elastoplastic and contact analysis based on consistent dynamic formulation of co rotational planar elements abstract co rotational formulation is one of the approaches applicable to geometrically nonlinear problems in structural analysis based on the assumptions of small degree of strain and large displacement the cr formulation allows an accurate geometrically nonlinear structural analysis in this paper an improved cr formulation for dynamic nonlinear analysis is developed for the planar element also extension of the local formulation is conducted for an elastoplastic problem a simplified approach for planar elastoplastic analyses is proposed by maintaining the original feature of the cr formulation moreover a modified approach in the local formulation is suggested in order to improve the level of accuracy in the plastic state contact analysis using the lagrange multiplier is then implemented during the present validation procedure of the proposed approaches four different planar elements are employed those elements are investigated with regard to efficiency and accuracy in a general geometrically nonlinear and a geometrically nonlinear elastoplastic problem respectively it is found that the present dynamic formulations gives both accuracy and consistency for all types of the plane element also comparison regarding the choice of the local formulation for the elastoplastic problem is systematically conducted and demonstrated

co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

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

higher order moreau s sweeping process mathematical formulation and numerical simulation in this paper we present an extension of moreau s sweeping process for higher order systems the dynamical framework is carefully introduced qualitative dissipativity stability existence regularity and uniqueness results are given the time discretization of these nonsmooth systems with a time stepping algorithm is also presented this differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary slackness variables applications of such high order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

stability and robustness for saddle point dynamics through monotone mappings abstract motivated by recent interest in saddle point dynamics where given a convex in x and concave in y function trajectories follow the steepest descent in x and the steepest ascent in y and where convergence of trajectories to saddle points is desired this note revisits the maximal monotone mapping approach to saddle point dynamics mildly improves one convergence result and proposes new results on the robustness of pointwise asymptotic stability of the set of saddle points the results apply to nonsmooth convex concave functions and constraints and as a special case to projected saddle point dynamics

on a new class of differential variational inequalities and a stability result this paper addresses a new class of differential variational inequalities that have recently been introduced and investigated in finite dimensions as a new modeling paradigm of variational analysis to treat many applied problems in engineering operations research and physical sciences this new subclass of general differential inclusions unifies ordinary differential equations with possibly discontinuous right hand sides differential algebraic systems with constraints dynamic complementarity systems and evolutionary variational systems the purpose of this paper is two fold firstly we show that these differential variational inequalities when considering slow solutions and the more general level of a hilbert space contain projected dynamical systems another recent subclass of general differential inclusions this relation follows from a precise geometric description of the directional derivative of the metric projection in hilbert space which is based on the notion of the quasi relative interior secondly we are concerned with stability of the solution set to this class of differential variational inequalities here we present a novel upper set convergence result with respect to perturbations in the data including perturbations of the associated set valued maps and the constraint set here we impose weak convergence assumptions on the perturbed set valued maps use the monotonicity method of browder and minty and employ mosco convergence as set convergence also as a consequence we obtain a stability result for linear complementarity systems

passivity and complementarity this paper studies the interaction between the notions of passivity of systems theory and complementarity of mathematical programming in the context of complementarity systems these systems consist of a dynamical system given in the form of state space representation and complementarity relations we study existence uniqueness and nature of solutions for this system class under a passivity assumption on the dynamical part a complete characterization of the initial states and the inputs for which a solution exists is given these initial states are called consistent states for the inconsistent states we introduce a solution concept in the framework of distributions

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

distributed algorithm for solving convex inequalities in this note a distributed subgradient based algorithm is proposed for continuous time multi agent systems to search a feasible solution to convex inequalities the algorithm involves each agent achieving a state constrained by its own inequalities while exchanging local information with other agents under a time varying directed communication graph with the validity of a mild connectivity condition associated with the communication graph it is shown that all agents will reach agreement asymptotically and the consensus state is in the solution set of the inequalities furthermore the method is also extended to solving the distributed optimization problem of minimizing the sum of local objective functions subject to convex inequalities simulation examples are presented to demonstrate the effectiveness of the theoretical results

absolute stability and the lagrange dirichlet theorem with monotone multivalued mappings abstract this note presents an extension of the absolute stability problem and of the lagrange dirichlet theorem when the nonlinearities entering the model are considered within the class of monotone multivalued mappings consequently including operators with piecewise linear graphs that may represent physical effects like coulomb friction dead zones saturations elasto plasticity and unilateral constraints

