existence theorems for the dirichlet problem without growth restrictions x 0 x 1 0 x 0 x 1 0 have virtually identical growth as lx 1 co however the first problem has no solutions while the second one has one solution the essential point here is the location of zeros of polynomials y2 7 and y2 ii actually granas guenther and lee 3 have proved that the problem x g x x 0 x 1 0 has at least one solution if g has two zeros of opposite sign in this paper we shall prove the following result 0 1

existence theorems for a second order three point boundary value problem abstract letf 0 1 r 2 r be continuous ande c 0 1 let i 0 1 ai r all of theai s having the same sign i 1 2 m 2 0 x t f t x t x t e t t 0 1 e x 0 0 x 1 i 1 m 2 a i x i bc m we discuss existence theorems for the problem e bcm under some sign condition offabout the origin our analysis is based on a nonlinear alternative of leray schauder

effective models of composite periodic plates ii simplifications due to symmetries abstract this paper is aimed at investigating how material and geometrical symmetries of a composite plate simplify the formulae derived in part i by the asymptotic method it occurs that the symmetry with respect to the middle plane results in splitting the subsequent overall and local problems into membrane and bending problems additional assumptions of orthotropy of the material and of certain symmetries of the periodicity cells imply far reaching simplifications e g the vanishing of some terms in the first order correctors for displacements and the cancelation of discrepancies in the formulation of some boundary conditions in the last section a computational algorithm for evaluating the effective stiffnesses is suggested

higher order effective modeling of periodic heterogeneous beams i asymptotic expansion method this paper is concerned with the elastostatic behavior of heterogeneous beams with a cross section and elastic moduli varying periodically along the beam axis by using the two scale asymptotic expansion method the interior solution is formally derived up to an arbitrary desired order in particular this method is shown to constitute a systematic way of improving bernoulli s theory by including higher order terms without any assumption in contrast to timoshenko s theory or other refined beam models moreover the incompatibility between the interior asymptotic expansions and the real boundary conditions is emphasized and the necessity of a specific treatment of edge effects is thus underlined

mori tanaka estimates of the effective elastic properties of stress gradient composites a stress gradient material model was recently proposed by forest and sab mech res comm 40 16 25 2012 as an alternative to the well known strain gradient model introduced in the mid 60s we propose a theoretical framework for the homogenization of stress gradient materials we derive suitable boundary conditions ensuring that hill mandel s lemma holds as a first result we show that stress gradient materials exhibit a softening size effect to be defined more precisely in this paper while strain gradient materials exhibit a stiffening size effect this demonstrates that the stress gradient and strain gradient models are not equivalent as intuition would have it but rather complementary using the solution to eshelby s spherical inhomogeneity problem that we derive in this paper we propose mori tanaka estimates of the effective properties of stress gradient composites with spherical inclusions thus opening the way to more advanced multi scale analyses of stress gradient materials

a bending gradient model for thick plates part i theory abstract this is the first part of a two part paper dedicated to a new plate theory for out of plane loaded thick plates where the static unknowns are those of the kirchhoff love theory 3 in plane stresses and 3 bending moments to which six components are added representing the gradient of the bending moment the new theory called the bending gradient plate theory is described in the present paper it is an extension to arbitrarily layered plates of the reissner mindlin plate theory which appears as a special case of the bending gradient plate theory when the plate is homogeneous however we demonstrate also that in the general case the bending gradient model cannot be reduced to a reissner mindlin model in part two lebee and sab 2011 the bending gradient theory is applied to multilayered plates and its predictions are compared to those of the reissner mindlin theory and to full 3d pagano s exact solutions the main conclusion of the second part is that the bending gradient gives good predictions of both deflection and shear stress distributions in any material configuration moreover under some symmetry conditions the bending gradient model coincides with the second order approximation of the exact solution as the slenderness ratio l h goes to infinity

interactive decision making in fuzzy linear optimization problems abstract this paper presents an interactive method for solving a multi criteria linear program where coefficients of the objective functions and or of the constraints are known exactly but imprecisely assuming fuzzy aspiration levels for each of the goals and basing on a comparison of flat fuzzy numbers the original fuzzy problem is transformed into a crisp satisfactory model to determine a suitable compromise solution we will maximize the minimum of the surpluses over the aspiration levels this induces a problem with a nonlinear objective function which is equivalent to a linear program

