finite element multiple mode approach to nonlinear free vibrations of shallow shells two finite element fe modal formulations for large amplitude free vibration of isotropic and arbitrary laminated composite shallow shells are presented the system equation of motion is formulated first in the physical structural node degrees of freedom dof then the system is transformed into two distinctly different sets of general duffing type modal equations based on 1 modal amplitudes of coupled linear bending and in plane modes where in plane inertia is included in the formulation and 2 modal amplitudes of linear bending modes only where the in plane inertia is neglected multiple modes and the first order transverse shear deformation are considered in the formulations a shallow shell finite element is developed as an extension from the triangular mindlin min3 plate element with the improved shear correction factor by tessler time numerical integration is employed to determine the nonlinear periodic frequency characteristics the inaccuracy in characterizing a shallow shell response with coupled linear bending and in plane modes is demonstrated and discussed by comparing with the fe solution in structural node dof study cases include isotropic and composite panels of different shallow shell geometries

semilinear differential inclusions via weak topologies abstract the paper deals with the multivalued initial value problem x a t x x f t x for a a t a b x a x 0 in a separable reflexive banach space e the nonlinearity f is weakly upper semicontinuous in x and the investigation includes the case when both a and f have a superlinear growth in x we prove the existence of local and global classical solutions in the sobolev space w 1 p a b e with 1 p introducing a suitably defined lyapunov like function we are able to investigate the topological structure of the solution set our main tool is a continuation principle in frechet spaces and we prove the required pushing condition in two different ways some examples complete the discussion

on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

two point b v p for multivalued equations with weakly regular r h s abstract a two point boundary value problem associated to a semilinear multivalued evolution equation is investigated in reflexive and separable banach spaces to this aim an original method is proposed based on the use of weak topologies and on a suitable continuation principle in frechet spaces lyapunov like functions are introduced for proving the required transversality condition the linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one some applications are given to the study of periodic and floquet boundary value problems of partial integro differential equations and inclusions appearing in dispersal population models comparisons are included with recent related achievements

decision analysis under ambiguity abstract in selecting the preferred course of action decision makers are often uncertain about one or more probabilities of interest the experimental literature has ascertained that this uncertainty ambiguity might affect decision makers preferences then the decision maker might wish to incorporate ambiguity aversion in the analysis we investigate the modeling ambiguity attitudes in the solution of decision analysis problems through functionals well established in the decision theory literature we obtain the multiple event problems for subjective expected utility smooth ambiguity and maximin decision makers this allows us to establish the conditions under which these alternative decision makers face equivalent problems results for certainty equivalents and risk premia in the presence of both risk and ambiguity aversion are obtained a recent generalization of the classical arrow pratt quadratic approximation allows us to quantify the portions of a premium due to risk plxinsert and to ambiguity aversion the numerical implementation of the objective functions is addressed showing that all functionals can be estimated at no additional burden through monte carlo simulation the well known carter racing case study is addressed quantitatively to demonstrate the findings

asymptotic boundary value problems in banach spaces abstract a continuation principle is given for solving boundary value problems on arbitrary possibly infinite intervals to caratheodory differential inclusions in banach spaces for this aim the appropriate fixed point index is defined to condensing decomposable multivalued operators in frechet spaces this index extends and unifies the one for compact maps in andres et al trans amer math soc 351 1999 4861 4903 as well as the one for operators in banach spaces in bader ph d thesis university of munich 1995 as an application we prove the existence of an entirely bounded solution of a semilinear evolution inclusion

using aeroelastic modes for nonlinear panel flutter at arbitrary supersonic yawed angle it is commonly accepted that six in vacuo natural modes are needed for converged limit cycle oscillations of isotropic rectangular plates exposed to supersonic flow at zero yaw angle to the principle panel length for isotropic or orthotropic rectangular plates under an arbitrary nonzero yawed supersonic flow then 36 or 6 x 6 natural modes are needed for laminated anisotropic rectangular plates even at zero yaw angle 36 or fewer natural modes are needed to deal with such a large number of modes is computationally costly for flutter analysis causing complexity and difficulty in designing controllers for flutter suppression a thorough examination and understanding of the panel limit cycle behavior leads to the use of aeroelastic modes for supersonic nonlinear panel flutter analysis the system equations of motion are formulated first in structural node degrees of freedom aeroelastic modes are selected and determined and the system equations is expressed in the aeroelastic modal coordinates limit cycle amplitudes are then determined using numerical integration examples show that the number of modes could be greatly reduced by using aeroelastic modes for determining limit cycle oscillations of isotropic or anisotropic composite rectangular plates at zero or an arbitrary yawed flow angle only two aeroelastic modes are needed but six to seven aeroelastic modes are needed for designing controllers for flutter suppression