coupled analytical sensitivity analysis and optimization of three dimensional nonlinear aeroelastic systems we consider the problem of optimizing for steady state conditions a given nonlinear aeroelastic system by varying both aerodynamic and structural parameters we model the structure by e nite elements and predict the aerodynamic loads by a three dimensional e nite volume approximation of the euler equations we present a complete optimization methodology whose key components are a computer aided geometric design method for representing the design an analytical approach for sensitivity analysis a gradient based optimization algorithm and two staggered schemes for evaluating the aeroelastic responses and solving the coupled sensitivity equations we illustrate our methodology and demonstrate its potential with various aeroelastic optimizations of idealized and builtup wing structures

set valued sliding mode control of uncertain linear systems continuous and discrete time analysis in this paper we study the closed loop dynamics of linear time invariant systems with feedback control laws that are described by set valued maximal monotone maps the class of systems considered in this work is subject to both unknown exogenous disturbances and parameter uncertainty it is shown how the design of conventional sliding mode controllers can be achieved using maximal monotone operators which include the set valued signum function two cases are analyzed continuous time and discrete time controllers in both cases well posedness together with stability results are presented in discrete time we show how the implicit scheme proposed for the selection of control actions makes sense resulting in the chattering effect being almost suppressed even with uncertainty in the system

a co rotational quasi conforming 4 node resultant shell element for large deformation elasto plastic analysis abstract a co rotational quasi conforming formulation of a 4 node stress resultant shell element is presented for non linear analysis of plate and shell structures the tangent stiffness matrix in this quasi conforming formulation is explicitly integrated this makes the element computationally efficient in incremental non linear analysis it includes drilling degrees of freedom which improves membrane behavior and allows the modeling of stiffened plates and shells it is also free of shear locking behavior the formulation of the geometrical stiffness is derived using the full definition of green strain tensor the inclusion of the bending moment and transverse shear resultant forces in the geometric stiffness allows effective analysis of stability problems of moderately thick plates and shells the stresses are accurately taken at the nodal points without extrapolation the plasticity is traced by applying the von mises yield condition and prandtl reuss flow rule to discrete points through the thickness the multi layered approach is based on equally spaced stations including extreme fibers a modified trapezoidal rule is used for the numerical integration of the constitutive relation in the plasticity part numerous tests are carried out for the non linear validation of present 4 node shell element and the results are in good agreement with references

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

spectral factorization by optimal gain iteration an iterative algorithm for spectral factorization is presented the algorithm has the form of a frequency domain version of the newton raphson solution of the corresponding riccati equation although results are established without reference to an underlying state variable model application is made to a distributed filtering problem

a newton raphson method for moving average spectral factorization using the euclid algorithm an implementation of the newton raphson approach to compute the minimum phase moving average spectral factor of a finite positive definite correlation sequence is presented each step in the successive approximation method involves a system of linear equations that is solved using either the levinson algorithm backwards the jury stability test or a symmetrized version of the euclid algorithm various properties of the newton raphson map are studied the algorithm is generalized to other symmetries other than with respect to the unit circle the special case of the symmetry with respect to the imaginary axis is presented and related to the routh hurwitz stability test for continuous time transfer function

drag minimization based on the navier stokes equations using a newton krylov approach a methodology is presented for performing numerical aerodynamic shape optimization based on the three dimensional reynolds averaged navier stokes rans equations an initial multiblock structured mesh is first fit with b spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on b spline surfaces the rans equations and the one equation spalart allmaras turbulence model are solved in a fully coupled manner using an efficient parallel newton krylov algorithm with approximate schur preconditioning gradient evaluations are performed using the discrete adjoint approach with analytical differentiation of the discrete flow and mesh movement equations the overall methodology remains robust even in the presence of large shape changes several examples of lift constrained drag minimization are provided including a study of the common research model wing geometry a wing body tail geometry with a prescribed spanwise load distributi

optimal vibration control of curved beams using distributed parameter models abstract the design of linear quadratic optimal controller using spectral factorization method is studied for vibration suppression of curved beam structures modeled as distributed parameter models the equations of motion for active control of the in plane vibration of a curved beam are developed firstly considering its shear deformation and rotary inertia and then the state space model of the curved beam is established directly using the partial differential equations of motion the functional gains for the distributed parameter model of curved beam are calculated by extending the spectral factorization method moreover the response of the closed loop control system is derived explicitly in frequency domain finally the suppression of the vibration at the free end of a cantilevered curved beam by point control moment is studied through numerical case studies in which the benefit of the presented method is shown by comparison with a constant gain velocity feedback control law and the performance of the presented method on avoidance of control spillover is demonstrated

