non linear analysis the formulation discussed in this work adheres to a mixed variational principle the independent fields being the generalized displacements and the sectional stress resultants in a companion paper we address the linearization of the governing weak form the finite element implementation of the proposed methodology with a novel incremental treatment of finite rotations and the development of a helicoidal model for rigid body dynamics using finite elements in time

on the parametrization of finite rotations in computational mechanics a classification of concepts with application to smooth shells this paper concerns the computational treatment of large rotations with application to the finite element discretisation of smooth shells formulations based on various rotational parametrizations are reviewed and classified with respect to their update structure category ii is based on total rotational degrees of freedom leading to an additive update structure whereas category i relies on linearized rotational degrees of freedom leading to a multiplicative update structure based on this classification new formulations are developed among them are the rodrigues formula applied within category ii with additive update structure for the two components of the rotation vector and two successive elementary rotations in the sense of euler angles applied within category i yielding a singularity free formulation the numerical examples confirm that every rotational parametrization when applied within category ii leads to singularities whereas the application within category i enables the calculation of overall rotations unrestricted in size without any singularity

supernatural quad4 a template formulation abstract a universal template for a 4 node quadrilateral in plane stress is constructed using a combination of old and new techniques the use of natural quantities strongly advocated by j h argyris since his continua and discontinua 1965 exposition is further expanded the qualifier supernatural means that all governing equations kinematic constitutive and equilibrium are expressed in both cartesian and natural forms these two sets are used to build different components of the template with timely help from a computer algebra system a template that include all possible quadrilateral elements that pass the individual element test of bergan and hanssen emerges it yields an infinite number of hitherto undiscovered instances that may be customized to fit special needs a striking example is the construction of a two trapezoid macroelement that is bending exact about one direction for any amount of distortion this concludes a five decade search that begins with the formulation of the wing cover rectangular panel in argyris 1954 seminal serial on energy methods and structural analysis

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

an adaptive nonmonotone trust region method with curvilinear search for minimax problem in this paper we propose an adaptive nonmonotone algorithm for minimax problem unlike traditional nonmonotone method the nonmonotone technique applied to our method is based on the nonmonotone technique proposed by zhang and hager h c zhang w w hager a nonmonotone line search technique and its application to unconstrained optimization siam j optim 14 4 2004 1043 1056 instead of that presented by grippo et al l grippo f lampariello s lucidi a nonmonotone line search technique for newton s method siam j numer anal 23 4 1986 707 716 meanwhile by using adaptive technique it can adaptively perform the nonmonotone trust region step or nonmonotone curvilinear search step when the solution of subproblems is unacceptable global and superlinear convergences of the method are obtained under suitable conditions preliminary numerical results are reported to show the effectiveness of the proposed algorithm

a survey of parametrized variational principles and applications to computational mechanics abstract this survey paper describes recent developments in the area of parametrized variational principles pvps and selected applications to finite element computational mechanics a pvp is a variational principle containing free parameters that have no effect on the euler lagrange equations the theory of single field pvps based on gauge functions also known as null lagrangians is a subset of the inverse problem of variational calculus that has limited value on the other hand multifield pvps are more interesting from theoretical and practical standpoints following a tutorial introduction the paper describes the recent construction of multifield pvps in several areas of elasticity and electromagnetics it then discusses three applications to finite element computational mechanics the derivation of high performance finite elements the development of element level error indicators and the construction of finite element templates the paper concludes with an overview of open research areas

a smooth method for the finite minimax problem we consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions we prove that under usual assumptions it is possible to construct a continuously differentiable function whose minimizers yield the minimizers of the max function and the corresponding minimum values on this basis we can define implementable algorithms for the solution of the minimax problem which are globally convergent at a superlinear convergence rate preliminary numerical results are reported

on the fundamental equations of electromagnetoelastic media in variational form with an application to shell laminae equations abstract the fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials and the uniqueness of solutions is examined alternatively the fundamental equations are stated as the euler lagrange equations of a unified variational principle which operates on all the field variables the variational principle is deduced from a general principle of physics by modifying it through an involutory transformation then a system of two dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell also a theorem is given which states the conditions sufficient for the uniqueness in solutions of the shell equations on the basis of a discrete layer modeling the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness the resulting equations in differential and fully variational invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well the invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell plate or laminae the results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material geometry and or effects