fuzzy stochastic linear programming survey and future research directions in many real life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist there are no reliable transformations between them this calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models fuzzy stochastic linear programming is an attempt to fulfill this need it deals with modelling and problem solving issues related to situations where randomness and fuzziness co occur in a linear programming framework in this paper we provide a survey of the essential elements methods and algorithms for this class of linear programming problems along with promising research directions being a survey the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest

analysis of a beam cross section under coupled actions including transversal shear abstract an efficient finite elements fe based method of cross sectional analysis of a longitudinally homogeneous beam with an arbitrary cross section and material model assumed submitted to tension compression bending torsion and shear is developed a new formulation of this classical problem is done as a special case of the homogenization theory it takes into account 3d strain and stress state fulfilling equilibrium compatibility and constitutive equations at any point stress free conditions on lateral surfaces but preserves control by cross sectional stress resultant forces and corresponding generalized strains a source of problems caused by the presence of a shear force is explained and a way of overcoming it is shown in the paper both variational formulation of the problem and its 2d fe solution are given benchmark cases including shear of a square a composite l section an orthotropic square and an elasto plastic analysis of shearing of a square section show correctness of the method finally two practical cases of application of the method to an analysis of reinforced concrete beam sections are shown

asymptotic generalization of reissner mindlin theory accurate three dimensional recovery for composite shells abstract a rigorous and systematic dimensional reduction of a shell like structure is undertaken it starts with geometrically nonlinear three dimensional 3 d anisotropic elasticity theory and takes advantage of small parameters associated with the geometry this reduction is carried out using the variational asymptotic method and splits the 3 d problem into a linear one dimensional 1 d through the thickness analysis and a nonlinear two dimensional 2 d shell analysis the 2 d equations are put into the form of a nonlinear reissner mindlin shell theory details of which are dealt with in a separate paper the focus of this paper is on the through the thickness analysis which is solved by a 1 d finite element method and which provides two useful pieces of information a generalized 2 d constitutive law for the shell equations and a set of recovery relations that can be used to express the 3 d field variables through the thickness in terms of 2 d shell variables calculated in the shell analysis the resulting analysis can be incorporated into standard reissner mindlin shell finite element codes numerical results are compared with the exact solution and the excellent agreement validates the fidelity of this modeling approach

possibilistic linear programming for managing interest rate risk abstract in this study we consider the linear programming problem with the objective of the investment discounted value where the interest rate is imprecise and has a triangular possibilistic distribution an crisp auxiliary bi objective linear programming model is proposed to resolve this possibilistic nature furthermore we develop an extended zimmermann approach called augmented max min approach for solving this auxiliary bi objective linear programming problem and other multiple objective linear programming problems finally a numerical bank balance sheet problem where interest rates price of futures contract loan demand deposit supply and ratio of desired loan to deposit are assumed to be fuzzy is solved for illustrating the new approach

effective models of composite periodic plates i asymptotic solution abstract this paper is concerned with the statical problem of plates with oscillating material properties and rapidly varying face shapes both the material moduli and the geometrical data vary periodically with the same period by using the asymptotic method of caillerie 1982 c r acad sci paris 294 ii 159 the higher order terms of the expansion for deformations and stresses are arrived at these terms are determined by a subsequent homogenized problem for new auxiliary functions of a local variable appropriate basic cell problems are established proof that the conventional asymptotic expansion does not comprise boundary effects at the clamped edge is also given

higher order effective modeling of periodic heterogeneous beams ii derivation of the proper boundary conditions for the interior asymptotic solution abstract this paper constitutes the second part of a study devoted to the 1d modeling of beam like structures of arbitrary cross section with periodic properties along the axis in the first part the asymptotic expansion method has been described and the equations involving the successive terms of the outer solution have been given in particular it has been shown that neither the leading term nor the full outer solution are able to satisfy arbitrary prescribed edge data a specific study is thus necessary and it is presented in this paper the method used is the decay analysis initially proposed for homogeneous plates by gregory and wan j elast 14 1984 27 this approach consists in deriving the appropriate set of boundary conditions for the outer expansion solution for any arbitrary edge data stress displacement or mixed data these boundary conditions are obtained from the solution of canonical beam problems without computing any inner solution the method is illustrated through numerical examples on a lattice structure the results obtained prove the importance of a correct treatment of the edge effects in order that the inclusion of higher order terms in the beam model serves actually to increase the accuracy of the outer expansion solution