sensitivity of complex internally coupled systems a method is presented for computing sensitivity derivatives with respect to independent input variables for complex internally coupled systems while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis the method entails two alternative algorithms the first is based on the classical implicit function theorem formulated on residuals of governing equations and the second develops the system sensitivity equations in a new form using the partial local sensitivity derivatives of the output with respect to the input for each part of the system a few application examples are presented to illustrate the discussion the method has potential to answer the what if questions by presenting engineers wigi sensitivity information on design tradeoffs to guide human judgment and formal optimization in addition the method is compatible with the modern technology of distributed computing as well as traditional division of design tasks among groups of specialists in the design process the capability to quantify the effects of proposed design changes may provide the basis for a mathematical model of design

on the equivalence between complementarity systems projected systems and differential inclusions in this note we prove the equivalence under appropriate conditions between several dynamical formalisms projected dynamical systems two types of differential inclusions and a class of complementarity dynamical systems each of these dynamical systems can also be considered as a hybrid dynamical system this work both generalizes previous results and sheds some new light on the relationship between known formalisms besides it exclusively uses tools from convex analysis

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

switching relay and complementarity systems a tutorial on their well posedness and relationships this paper reviews the relationships between switching systems defined from a partition of the state space into convex cells and relay or complementarity dynamical systems which are other classes of discontinuous systems well posedness results i e results on the existence and the uniqueness of solutions for different classes of relay and complementarity systems which are also switching systems are presented the reverse issue when can a switching system be rewritten equivalently as a relay or a complementarity system is also tackled many examples from mechanics circuits and biology illustrate the developments throughout the paper the paper focuses on systems with continuous solutions i e with no state jumps convexity is the central property

robust output regulation of strongly passive linear systems with multivalued maximally monotone controls the use of multivalued controls derived from a special maximally monotone operator are studied in this paper starting with a strongly passive linear system with possible parametric uncertainty and external disturbances a multivalued control law is derived ensuring regulation of the output to a desired value the methodology used falls in a passivity based control context where we study how the multivalued control affects the dissipation equation of the closed loop system from which we derive its robustness properties finally some numerical examples together with implementation issues are presented to support the main result

quadratic optimal control of linear complementarity systems first order necessary conditions and numerical analysis this article is dedicated to the analysis of quadratic optimal control of linear complementarity systems lcss which are a class of strongly nonlinear and nonsmooth dynamical systems necessary first order conditions are derived that take the form of an lcs with inequality constraints hence are numerically tractable sufficiency is proved in a specific sense numerical examples illustrate the theoretical developments and demonstrate the efficiency of the complementarity approach

coupled adjoint based sensitivities in large displacement fluid structure interaction using algorithmic differentiation summary a methodology for the calculation of gradients with respect to design parameters in general fluid structure interaction problems is presented it is based on fixed point iterations on the adjoint variables of the coupled system using algorithmic differentiation this removes the need for the construction of the analytic jacobian for the coupled physical problem which is the usual limitation for the computation of adjoints in most realistic applications the formulation is shown to be amenable to partitioned solution methods for the adjoint equations it also poses no restrictions to the nonlinear physics in either the fluid or structural field other than the existence of a converged solution to the primal problem from which to compute the adjoints we demonstrate the applicability of this procedure and the accuracy of the computed gradients on coupled problems involving viscous flows with geometrical and material non linearities in the structural domain this article is protected by copyright all rights reserved

on reflecting boundary problem for optimal control this paper deals with mayer s problem for controlled systems with reflection on the boundary of a closed subset k the main result is the characterization of the possibly discontinuous value function in terms of a unique solution in a suitable sense to a partial differential equation of hamilton jacobi bellman type

moreau s decomposition in banach spaces moreau s decomposition is a powerful nonlinear hilbertian analysis tool that has been used in various areas of optimization and applied mathematics in this paper it is extended to reflexive banach spaces and in the context of generalized proximity measures this extension unifies and significantly improves upon existing results

higher order subiteration free staggered algorithm for nonlinear transient aeroelastic problems the objective of this note is to present a new subiteration free implicit implicit staggered algorithm that has the same computational complexity as the css procedure and yet delivers a superior time accuracy that is similar to that of a monolithic implicit scheme or a strongly coupled full subiterations partitioned method hence this algorithm retains the computational efficiency and implementation advantages of partitioned mthods while offering the higher time accuracy of fully coupled implicit schemes