the cosserat surface as a shell model theory and finite element formulation abstract relying on the concept of a cosserat continuum the reduction of the three dimensional equations of a shell body to two dimensions is carried out in a direct manner by considering the cosserat continuum to be a two dimensional surface by that a non linear shell theory including transverse shear strains with exact description of the kinematical fields is derived the strain measures are taken to be the first and the second cosserat deformation tensors allowing for an explicit use of a three parametric rotation tensor thus inplane rotations also called drilling degrees of freedom are included in a natural way the structure of the configuration space is discussed and two possible definitions of it are given equipped once with a killing metric and once with an euclidean one a partially mixed variational principle is proposed on the base of which an efficient hybrid finite element formulation which does not exhibit locking phenomena is developed various numerical examples of shell deformations at finite rotations with excellent element performance are presented

stress resultant geometrically exact form of classical shell model and vector like parameterization of constrained finite rotations summary in this work we consider the geometrically exact shell model subjected to 7nite rotations making use of rotation vector parameters for handling the corresponding constrained rotation for smooth shells a modi7cation of such a parameterization which is based on the incremental rotation vector and thus capable of avoiding the singularity problem is also discussed copyright 2001 john wiley sons ltd

an efficient algorithm for the smallest enclosing ball problem in high dimensions abstract consider the problem of computing the smallest enclosing ball of a set of m balls in r n this problem arises in many applications such as location analysis military operations and pattern recognition etc in this paper we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max 0 t and then develop a simple algorithm particularly suitable for problems in high dimensions this algorithm could efficiently handle problems of dimension n up to 10 000 under a moderately large m as well as problems of dimension m up to 10 000 under a moderately large n numerical results are given to show the efficiency of algorithm

adaptive control of arma plants using worst case design by semi infinite optimization this paper presents a new approach to on line control system tuning based on worst case design using semi infinite optimlzation together with a plant uncertainty identification scheme which this approach requires

a barrier function method for minimax problems this paper presents an algorithm based on barrier functions for solving semi infinite minimax problems which arise in an engineering design setting the algorithm bears a resemblance to some of the current interior penalty function methods used to solve constrained minimization problems global convergence is proven and numerical results are reported which show that the algorithm is exceptionally robust and that its performance is comparable while its structure is simpler than that of current first order minimax algorithms

the helicoidal modeling in computational finite elasticity part ii multiplicative interpolation abstract the approximate substitute model of the position and orientation fields over a finite multi coordinate domain is built in a consistent way with the helicoidal modeling of the continuum as proposed in part i for a discrete application of variational principles in computational elasticity the set of the position and orientation referred to as oriento position is made dependent multiplicatively on the nodal values through relative rototranslations and an implicit interpolation formula is written by weighting the relative helices the proposed interpolation scheme is frame invariant and path independent and the resulting weighted average oriento position is obtained numerically a consistent linearization of the model field is carried out by developing explicit formulae for the derivatives up to third order of orthogonal tensors the parent interpolation of the orientation field which can be useful by itself in the context of classical modeling is also discussed

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

on the differentiation of the rodrigues formula and its significance for the vector like parameterization of reissner simo beam theory in this paper we present a systematic way of differentiating up to the second directional derivative i the rodrigues formula and ii the spin rotation vector variation relationship to achieve this goal several trigonometric functions are grouped into a family of scalar quantities which can be expressed in terms of a single power series these results are then applied to the vector like parameterization of reissner simo beam theory enabling a straightforward derivation and leading to a clearer formulation in particular and in contrast with previous formulations a relatively compact and obviously symmetric form of the tangent operator is obtained the paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples copyright 2002 john wiley sons ltd

computational aspects of vector like parametrization of three dimensional finite rotations theoretical and computational aspects of vector like parametrization of three dimensional finite rotations which uses only three rotation parameters are examined in detail in this work the relationship of the proposed parametrization with the intrinsic representation of finite rotations via an orthogonal matrix is clearly identified careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of reissner s non linear beam theory pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2 node three dimensional beam element a number of numerical simulations in three dimensional finite rotation analysis are presented in order to illustrate the proposed approach