nonlinear boundary value problems for multivalued differential equations in banach spaces with f j x x 0 xmultivalued map j a b compact real interval x banach space a t x is a continuous operator on x for each t x e j x x l c j x x is a linear continuous operator from the space of all continuous functions x j x whose range is contained in x h c j x x is a continuous operator nonlinear in general such problems have been studied repeatedly in the literature with different hypotheses on a f l h the pioneering work with conditions similar to the ones used in the present paper but for ordinary differential equations is the note by scrucca l where the operator a was independent from the state variable x e x anichini 2 has studied analogous problems in the context of ordinary differential systems in ir in which the operator a also depends on x e ir in the case of multivalued differential systems kartsatos 3 has also considered boundary value problems for v valued differential equations but over an unbounded time interval zecca and zezza 4 have extended the work of kartsatos to differential equations in banach spaces in both 3 and 4 the operator a is dependent only on t e j recently papageorgiu 5 has established the existence of mild solutions on a compact interval with the operator a depending only on t e j but in general is unbounded the fundamental tools used in the existence proofs of all above mentioned works are essentially fixed point theorems schauder s theorem in 11 eilenberg montgomery s theorem in 2 ky fan s theorem in 3 4 5 here we use a fixed point theorem due to martelli 6 the idea of the present paper has originated from the study of an analogous problem examined by anichini and conti 7 for ordinary differential systems in m and carbone et al 8 for multivalued differential systems again in ir

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

a smooth model of decision making under ambiguity we propose and axiomatize a model of preferences over acts such that the decision maker prefers act f to act g if and only if e e u f e e u g where e is the expectation operator u is a vn m utility function is an increasing transformation and is a subjective probability over the set of probability measures that the decision maker thinks are relevant given his subjective information a key feature of our model is that it achieves a separation between ambiguity identified as a characteristic of the decision maker s subjective information and ambiguity attitude a characteristic of the decision maker s tastes we show that attitudes towards risk are characterized by the shape of u as usual while attitudes towards ambiguity are characterized by the shape of we also derive x 1 e x as the special case of constant ambiguity aversion ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures this characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by epstein zhang 2001 and ghirardato marinacci 2002 one advantage of this model is that the welldeveloped machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes the model is also distinct from many in the literature on ambiguity in that allows smooth rather than kinked indifference curves this leads to different behavior and improved tractability while still sharing the main features e g ellsberg s paradox etc the maxmin eu model e g gilboa and schmeidler 1989 with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion two illustrative applications to portfolio choice are offered

an improved variational method for finite element stress recovery and a posteriori error estimation abstract a new variational formulation is presented which serves as a foundation for an improved finite element stress recovery and a posteriori error estimation in the case of stress predictions interelement discontinuous stress fields from finite element solutions are transformed into a c 1 continuous stress field with c 0 continuous stress gradients these enhanced results are ideally suited for error estimation since the stress gradients can be used to assess equilibrium satisfaction the approach is employed as a post processing step in finite element analysis the variational statement used herein combines discrete least squares penalty constraint and curvature control functionals thus enabling automated recovery of smooth stresses and stress gradients the paper describes the mathematical foundation of the method and presents numerical examples including stress recovery in two dimensional structures and built up aircraft components and error estimation for adaptive mesh refinement procedures

a posteriori error analysis of the linked interpolation technique for plate bending problems we develop a posteriori error estimates for the so called linked interpolation technique to approximate the solution of plate bending problems we show that the proposed residual based estimator is both reliable and efficient