a unified co rotational framework for solids shells and beams abstract the paper describes a unified framework for applying the co rotational method to the analysis of solids shells and beams the general method stems from an unusual application of the technique which involves solid elements the proposed framework allows a formulation that is simpler than many of the earlier procedures and in addition gives a direct indication of the terms in the tangent stiffness which may be ignored

continuum modeling of flexible structures with application to vibration control in this paper we consider the construction of hybrid models for flexible structures including both the natural spatially distributed dynamics of low mass density structures and the lumped models associated with rigid body dynamics for the purposes of active control of structural vibrations we argue that by using transform methods the standard approach to transfer function or mechanical impedance modeling can be extended to provide a complete formulation of a hybrid model with localized control we proceed to give a systematic procedure for obtaining the required transfer functions and green s functions for the hybrid model dynamics consisting of one dimensional elastic elements such as beams rods and cables together with rigid body lumped models we focus on a well known family of models for elastic elements together with various reductions and indicate the construction of well posed state space models for these systems using the resulting state space we next demonstrate the construction of a complete frequency domain characterization of the elemental system response using transfer functions and green s functions hybrid constructions are discussed for various interconnections of distributed and lumped elements and a simple illustrative example is given we highlight the extent to which the required computations can be performed automatically on a digital computer using a computer algebra system

aeroelastic design optimization for laminar and turbulent flows abstract the design of flexible structures undergoing aeroelastic deformations is a challenging task in particular if the prediction of the fluid loads and the evaluation of the aerodynamic performance criteria require accounting for laminar and turbulent effects this paper presents a general optimization methodology for fluid structure interaction problems based on turbulent flow models the structure is modeled via a geometrically nonlinear finite element method the flow field is computed by solving a finite volume approximation of the navier stokes equations on moving grids augmented by turbulence models the global design sensitivity equations are presented and solution methods for computing the numerically consistent and approximated design sensitivities are introduced the accuracy of the sensitivity analysis methods are studied by numerical examples for three dimensional problems the potential of the overall optimization methodology is illustrated by the shape and thickness optimization of a realistic wing the numerical examples suggest that the derivatives of the turbulence variables can be neglected in the sensitivity analysis without noticeable errors comparing the optimization results for euler and navier stokes flow models shows the importance of accounting for viscous laminar and turbulent effects for fine tuning the design and obtaining reliable optimization results

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

linear complementarity systems we introduce a new class of dynamical systems called linear complementarity systems the time evolution of these systems consists of a series of continuous phases separated by events which cause a change in dynamics and possibly a jump in the state vector the occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming the framework we describe is suitable for certain situations in which both differential equations and inequalities play a role for instance in mechanics electrical networks piecewise linear systems and dynamic optimization we present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions

on constrained steady state regulation dynamic kkt controllers this technical note presents a solution to the problem of regulating a general nonlinear dynamical system to an economically optimal operating point the system is characterized by a set of exogenous inputs as an abstraction of time varying loads and disturbances the economically optimal operating point is implicitly defined as a solution to a given constrained convex optimization problem which is related to steady state operation the system outputs and the exogenous inputs represent respectively the decision variables and the parameters in the optimization problem the proposed solution is based on a specific dynamic extension of the karush kuhn tucker optimality conditions for the steady state related optimization problem which is conceptually related to the continuous time arrow hurwicz uzawa algorithm furthermore it can be interpreted as a generalization of the standard output regulation problem with respect to a constant reference signal

well posedness stability and invariance results for a class of multivalued lur e dynamical systems this paper analyzes the existence and uniqueness issues in a class of multivalued lur e systems where the multivalued part is represented as the subdifferential of some convex proper lower semicontinuous function through suitable transformations the system is recast into the framework of dynamic variational inequalities and the well posedness existence and uniqueness of solutions is proved stability and invariance results are also studied together with the property of continuous dependence on the initial conditions the problem is motivated by practical applications in electrical circuits containing electronic devices with nonsmooth multivalued voltage current characteristics and by state observer design for multivalued systems