some comments on the higher order theories of piezoelectric piezothermoelastic and thermopiezoelectric rods and shells in this note the derivations of the higher order 1 d or 2 d theories are discussed for the dynamic analysis of electroelastic i e piezoelectric piezothermoelastic and thermopiezoelectric structural elements of uniform cross section or uniform thickness certain oversights are clarified concerning the higher order theories including their variational formulation invariant form and uniqueness of solutions that obscure the availability of earlier contributions in the open literature in this respect a higher order theory with some applications by wu et al most recently appeared in this journal int j solids struct 39 2002 5325 is mentioned as one of the examples

analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements this paper adresses the problem of determining upper and lower bounds for the effectivity index on the a posteriori estimate of the error in the finite element method these bounds are given explicitly for a certain concrete estimator for linear elements and unstructured triangular meshes they depend strongly on the geometry of the triangles and relatively weakly on the smoothness of the solution an example shows that the bounds are not over pessimistic in babuska plank and rodriguez 4 detailed numerical experimentation is given

geometrically exact 3d beam theory implementation of a strain invariant finite element for statics and dynamics geometrically exact 3d beam theory has been used as a basis for development of a variety of finite element formulations it has recently become apparent that the important requirement of objectivity of adopted strain measures although provided by the theory itself does not automatically extend to a finite element formulation in this paper we present a new finite element formulation of the geometrically exact 3d beam theory specifically designed to preserve the objectivity of the adopted strain measures in order to do so the current local rotations are interpolated in a manner similar to that adopted in co rotational approaches however no approximations typical for co rotational approaches are introduced into the procedure so in contrast to co rotational formulations the present formulation fully preserves the geometric exactness of the theory a range of numerical examples serves to illustrate the problem and to assess the formulation

strain measures integrability condition and frame indifference in the theory of oriented media this paper is concerned with the appropriate choice of state variables within the continuum model or oriented media it is shown that residual deformation strain and wryness can be considered as such quantities the compatibility conditions for them are derived which make the inverse problem of determining the displacement and director triad fields well posed the principle of frame indifference justifies the use of these quantities as state variables in the free energy density governing and constitutive equations are studied in detail a comparison with the continuum model of crystals with continuously distributed dislocations is provided

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

an algorithm for the inequality constrained discrete min max problem in this paper we discuss an approach using an augmented lagrangian formulation to directly solve the inequality constrained min max problem the algorithm involves a sequential quadratic programming subproblem an adaptive penalty parameter selection rule and a stepsize strategy convergent to unit steps that ensures progress toward optimality and feasibility of the inequality constraints it is shown that the penalty parameter does not grow indefinitely the convergence of the algorithm is established and its numerical effectiveness is demonstrated with test examples

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

superlinearly convergent approximate newton methods for lc 1 optimization problems in the literature the proof of superlinear convergence of approximate newton or sqp methods for solving nonlinear programming problems requires twice smoothness of the objective and constraint functions sometimes the second order derivatives of those functions are required to be lipschitzian in this paper we present approximate newton or sqp methods for solving nonlinear programming problems whose objective and constraint functions have locally lipschitzian derivatives and establishq superlinear convergence of these methods under the assumption that these derivatives are semismooth this assumption is weaker than the second order differentiability the extended linear quadratic programming problem in the fully quadratic case is an example of nonlinear programming problems whose objective functions have semismooth but not smooth derivatives

the helicoidal modeling in computational finite elasticity part iii finite element approximation for non polar media the helicoidal modeling of the continuum as proposed in part i is applied to finite elasticity analyses of simple materials unable of couple stressing first the non polar medium is introduced via a constitutive postulate and results in a sort of constrained medium having the axial vector of the biot stress tensor as a primary unknown field and the statement of polar decomposition of the deformation gradient as a governing equation next the variational formulation is accommodated to the non polar case and the ensuing principle is approximated by the finite element method the nonlinear finite elements have the nodal oriento positions as degrees of freedom and are based on the multiplicative interpolation developed in part ii the interpolation and an analysis methodology based on the multiplicative updating of the kinematical unknowns ensure frame invariant and path independent solutions several examples with either linear or nearly incompressible neo hookean elastic materials attest the performance of the proposed modeling in high deformation problems with large three dimensional rototranslations