continuity compactness and degree theory for operators in systems involving p laplacians and inclusions the study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in sobolev spaces we show that under natural assumptions this operator has the properties which allow to apply degree theory fixed point index for multivalued maps more precisely this operator is upper semicontinuous and compact with nonempty convex compact values for the particular case of systems involving p laplacians we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available

a bayesian approach to managing learning curve uncertainty this paper introduces a bayesian decision theoretic model of optimal production in the presence of learning curve uncertainty the well known learning curve model is extended to allow for random variation in the learning process with uncertainty regarding some parameter of the variation a production run generates excess value above its current revenue for a bayesian manager in two ways it pushes the firm further along the learning curve increasing the likelihood of lower costs for future runs and it provides information through the observed costs that reduces the uncertainty regarding the rate at which costs are decreasing we provide conditions under which one of the classical deterministic learning curve results namely that optimal production exceeds the myopic level carries over to the extended framework we demonstrate that another classical deterministic learning curve result namely that optimal production increases with cumulative production does not hold in the bayesian setting

erratum and addendum to two point b v p for multivalued equations with weakly regular r h s abstract in this paper we define a topological index for compact multivalued maps in convex metrizable subsets of a locally convex topological vector space in order to correct the proofs of theorems 4 1 and 4 2 in benedetti et al 2011 1

a shear flexible facet shell element for large deflection and instability analysis abstract a facet shell element based on an anisoparametric plate bending element and a quadratic plane stress element with vertex rotations is formulated for geometrically nonlinear analysis of shells the updated lagrangian formulation which proves to be effective for three node elements is employed the restriction of small rotation between the increments is removed by using hsiao s finite rotation method in which the rigid body motion is eliminated from the total displacement the displacement control is used to alleviate the singularity of the tangential stiffness matrix in the limit point type problems numerical solutions are presented for beams plates and shells to evaluate the performance of the element

periodic solutions for a class of differential inclusions in general banach spaces abstract let x be a real banach space a d a x x an m accretive operator and f r d a x a multi function which is 2 periodic with respect to its first argument has nonempty closed convex and weakly compact values and is strongly weakly upper semicontinuous in this paper we prove the existence of at least one solution for the problem u t a u t f t f t f t u t u t u t 2 in the case in which f satisfies an appropriate sign condition

flutter and thermal deflection suppression of composite plates using shape memory alloy an efficient finite element method for predicting critical temperature postbuckling deflection and flutter response is developed for composite plates embedded with prestrained shape memory alloy sma fibers the large panel deflection and the temperature dependent material properties of sma and composites are considered in the formulation the finite element formulation and solution procedure of the incremental updated lagrangian method for nonlinear temperature dependent material properties are presented briefly flow yaw angle at supersonic speed is also considered for the static solution the system equations are solved by using the newton raphson iteration method to determine aerothermal postbuckling deflection under the combined aerodynamic and thermal loads for the dynamic flutter response the modal method and time domain numerical integration are employed results show that the critical buckling temperature can be raised high enough so that buckling deflection can be eliminated and the desired flat and stable region in the temperature dynamic pressure operating domain can be enlarged greatly for composite surface panels embedded with sma for supersonic vehicle applications weight savings based on critical temperature when sma is used are also presented

classical subjective expected utility we consider decision makers who know that payoff relevant observations are generated by a process that belongs to a given class m as postulated in wald wald a 1950 statistical decision functions wiley new york we incorporate this waldean piece of objective information within an otherwise subjective setting a la savage savage lj 1954 the foundations of statistics wiley new york and show that this leads to a two stage subjective expected utility model that accounts for both state and model uncertainty

assumed strain formulation for triangular c0 plate elements based on a weak form of the kirchhoff constraints application of a weak form of the kirchhoff constraints in the formulation of triangular assumed shear strain c0 plate element is described it is shown that compared to a similar formulation of the quadrilateral elements formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression with those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

a continuation approach to superlinear periodic boundary value problems this paper deals with the problem of the existence of t periodic solutions for the first order differential system x i t x 1 1 where f 0 t x r r is a caratheodory function in what follows we prove some results for the solvability of the periodic bvp in the case when the dimension of the space is even such a limitation is motivated by our interest in applications to the second order equation d g t u u o 1 2 which takes the form of 1 1 when it is written as the equivalent system u v 0 g t u v 1 3

a free formulation based flat shell element for non linear analysis of thin composite structures a flat shell element based on the free formulation finite element concept is developed for analysing geometrically non linear thin composite shells a corotational form of the updated lagrangian formulation is utilized numerical results for typical validation problems are presented in order to demonstrate the accuracy and validity of this element these results are obtained by solving the incremental equilibrium equations through the cylindrical arc length method