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

a new approach to some possibilistic linear programming problems abstract in practice the unit costs profits of new products or new projects the lending and borrowing interest rates and cash flows are always imprecise we provide an auxiliary multiple objective linear programming model to solve a linear programming problem with imprecise objective and or constraint coefficients our strategy is to maximize the most possible value of the imprecise profit at the same time we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit this strategy is equivalent to the practical considerations of financial problems in this paper a numeric investment problem is solved for illustrating the new approach

a stochastic possibilistic programming model for bank hedging decision problems abstract for a practical bank hedging decision optimization problem interest rates and price of futures contract may involve both fuzziness and randomness for subjective nature of satisfaction maximum desired values of loan demand deposit supply and ratio of desired loan to deposit are often fuzzy in this study we consider and solve a stochastic possibilistic programming model of bank hedging decision problems with the above characters we first use the expected value to obtain an auxiliary possibilistic linear programming problem which is further resolved by use of level cut an crisp auxiliary bi objective linear programming model is then proposed and solved by our augmented maximum approach for illustration purpose a numerical bank hedging decision problem is solved

process planning in a fuzzy environment abstract mixed integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted as precise forecasts are difficult to obtain process planning usually involves uncertainty and ambiguity in the data this paper presents an application of fuzzy programming to process planning the forecast parameters are assumed to be fuzzy with a linear or triangular membership function the process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals the model is transformed to a deterministic mixed integer linear program or mixed integer nonlinear program depending on the type of uncertainty involved in the problem for the nonlinear case a global optimization algorithm is developed for its solution this algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms

asymptotic construction of reissner like composite plate theory with accurate strain recovery abstract the focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry the development starts with formulation of the three dimensional 3 d anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two dimensional 2 d variables the variational asymptotic method is then used to rigorously split this 3 d problem into a linear one dimensional normal line analysis and a nonlinear 2 d plate analysis accounting for classical as well as transverse shear deformation the normal line analysis provides a constitutive law between the generalized 2 d strains and stress resultants as well as recovering relations to approximately but accurately express the 3 d displacement strain and stress fields in terms of plate variables calculated in the plate analysis it is known that more than one theory may exist that is asymptotically correct to a given order this nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple reissner like plate theory although it is not possible in general to construct an asymptotically correct reissner like composite plate theory an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of the reissner like formulation numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory the present theory has excellent agreement with the previous theory and exact results

topological degree method in functional boundary value problems let x be the banach space of co functions on j o 11 endowed with the sup norm il 11 denote by 9 the set of all operators k x x which are continuous and bounded i e k a is bounded for any bounded s1 c x and the set of all functionals y x r which are linear bounded and increasing i e x y e x x t y t on j y x y y in the paper we consider the second order differential equation

existence theorems for a class of singular two point b v p of second order differential equations wherea b o l randf o 1 xr 2 r are continuous functions a and b are positive in 0 l and e denotes the space of boundary conditions the importance and origins of these problems can be found in granas et al 4 chap 31 see also 2 we are mainly interested in the singular case a 0 a 1 b 0 b 1 0 but our study includes the regular case a 0 and b 0 in 0 11 actually the singular case is deduced from the regular one through a sequence of regular problems

linear programming under randomness and fuzziness this paper is concerned with the use of fuzzy sets theory well suited for nuanced human behavior to extend the applicability of linear programming in a way to let both randomness and fuzziness uncertainties be taken into account a fuzzy stochastic linear programming problem is considered and ways to handle it suggested the basic idea behind our approaches is to translate the original problem in deterministic terms via tools provided by fuzzy sets theory to get a classical one some conditions for the resulting problems to be solved without extra computational effort are stressed and illustrative examples given

effective models of composite periodic plates iii two dimensional approaches abstract this paper is concerned with two dimensional approximations of the three dimensional local problems of caillerie 1984 math meth appl sci 6 159 191 and kohn and vogelius 1984 int j solids structures 20 333 350 the solutions to these problems make it possible to evaluate the effective stiffnesses of periodic plates the kirchhoff type approximation results in the formulae shown by duvaut 1976 in theoretical and applied mechanics edited by w t koiter pp 119 132 north holland amsterdam by imposing hencky reissner type constraints one is led to new formulae which have a wider range of applicability the paper also discusses the formulae which result from homogeneizing two dimensional kirchhoff s reissner hencky s and reddy s equations of plates with periodic structure

on some optimisation models in a fuzzy stochastic environment this paper is on fuzzy stochastic optimisation an area that is quickly coming to the forefront of mathematical programming under uncertainty an even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid imprecision more precisely we consider a range of situations in which random factors and fuzzy information co occur in an optimisation setting related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set uncertain probability and fuzzy random variable making good use of uncertainty principles we also discuss ways to deal with the resulting problems numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches we shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field