a nonlinear augmented lagrangian for constrained minimax problems abstract a novel smooth nonlinear augmented lagrangian for solving minimax problems with inequality constraints is proposed in this paper which has the positive properties that the classical lagrangian and the penalty function fail to possess the corresponding algorithm mainly consists of minimizing the nonlinear augmented lagrangian function and updating the lagrange multipliers and controlling parameter it is demonstrated that the algorithm converges q superlinearly when the controlling parameter is less than a threshold under the mild conditions furthermore the condition number of the hessian of the nonlinear augmented lagrangian function is studied which is very important for the efficiency of the algorithm the theoretical results are validated further by the preliminary numerical experiments for several testing problems reported at last which show that the nonlinear augmented lagrangian is promising

objectivity of strain measures in the geometrically exact three dimensional beam theory and its finite element implementation the paper discusses the issue of discretization of the strainconfiguration relationships in the geometrically exact theory of threedimensional 3d beams which has been at the heart of most recent

parametrized variational principles encompassing compressible and incompressible elasticity abstract a parametrized five field variational principle that can accommodate both compressible and incompressible hyperelasticity is presented the primary variables are mean and deviatoric stresses mean and deviatoric strains and displacements through appropriate selection of parameters the functional of this general principle specializes to those previously presented by atluri reissner herrmann and franca

geometrically non linear method of incompatible modes in application to finite elasticity with independent rotations reference epfl article 102720view record in web of science record created on 2007 04 23 modified on 2016 08 08

generalized monotone line search sqp algorithm for constrained minimax problems in this article non linear minimax problems with general constraints are discussed by means of solving one quadratic programming an improved direction is yielded and a second order correction direction can also be at hand via one system of linear equations so a new algorithm for solving the discussed problems is presented in connection with a special merit function the generalized monotone line search is used to yield the step size at each iteration under mild conditions we can ensure global and superlinear convergence finally some numerical experiments are operated to test our algorithm and the results demonstrate that it is promising

uniform approximation of min max functions by smooth splines in some optimization problems min f 1 f n usually appears as the objective or in the constraint these optimization problems are typically non smooth and so are beyond the domain of smooth optimization algorithms in this paper we construct smooth splines to approximate min f 1 f n uniformly so that such optimization problems can be dealt with as smooth ones

analysis and finite element approximation of compressible and incompressible linear isotropic elasticity based upon a variational principle abstract we propose a variational principle for compressible and incompressible linear isotropic elasticity involving four dependent variables the strain tensor the augmented stress tensor pressure and displacement the variational formulation derived from the principle is analyzed employing a general result due to brezzi finite element methods using the galerkin and sbb methods are shown to converge for a wide family of finite element interpolations

the optimality conditions for generalized minimax programming in this paper we first weaken some assumptions in jiao et al 2005 9 and discuss the continuity and the directional differentiability of the objective function furthermore we investigate the optimality conditions for unconstrained and constrained generalized minimax programming these optimality conditions are mixed ones that include different conditions at different directions which is suitable for the non differentiable objective function for constrained problem we exploit two kinds of analysis methods to obtain some different optimality conditions moreover we show these optimality conditions by some examples

direct and sparse construction of consistent inverse mass matrices general variational formulation and application to selective mass scaling summary classical explicit finite element formulations rely on lumped mass matrices a diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector recently non diagonal mass matrices for explicit finite element analysis fea have received attention due to the selective mass scaling sms technique sms allows larger time step sizes without substantial loss of accuracy however an expensive solution for accelerations is required at each time step in the present study this problem is solved by directly constructing the inverse mass matrix first a consistent and sparse inverse mass matrix is built from the modified hamiltons principle with independent displacement and momentum variables usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix rmm secondly a variational mass scaling technique is applied to the rmm it is based on the penalized hamiltons principle with an additional velocity variable and a free parameter using element wise bases for velocity and a local elimination yields variationally scaled rmm thirdly examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed copyright 2014 john wiley sons ltd

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

the helicoidal modeling in computational finite elasticity part i variational formulation the finite elasticity mechanics of continua capable of a polar description is formulated by an alternative modeling to keeping position and orientation as uncoupled fields the rototranslation between two material particles can be described by a single complex tensorial quantity which is recognized to be orthogonal its linearization gives the characteristic curvature and differential vectors underlying the helicoidal modeling in both the sense of the body geometric description and the evolution of a deforming body after due introduction to dual tensors and rototranslations the polar description of the continuum is addressed with particular care to mixed differentiations of the rototranslation field then a thorough variational framework is established for the most general polar continuum under hyperelasticity hypothesis and the three field two field and one field principles are drawn and linearized the proposed modeling is expected to be profitably exploited in non linear finite element analyses of solids undergoing finite displacements rotations and strains