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

testing theories of financial decision making we describe the observable content of some of the most widely used models of decision under uncertainty models of translation invariant preferences in particular we characterize the models of variational maxmin constant absolute risk aversion and constant relative risk aversion utilities in each case we present a revealed preference axiom that is satisfied by a dataset if and only if the dataset is consistent with the corresponding utility representation we test our axioms using data from an experiment on financial decisions

robust bddc preconditioners for reissner mindlin plate bending problems and mitc elements a balancing domain decomposition method by constraints bddc is constructed and analyzed for the reissner mindlin plate bending problem discretized with mixed interpolation of tensorial components mitc finite elements this bddc algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints after the implicit elimination of the interior degrees of freedom in each subdomain the resulting plate schur complement is solved by the preconditioned conjugate gradient method the preconditioner is based on the solution of local reissner mindlin plate problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse reissner mindlin plate problem for the primal degrees of freedom the main results of the paper are the proof and numerical verification that the proposed bddc plate algorithm is scalable quasi optimal and most important robust with respect to the plate thickness while this result is due to an underlying mixed formulation of the problem both the interface plate problem and the preconditioner are positive definite the numerical results also show that the proposed algorithm is robust with respect to discontinuities of the material properties

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

a fuzzy set approach for evaluating and enhancing the mid term competitiveness of a semiconductor factory fuzzy set theory is applied in this study to establish a systematic procedure for evaluating the mid term competitiveness of a semiconductor manufacturing factory subsequently to enhance the overall competitiveness of the semiconductor manufacturing factory a capacity re allocation mechanism is designed to improve the competitiveness of less competitive products without raising the expense of the other products and diminishing their competitiveness for this purpose a fuzzy nonlinear programming fnp model is constructed and is then converted into an equivalent np problem that can be solved with the existing optimization problem solving package to prove the usefulness of the proposed methodology a real case containing the data collected from a dram manufacturing factory was investigated after reallocating its capacity the competitiveness of the whole factory was indeed enhanced besides the capacity plan developed by the capacity re allocation mechanism was shown to be both efficient and practical

non linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates a theoretical analysis is presented for the large amplitude vibration of symmetric and unsymmetric composite plates using the non linear finite element modal reduction method the problem is first reduced to a set of duffing type modal equations using the finite element modal reduction method the main advantage of the proposed approach is that no updating of the non linear stiffness matrices is needed without loss of generality accurate frequency ratios for the fundamental mode and the higher modes of a composite plate at various values of maximum deflection are then determined by using the runge kutta numerical integration scheme the procedure for obtaining proper initial conditions for the periodic plate motions is very time consuming thus an alternative scheme the harmonic balance method is adopted and assessed as it was employed to formulate the large amplitude free vibration of beams in a previous study and the results agreed well with the elliptic solution the numerical results that are obtained with the harmonic balance method agree reasonably well with those obtained with the runge kutta method the contribution of each linear mode to the maximum deflection of a plate can also be obtained the frequency ratios for isotropic and composite plates at various maximum deflections are presented and convergence of frequencies with the number of finite elements number of linear modes and number of harmonic terms is also studied copyright 2005 john wiley sons ltd

controlling a stochastic process with unknown parameters the problem of controlling a stochastic process with unknown parameters over an infinite horizon with discounting is considered agents express beliefs about unknown parameters in terms of distributions under general conditions the sequence of beliefs converges to a limit distribution the limit distribution may or may not be concentrated at the true parameter value in some cases complete learning is optimal in others the optimal strategy does not imply complete learning the paper concludes with examination of some special cases and a discussion of a procedure for generating examples in which incomplete learning is optimal copyright 1988 by the econometric society