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

the construction of free free flexibility matrices for multilevel structural analysis abstract this article considers a generalization of the classical structural flexibility matrix it expands on previous papers by taking a deeper look at computational considerations at the substructure level direct or indirect computation of flexibilities as influence coefficients has traditionally required pre removal of rigid body modes by imposing appropriate support conditions mimicking experimental arrangements with the method presented here the flexibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free free stiffness matrix this generalized inverse preserves the stiffness spectrum the definition is element independent and only involves access to the stiffness generated by a standard finite element program and the separate construction of an orthonormal rigid body mode basis the free free flexibility has proven useful in special application areas of finite element structural analysis notably massively parallel processing model reduction and damage localization it can be computed by solving sets of linear equations and does not require processing an eigenproblem or performing a singular value decomposition if substructures contain thousands of d o f exploitation of the stiffness sparseness is important for that case this paper presents a computation procedure based on an exact penalty method and a projected rank regularized inverse stiffness with diagonal entries inserted by the sparse factorization process these entries can be physically interpreted as penalty springs this procedure takes advantage of the stiffness sparseness while forming the full free free flexibility or a boundary subset and is backed by an in depth null space analysis for robustness

on the choice of the linear element for corotational triangular shells the corotational formulation for triangular thin shell elements presented in a eriksson c pacoste element formulation and numerical techniques for stability problems in shells comput methods

unsteady euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis an euler solution algorithm is presented for unsteady aerodynamic analysis of complex aircr aft configurations the flow solver involves a multistage runge kutta time stepping scheme that uses a finite volume spatial discretization on an unstructured grid made up of tetrahedra a significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft the mesh algorithm is a general procedure that can treat realistic motions and deformations of complex aircraft configurations steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the euler solver and dynamic mesh algorithm the unsteady flow results were obtained for the aircraft oscillating harmonically in a complete vehicle bending mode effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated the paper presents descriptions of the euler solver and dynamic mesh algorithm along with results that assess the capability

continuous time integral dynamics for a class of aggregative games with coupling constraints we consider continuous time equilibrium seeking in a class of aggregative games with strongly convex cost functions and affine coupling constraints we propose simple semidecentralized integral dynamics and prove their global asymptotic convergence to a variational generalized aggregative or nash equilibrium the proof is based on lyapunov arguments and invariance techniques for differential inclusions

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

scalable parallel approach for high fidelity steady state aeroelastic analysis and adjoint derivative computations aeroelastic systems achieve the best performance when the aerodynamic shape and structural sizing are optimized concurrently but such an optimization is challenging when high fidelity aerodynamic and structural models are required this paper addresses this challenge through several significant improvements fully coupled newton krylov methods are presented for the solution of aerostructural systems and for the corresponding adjoint systems the coupled adjoint method presented can compute gradients with respect to thousands of multidisciplinary design variables accurately and efficiently this is enabled by several improvements in the computation of the multidisciplinary terms in the coupled adjoint the parallel scalability of the methods is demonstrated for a full aircraft configuration using an euler computational fluid dynamics model with more than 8 106 state variables and a detailed structural finite element model of the wing with more than 1 106 degrees of freedom the coupled newton krylov metho

a simplified co rotational method for quadrilateral shell elements in geometrically nonlinear analysis summary this paper presents a simplified co rotational formulation for quadrilateral shell elements inheriting the merit of element independence from the traditional co rotational approach in literature with the objective of application to nonlinear analysis of civil engineering structures the authors further simply the formulation of the geometrical stiffness using the small strain assumption which is valid in the co rotational approach with the warping effects considered as eccentricities compared with the traditional element independent co rotational method the projector is neglected both in the tangent stiffness matrix and the internal force vector for simplicity in formulation meanwhile a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications

partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes summary this work presents a partitioned finite element formulation for flexible multibody systems based on the floating frame ff approach under the assumption of small deformations but arbitrarily large rotations of the bodies in classical ff of reference methods deformational modes are normally computed by modal analysis in this approach free floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non linear finite rotations in this way all deformational modes are retained and no modal selection is needed the main difference between this work and a classical ff of reference formulation is an algebraic separation of pure deformational modes from rigid body motions the proposed methodology presents the following advantages first the position and orientation of the ff has no restriction and can be freely located in the body with identical results second the formulation uses only the linear finite element matrices of a classical vibration problem hence they can be easily obtained from linear fem packages third no selection of modes is needed all deformational modes are retained through the filtering process and finally thanks to the use of localized lagrangian multipliers llm a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers copyright 2014 john wiley sons ltd

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

variational formulation in the geometrically nonlinear thin elastic shell theory abstract the variational formulation for thin elastic shells undergoing large deflections is discussed no restrictions are imposed on the magnitude of the rotational part of the deformation gradient yet it is assumed that the strains remain small everywhere in the shell ten functional and associated variational principles are derived including the hu washizu the hellinger reissner the generalized complementary energy and the stationary potential energy principles the total lagrangian description tld is exclusively used