a smoothing self adaptive levenberg marquardt algorithm for solving system of nonlinear inequalities abstract in this paper we consider the smoothing self adaptive levenberg marquardt algorithm for the system of nonlinear inequalities by constructing a new smoothing function the problem is approximated via a family of parameterized smooth equations h x 0 a smoothing self adaptive levenberg marquardt algorithm is proposed for solving the system of nonlinear inequalities based on the new smoothing function the levenberg marquardt parameter k is chosen as the product of k h k with 0 2 being a positive constant we will show that if h k provides a local error bound which is weaker than the non singularity the proposed method converges superlinearly to the solution for 0 1 while quadratically for 1 2 numerical results show that the new method performs very well for system of inequalities

couple stress based strain gradient theory for elasticity the deformation behavior of materials in the micron scale has been experimentally shown to be size dependent in the absence of stretch and dilatation gradients the size dependence can be explained using classical couple stress theory in which the full curvature tensor is used as deformation measures in addition to the conventional strain measures in the couple stress theory formulation only conventional equilibrium relations of forces and moments of forces are used the couple s association with position is arbitrary in this paper an additional equilibrium relation is developed to govern the behavior of the couples the relation constrained the couple stress tensor to be symmetric and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system on the basis of this modification a linear elastic model for isotropic materials is developed the torsion of a cylindrical bar and the pure bending of a flat plate of infinite width are analyzed to illustrate the effect of the modification

parametrized variational principles for micropolar elasticity abstract a parametrized six field variational principle for micropolar compressible linear elasticity is presented the primary variables are symmetric and skew stresses symmetric and skew strains micropolar rotations and displacements the governing functional is characterized by six free parameters the connection between this formulation and the functionals with relaxed stress symmetry and independent rotations fields proposed by reissner and hughes brezzi for classical non polar linear elasticity is examined it is shown that the hughes brezzi functionals are special cases of the parametrized functional but that the reissner functionals are not the former may be interpreted as a regularization consistent stabilization of the reissner functionals that places them within the framework of micropolar elasticity an eight field parametrized principle that accounts for couple stresses is briefly described in the appendix

the logical content of triangular bases of fuzzy sets in łukasiewicz infinite valued logic abstract continuing to pursue a research direction that we already explored in connection with godel dummett logic and ruspini partitions we show here that ukasiewicz logic is able to express the notion of pseudo triangular basis of fuzzy sets a mild weakening of the standard notion of triangular basis en route to our main result we obtain an elementary logic independent characterisation of triangular bases of fuzzy sets

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

lattice ordered abelian groups and schauder bases of unimodular fans baker beynon duality theory yields a concrete representation of any finitely generated projective abelian lattice ordered group g in terms of piecewise linear homogeneous functions with integer coefficients defined over the support e of a fan a unimodular fan a over s determines a schauder basis of g its elements are the minimal positive free generators of the pointwise ordered group of a linear support functions conversely a schauder basis h of g determines a unimodular fan over its maximal cones are the domains of linearity of the elements of h the main purpose of this paper is to give various representation free characterisations of schauder bases the latter jointly with the de concini procesi starring technique will be used to give novel characterisations of finitely generated projective abelian lattice ordered groups for instance g is finitely generated projective iff it can be presented by a purely lattice theoretical word

mixed variational formulations for continua with microstructure in this paper we obtain mixed variational formulations for the fully linear elastic equilibrium problem of continua with vectorial microstructure by the application of the semi inverse method proposed by ji huan he applications to microcracked and piezoelectric bodies are then investigated

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

a smoothing trust region newton cg method for minimax problem abstract this paper presents a smooth approximate method with a new smoothing technique and a standard unconstrained minimization algorithm in the solution to the finite minimax problems the new smooth approximations only replace the original problem in some neighborhoods of the kink points with a twice continuously differentiable function its gradient and hessian matrix are the combination of the first and the second order derivative of the original functions respectively compared to the other smooth functions such as the exponential penalty function the remarkable advantage of the new smooth function is that the combination coefficients of its gradient and the hessian matrix have sparse properties furthermore the maximal possible difference value between the optimal values of the smooth approximate problem and the original one is determined by a fixed parameter selected previous an algorithm to solve the equivalent unconstrained problem by using the trust region newton conjugate gradient method is proposed in the solution process finally some numerical examples are reported to compare the proposed algorithm with sqp algorithm that implements in matlab toolbox and the algorithm in e polak j o royset r s womersley algorithms with adaptive smoothing for finite minimax problems journal of optimization theory and applications 119 3 2003 459 484 based on the exponential penalty function the numerical results prove that the proved algorithm is efficient