on the existence of mild solutions of semilinear evolution differential inclusions abstract in this paper we deal with a cauchy problem governed by the following semilinear evolution differential inclusion x t a t x t f t x t and with initial data x 0 x 0 e where a t t 0 d is a family of linear operators in the banach space e generating an evolution operator and f is a caratheodory type multifunction we prove the existence of local and global mild solutions of the problem moreover we obtain the compactness of the set of all global mild solutions in order to obtain these results we define a generalized cauchy operator our existence theorems respectively contain the analogous results provided by kamenskii obukhovskii and zecca condensing multivalued maps and semilinear differential inclusions in banach spaces de gruyter ser nonlinear anal appl vol 7 de gruyter berlin 2001 for inclusions with constant operator

a two node beam element including transverse shear and transverse normal deformations a variational higher order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented the theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness additionally independent expansions are introduced for the through thickness displacement gradients with the requirement of a least square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top bottom beam surfaces the theory is shown to be well suited for finite element development requiring simple c0 and c 1 continuous displacement interpolation fields to demonstrate the computational utility of the theory a simple two node stretching bending finite element is formulated the analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available it is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement strain and stress predictions particularly in the analysis of deep beams

first order shear deformation p version finite element for laminated plate nonlinear vibrations a p version hierarchical finite element for moderately thick composite laminated plates is presented where the effects of the rotary inertia transverse shear and geometrical nonlinearity are taken into account the time domain free vibration equations of motion are obtained by applying the principle of virtual work those equations are mapped into the frequency domain by the harmonic balance method and solved by a predictor corrector procedure the linear natural frequencies of vibration of several plates are determined and the convergence properties of the element are investigated it is shown that the element is not prone to shear locking and that a moderate number of degrees of freedom is sufficient for accuracy the influences of the plate s thickness of the width to length ratio and of the fiber orientation on nonlinear free vibrations are investigated

nonlinear flutter of composite panels under yawed supersonic flow using finite elements a finite element formulation is presented for the effects of arbitrary flow direction on the large amplitude supersonic flutter of composite panels the von karman large deflection plate theory is used to account for large amplitude limit cyde oscillations quasisteady first order piston theory aerodynamics is employed for aerodynamic loading and first order shear deformation theory is used for laminated composite panels an efficient solution procedure is presented by using the modal transformation to reduce the number of nonlinear panel flutter equations and then applying the linearized updated mode with nonlinear time function approximation to the reduced nonlinear panel flutter modal equations a modal participation is defined and the minimum number of linear modes for accurate and converged limit cycle response can be ensured examples are given for isotropic and composite panels at yawed supersonic flow

nonlocal problem for differential complementarity systems in this paper by using the topological degree theory for multivalued maps and the bounding function method we give sufficient conditions for the existence of solutions to a nonlocal problem of differential complementarity systems an example is given

c0 finite element discretization of kirchhoff s equations of thin plate bending an alternative formulation of kirchhoff s equations is given which is amenable to a standard c 0 finite element discretization in this formulation the potential energy of the plate is formulated entirely in terms of rotations whereas the deflections are the outcome of a subsidiary problem the nature of the resulting equations is such that c 0 interpolation can be used on both rotations and deflections in particular general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method unlike other finite element methods which are based on three dimensional or mindlin formulations the present approach deals directly with kirchhoff s equations of thin plate bending excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns

multiproduct production planning in the presence of work force learning this paper explores the multiproduct production planning problem in the presence of work force learning mppl in this setting the work force productivity reflects a learning curve effect which can either increase or decrease learn or forget as a function of previous production volume this research advances the understanding of mppl along a number of dimensions we formulate mppl as a nonlinear mixed integer programming problem and establish problem complexity demonstrating that it is strongly np hard we also discuss some important economic properties of production planning in the presence of learning we then define a branch and bound algorithm for mppl as well as a tabu search heuristic tsh in addition we consider a previously defined heuristic for mppl and demonstrate that its performance can be arbitrarily bad computational experiments on a large set of test problems were performed to assess the performance of the algorithm and the tsh procedure and also to study the behavior of mppl problems the results of the experiments indicate that despite the underlying problem complexity the algorithm is able to solve reasonably large problems thus providing a basis for evaluating the heuristic solution quality the tsh consistently obtains high quality solutions to the test problems suggesting that the tabu search methodology offers an effective approach to complex production planning problems mppl problem difficulty is seen to vary with the number of periods in the planning horizon the relative degree of labor intensity and the relative demand behavior of products

finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow a finite element frequency domain method for predicting nonlinear flutter response of panels with temperature effects is presented by using the principle of virtual work the element nonlinear stiffness formulation for a panel under a combined thermal and aerodynamic loads is derived on the bases of von karman s large deflection plate theory the first order piston theory aerodynamics and the quasi steady thermal stress theory the system equations of motion can be mathematically separated into two sets of equations and then solved in sequence the first set of equations yields the panel thermal aerodynamic equilibrium and the second set of equations of motion leads to the flutter limit cycle oscillations stability and flutter boundaries can also be obtained from the two sets of system equations finite element large amplitude limit cycle flutter results at different uniform temperatures are obtained for a simply supported square panel and are compared with existing galerkin time integration and other finite element solutions effects of nonuniform temperature distributions panel length to width ratios and boundary conditions on flutter responses of rectangular and triangular panels are presented

finite element modal formulation for hypersonic panel flutter analysis with thermal effects a finite element time domain modal formulation for analyzing nonlinear flutter of panels subjected to hypersonic airflow has been developed von karman large deflection plate theory is used for description of the structural nonlinearity and third order piston theory is employed to consider the aerodynamic nonlinearity the thermal loadings of uniformly distributed surface temperatures and temperature gradients through the panel thickness are considered by the application of the modal truncation technique the number of governing equations of motion is reduced dramatically so that the computational costs are reduced significantly all possible types of panel behavior including flat and stable buckled but dynamically stable limit cycle oscillation lco periodic motion and chaotic motion were observed examples of the applications of the proposed methodology were flutter responses of isotropic and composite panels special emphasis was placed on the boundary between lco and chaos and on the route to chaos time history phase plane plot poincare map bifurcation diagram and lyapunov exponent are employed in the chaos study it is found that at low or moderately high dynamic pressures the fluttering panel typically takes a period doubling route to evolve into chaos whereas at high dynamic pressures the route generally involves bursts of chaos and rejuvenations of periodic motions

finite element time domain modal formulation for nonlinear flutter of composite panels a finite element time domain modal approach is presented for determining the nonlinear flutter characteristics of composite panels at elevated temperatures the von karman large deflection strain displacement relations quasisteady first order piston theory aerodynamics and quasisteady thermal stress theory are used to formulate the nonlinear panel flutter finite element equations of motion in nodal displacements a set of nonlinear modal equations of motion of much smaller degrees of freedom for the facilitation in time numerical integration is then obtained through a modal transformation and reduction all five types of panel behavior flat buckled limit cycle periodic and chaotic motions can be determined

a mixed formulation of c0 linear triangular plate shell element the role of edge shear constraints a simple and effective linear c0 triangular element for plates and shells is developed on the basis of the hellinger reissner mixed variational principle with independently assumed stress and displacement fields two main features are emphasized in this development concerning the assumed transverse shear stress field firstly this assumption results in edge type penalty constraints in the thin plate shell regimes secondly the element is used in the form of a four triangle cross diagonal macroelement mesh as a result the element is shown to be free from shear locking in thin plate shell applications and it satisfied all the appropriate patch tests required for kirchhoff plate models in addition the element exhibits good overall convergence properties in a variety of test problems for plates and shells finally from the computational standpoint the element is very efficient since all stiffness component matrices are derived in explicit forms

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

on the solution sets of differential inclusions and the periodic problem in banach spaces abstract in this paper the topological structure of the solution set of a constrained semilinear differential inclusion in a banach space e is studied it is shown that the set of all mild solutions with values in a closed and in general thin subset d e is an r set provided natural boundary conditions and appropriate geometrical assumptions on d which hold e g when d is convex are satisfied applications to the periodic problem and to the existence of equilibria are given

a c0 triangular plate element with one point quadrature on developpe un element de plaque triangulaire du type de mindlin qui utilise des champs lineaires pour les rotations et les deflexions transversales l element ne necessite qu un seul point de quadrature ce qui est tres interessant pour l analyse non lineaire