finite element formulation of geometrically exact three dimensional beam theories based on interpolation of strain measures this paper presents a new finite element formulation of the geometrically exact finite strain beam theory the governing equations of the beam element are derived in which the strain vectors are the only unknown functions the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal is enforced to be satisfied at chosen points the solution is found by a collocation algorithm the linearity of the strain space not only simplifies the application of newton s method on the non linear configuration space but also leads to the strain objectivity of the proposed method the accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples c 2003 elsevier b v all rights reserved

coupled thermoelastic shell equations with second sound for high frequency vibrations of temperature dependent materials guided by the three dimensional theory of coupled thermoelasticity with second sound a system of shear deformable shell equations is consistently derived in invariant differential and variational forms for the high frequency vibrations of temperature dependent materials the first part of the paper is concerned with a unified variational principle describing the fundamental equations of thermoelasticity the differential type of variational principle is presented by expressing hamilton s principle for the thermal part of a thermoelastic region and then combining it with its mechanical part in the second part the hierarchic system of non isothermal shell equations is systematically established by use of the variational principle together with mindlin s kinematic hypothesis for shells the system of two dimensional approximate equations which may take account of all the significant mechanical and thermal effects including the temperature dependency of material governs the extensional thickness shear flexural and torsional as well as coupled vibrations of shells of uniform thickness lastly in the third part emphasis is placed on certain cases involving special material geometry and kinematics besides a theorem is devised so as to enumerate the initial and boundary conditions sufficient for the uniqueness in solutions of the system of non isothermal shell equations

an intrinsic beam model based on a helicoidal approximation part ii linearization and finite element implementation the helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space curved and twisted beams undergoing large displacements and finite rotations starting from the governing weak form expressed by the principle of virtual work a consistent linearization is obtained in the following and a novel updated lagrangian finite element implementation is thoroughly discussed the unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences for this purpose meaningful example problems regarding the non linear static response of beams are addressed in the following and the results are compared with those available from the literature furthermore a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry the underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step

a derivative free algorithm for linearly constrained finite minimax problems in this paper we propose a new derivative free algorithm for linearly constrained finite minimax problems due to the nonsmoothness of this class of problems standard derivative free algorithms can locate only points which satisfy weak necessary optimality conditions in this work we define a new derivative free algorithm which is globally convergent toward standard stationary points of the finite minimax problem to this end we convert the original problem into a smooth one by using a smoothing technique based on the exponential penalty function of kort and bertsekas this technique depends on a smoothing parameter which controls the approximation to the finite minimax problem the proposed method is based on a sampling of the smooth function along a suitable search direction and on a particular updating rule for the smoothing parameter that depends on the sampling stepsize numerical results on a set of standard minimax test problems are reported

locking free finite element methods for linear and nonlinear elasticity in 2d and 3d abstract the uniform convergence of finite element approximations based on a modified hu washizu formulation for the nearly incompressible linear elasticity is analyzed we show the optimal and robust convergence of the displacement based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements these choices include bases that are well known as well as newly constructed bases starting from a suitable three field problem we extend our dependent three field formulation to geometrically nonlinear elasticity with saint venant kirchhoff law additionally an dependent three field formulation for a general hyperelastic material model is proposed a range of numerical examples using different material laws for small and large strain elasticity is presented

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

finite element simulation of dynamic strain localization a multi scale problem abstract a finite element procedure for the post localization analysis of elasto plastic solids is developed to ensure unique solutions the duvaut lions visco plastic regularization procedure 1 is implemented a bifurcation analysis of the underlying backbone elasto plastic material is performed to locate the shear band and to define its orientation the width of the shear band is assumed to be much smaller than the characteristic element size h to capture the structure of the shear band the kinematics is enriched by incorporating additional degrees of freedom in a patch within the element and overlying the shear band within each localized element compatibility is ensured between the strain fields inside and outside the patch a petrov galerkin type procedure to account for the narrow width of the patch is implemented the results indicate formation of mesh and patch invariant shear bands finally the effects of varying material parameters are studied the results are found to be consistent with known localization characteristics

fuzzy transforms theory and applications the technique of direct and inverse fuzzy f transforms of three different types is introduced and approximating properties of the inverse f transforms are described all three types of the direct f transform are transformations from a function space to a finite dimensional vector space the first ordinary f transform is constructed on the basis of the ordinary algebra of reals while the other two types of the f transform are constructed on the basis of residuated lattice the core idea of the technique of f transforms is a fuzzy partition of a universe into fuzzy subsets factors clusters granules etc we claim that for a sufficient representation of a function defined on this universe we may consider its average values over fuzzy subsets from the partition thus a function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values a number of theorems establishing best approximation properties of the inverse f transforms are proved in fact three types of the inverse f transform are the best approximations in average from below and from above respectively as one of many possible applications we present a method of image compression and reconstruction on the basis of the f transform

feasible generalized monotone line search sqp algorithm for nonlinear minimax problems with inequality constraints in this paper the nonlinear minimax problems with inequality constraints are discussed and a sequential quadratic programming sqp algorithm with a generalized monotone line search is presented at each iteration a feasible direction of descent is obtained by solving a quadratic programming qp to avoid the maratos effect a high order correction direction is achieved by solving another qp as a result the proposed algorithm has global and superlinear convergence especially the global convergence is obtained under a weak mangasarian fromovitz constraint qualification mfcq instead of the linearly independent constraint qualification licq at last its numerical effectiveness is demonstrated with test examples

parametrized lagrange multiplier method and construction of generalized mixed variational principles for computational mechanics this paper provides a general means called the parametrized lagrange multiplier method plm for constructing new variational principles from any existing one plm is more powerful than the traditional lagrange multiplier tlm in many aspects it can explain many theoretical problems and do plenty which have been troublesome before in mathematics plm could be considered as an approach to solve a subset of the inverse problem of variational calculus in elasticity the variational principle constructed by plm is called the generalized mixed variational principle gmvp featuring some parameter functions called the splitting factors and playing an important role in overcoming the ill conditioned problems in finite element analysis this paper introduces plm and gmvp while their applications such as how to deal with the ill conditioned problems by means of gmvp will be discussed some time later in other papers

shell elements with drilling degree of freedoms based on micropolar elasticity theory based on the theory of micropolar elasticity new degenerated shell elements with drilling degree of freedoms are presented the proper stiffness on the drilling degree of freedom is derived and no spurious modes are encountered in these elements the implementation of these new shell elements on general structural finite element programs has many advantages especially for the analysis of a folded shell or the treatment of the twist moment normal to the shell several numerical examples are carried out to demonstrate the accuracy and applicability of the present elements the effects of the coupling factor and the body moment induced in magneto solid mechanics are also studied

approximate direct search minimax circuit optimization a direct search optimization strategy involving pattern searches pattern moves and a simplex algorithm has been applied to a number of frequency domain circuit problems we show that an approximate minimax result can be obtained with our simple approach which includes using a modified minimax error function in the examples attempted the method comes quite close to the accuracy if not the efficiency of true minimax optimizers and yields an accuracy as good as or better than a least pth p 10 gradient optimizer the method is broadly appropriate wherever it is difficult or inconvenient to calculate the gradients required for conventional minimax optimization

a variationally consistent αfem vcαfem for solution bounds and nearly exact solution to solid mechanics problems using quadrilateral elements a variationally consistent alpha finite element method vc fem for quadrilateral isoparametric elements is presented by constructing an assumed strain field in which the gradient of the compatible strain field is scaled with a free parameter the assumed strain field satisfies the orthogonal condition and the hellinger reissner variational principle is used to establish the discretized system of equations it is shown that the strain energy is a second order continuous function of and the vc fem can produce both lower and upper bounds to the exact solution in the strain energy for all elasticity problems by choosing a proper 0 upper based on this bound property an exact approach has been devised to give an ultra accurate solution that is very close to the exact one in the strain energy furthermore the exact approach also works well for volumetric locking problems by simply replacing the strain gradient matrix by a stabilization matrix in addition a regularization approach has also been suggested to overcome possible hourglass instability intensive numerical studies have been conducted to confirm the properties of the present vc fem and a very good performance has been found in comparing to a large number of existing fem models copyright 2010 john wiley sons ltd

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems