a refined quasi 3d isogeometric analysis for functionally graded microplates based on the modified couple stress theory the isogeometric analysis associated with a novel quasi 3d shear deformation theory is proposed to investigate size dependent behaviours of functionally graded microplates the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size dependent effects within the microplates meanwhile the quasi 3d theory which is constructed from a novel seventh order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors the nurbs based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher order derivative and continuity requirements the proposed approach is successfully applied to study the static bending free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions in which some benchmark numerical examples are presented a number of investigations are also conducted to illustrate the effects of the material length scale material index and aspect ratios on the responses of the microplates

nonlocal theory solution of two collinear cracks in the functionally graded materials in this paper the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti plane shear loading is investigated by means of nonlocal theory the traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials to make the analysis tractable it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack by use of the fourier transform the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the displacement on the crack surfaces to solve the triple integral equations the displacement on the crack surfaces is expanded in a series of jacobi polynomials unlike the classical elasticity solutions it is found that no stress singularity is present near the crack tips the nonlocal elastic solutions yield a finite hoop stress at the crack tip thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials the magnitude of the finite stress field depends on the crack length the distance between two cracks the parameter describing the functionally graded materials and the lattice parameter of the materials

vibration of two dimensional imperfect functionally graded 2d fg porous nano micro beams abstract this study presents analysis on the vibration behavior of the two dimensional functionally graded 2d fg nano and microbeams which are made of two kinds of porous materials for the first time based on timoshenko beam theory the material of the nano and microbeams is modeled as 2d fgms according to the power law the eringen s nonlocal elasticity and the modified couple stress theories are used respectively in case of nano and microbeams the boundary conditions are considered as clamped cc simply supported ss clamped simply supported cs and cantilever cf the governing equations are solved using the generalized differential quadrature method gdqm the effects of fg power indexes along length and thickness are studied along each other and also exclusively the parametric studies are presented for functionally graded along thickness fg functionally graded along length afg and 2d fg porous and perfect micro nanobeams under different boundary conditions

uniqueness for plane crack problems in dipolar gradient elasticity and in couple stress elasticity the present work deals with the uniqueness theorem for plane crack problems in solids characterized by dipolar gradient elasticity the theory of gradient elasticity derives from considerations of microstructure in elastic continua mindlin r d 1964 micro structure in linear elasticity arch ration mech anal 16 51 78 and is appropriate to model materials with periodic structure according to this theory the strain energy density assumes the form of a positive definite function of the strain as in classical elasticity and the second gradient of the displacement additional term specific cases of the general theory employed here are the well known theory of couple stress elasticity and the recently popularized theory of strain gradient elasticity these cases are also treated in the present study we consider an anisotropic material response of the cracked plane body within the linear version of gradient elasticity and conditions of plane strain or anti plane strain it is emphasized that for crack problems in general a uniqueness theorem more extended than the standard kirchhoff theorem is needed because of the singular behavior of the solutions at the crack tips such a theorem will necessarily impose certain restrictions on the behavior of the fields in the vicinity of crack tips in standard elasticity a theorem was indeed established by knowles and pucik knowles j k pucik t a 1973 uniqueness for plane crack problems in linear elastostatics j elast 3 155 160 who showed that the necessary conditions for solution uniqueness are a bounded displacement field and a bounded body force field in our study we show that the additional to the two previous conditions requirement of a bounded displacement gradient field in the vicinity of the crack tips guarantees uniqueness within the general form of the theory of dipolar gradient elasticity in the specific cases of couple stress elasticity and pure strain gradient elasticity the additional requirement is less stringent this only involves a bounded rotation field for the first case and a bounded strain field for the second case

a reformulation of constitutive relations in the strain gradient elasticity theory for isotropic materials abstract the general isotropic strain gradient elasticity theory with five higher order elastic constants is reformulated by introducing two different orthogonal decompositions of the strain gradient tensor just applying the mathematical reformulations no extra conditions needed the constitutive relations equilibrium equation and boundary conditions are reformulated in the reformulated theory the number of independent higher order elastic constants is proved to be three for isotropic materials which indicates that the five higher order elastic constants in the general isotropic strain gradient elasticity theory are dependent with each other therefore the general strain gradient elasticity theory contains only three independent material length scale parameters for isotropic materials in addition to the lame constants the new theory is different from the existed strain gradient elasticity theory with one or three material length scale parameters which introduces extra conditions during deriving process moreover the reformulated theory can be directly reduced to that of incompressible materials by assuming the terms associated with hydrostatic strains to be zero some examples such as torsion of cylindrical bars shearing of fixed end layers and pure bending of thin beams are performed to reveal the necessity of including multi length scale parameters in the strain gradient elasticity theory to predict size effects at micron scale

limiting average criteria for nonstationary markov decision processes this paper deals with the so called limiting average criteria for nonstationary markov decision processes with possibly unbounded rewards and borel state space a new set of conditions is provided under which the existence of both a solution to the optimality equations and the limiting average epsilon geq 0 optimal markov policies is derived also a rolling horizon algorithm for computing limiting average epsilon 0 optimal markov policies is developed furthermore the results in this paper are illustrated by several examples such as the water regulation problem

nonlinear size dependent dynamics of an imperfect shear deformable microplate abstract the nonlinear size dependent dynamics of a geometrically imperfect shear deformable microplate is investigated based on the modified couple stress theory an initial imperfection in the out of plane direction is taken into account the third order shear deformation theory is employed to model the system by retaining in plane displacements and inertia the governing equations of motion of the system are obtained employing an energy method through use of the lagrange equations which upon employing an assumed mode technique yields a set of second order nonlinear ordinary differential equations with coupled terms a high dimensional discretised system is considered and made double dimensional via a change of variables in order to obtain a set of first order nonlinear ordinary differential equations the resulting equations are solved using a direct time integration technique resulting in time dependent generalised coordinates for the in plane and out of plane displacements and two rotations from these generalised coordinates phase plane portraits and fast fourier transforms ffts are also obtained moreover the frequency response and force response curves of the system are obtained using a continuation technique stability analysis is conducted via the floquet theory the effect of the initial imperfection as well as the length scale parameter on the system response is also examined

constrained partially observed markov decision processes with probabilistic criteria for adaptive sequential detection dynamic programming equations are derived which characterize the optimal value functions for a partially observed constrained markov decision process problem with both total cost and probabilistic criteria more specifically the goal is to minimize an expected total cost subject to a constraint on the probability that another total cost exceeds a prescribed threshold the markov decision process is partially observed but it is assumed that the constraint costs are available to the controller i e they are fully observed the problem is motivated by an adaptive sequential detection application the application of the dynamic programming results to optimal adaptive truncated sequential detection is demonstrated using an example involving the optimization of a radar detection process

free vibration of size dependent mindlin microplates based on the modified couple stress theory this paper develops a mindlin microplate model based on the modified couple stress theory for the free vibration analysis of microplates this non classical plate model contains an internal material length scale parameter related to the material microstructures and is capable of interpreting the size effect that the classical mindlin plate model is unable to describe the higher order governing equations of motion and boundary conditions are derived using the hamilton principle the p version ritz method is employed to determine the natural frequencies of the microplate with different boundary conditions a detailed parametric study is conducted to study the influences of the length scale parameter side to thickness ratio and aspect ratio on the free vibration characteristics of the microplate it is found that the size effect is significant when the thickness of microplate is close to the material length scale parameter

free vibration analysis of embedded single layered nanoplates and graphene sheets by using the multiple time scale method an asymptotic approach using the eringen nonlocal elasticity theory and multiple time scale method is developed for the three dimensional 3d free vibration analysis of simply supported single layered nanoplates and graphene sheets gss embedded in an elastic medium in the formulation the small length scale effect is first introduced to the nonlocal constitutive equations by using a nonlocal parameter then the mathematical processes of nondimensionalization asymptotic expansion and successive integration are performed and finally recurrent sets of motion equations for various order problems are obtained the interactions between the nanoplates or gss and their surrounding medium are modeled as a two parameter pasternak foundation nonlocal classical plate theory cpt is derived as a first order approximation of the 3d nonlocal elasticity theory and the motion equations for higher order problems retain the same differential operators as those of nonlocal cpt although with different nonhomogeneous terms some 3d nonlocal elasticity solutions of the natural frequency parameters of nanoplates or gss with and without being embedded in the elastic medium and their corresponding through thickness distributions of modal field variables are given to demonstrate the performance of the 3d asymptotic nonlocal elasticity theory

size dependent nonlinear analysis and damping responses of fg cntrc micro plates abstract this paper presents a nonlinear numerical model which is based on the modified couple stress theory mcst and trigonometric shear deformation theory coupled with isogeometric analysis the present approach captures the small scale effects on the geometrically nonlinear behaviors of functionally graded carbon nanotube reinforced composite fg cntrc micro plate with four patterns distribution the equations of motion are established based on a galerkin weak form associated with von karman nonlinear strains the mcst utilizes only one material length scale parameter to predict the size effect in fg cntrc micro plate for which its material properties are derived from an extended rule of mixture the solutions of nonlinear static equation are obtained by using the newton raphson technique and the newmark time iteration procedure in association with picard method is assigned to get responses of the nonlinear dynamic problems in addition the rayleigh damping is applied to consider the influence of damping characteristic on the oscillation of fg cntrc micro plates comparisons are performed to verify the proposed approach afterward the numerical examples are used to show the effects of the distribution of carbon nanotubes cnt their volume fraction the material length scale parameter and the boundary conditions on the nonlinear static and dynamic behaviors of fg cntrc micro plates

multichain markov decision processes with a sample path constraint a decomposition approach we consider finite state finite action markov decision processes which accumulate both a reward and a cost at each decision epoch we study the problem of finding a policy that maximizes the expected long run average reward subject to the constraint that the long run average cost be no greater than a given value with probability one we establish that if there exists a policy that meets the constraint then there exists an e optimal stationary policy furthermore an algorithm is outlined to locate the e optimal stationary policy the proof of the result hinges on a decomposition of the state space into maximal recurrent classes and a set of transient states

mathematical modeling of vibration problem of nano sized annular sector plates using the nonlocal continuum theory via eight node discrete singular convolution transformation abstract in the present study free vibration analysis of nano sized annular sector plate is analyzed using the nonlocal continuum theory the method of discrete singular convolution dsc is used for numerical computations firstly equation of motion of thin plates is formulated via nonlocal elasticity then irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation the dsc procedures are then applied to discretization of the transformed set of governing equations and related boundary conditions the effects of nonlocal parameter mode numbers sector angle and radius ratio on the vibration frequencies are investigated in detail it is seen that the size effects are significant in vibration analysis of nano scaled annular sector plates and need to be included in the mechanical model

couple stress theory for solids by relying on the definition of admissible boundary conditions the principle of virtual work and some kinematical considerations we establish the skew symmetric character of the couple stress tensor in size dependent continuum representations of matter this fundamental result which is independent of the material behavior resolves all difficulties in developing a consistent couple stress theory we then develop the corresponding size dependent theory of small deformations in elastic bodies including the energy and constitutive relations displacement formulations the uniqueness theorem for the corresponding boundary value problem and the reciprocal theorem for linear elasticity theory next we consider the more restrictive case of isotropic materials and present general solutions for two dimensional problems based on stress functions and for problems of anti plane deformation finally we examine several boundary value problems within this consistent size dependent theory of elasticity

mathematical model of a three layer micro and nano beams based on the hypotheses of the grigolyuk chulkov and the modified couple stress theory abstract the mathematical model of three layered beams developed based on the hypothesis of the grigolyuk chulkov and the modified couple stress theory and the size depended equations governing the layers motions on the micro and nano scales is constructed the hamilton s principle yields the novel equations of motion as well as the boundary initial conditions regarding beams displacement the latter ones clearly exhibit the size dependent dynamics of the studied micro and nano beams and the introduced theory overlaps with the classical beam equations for large enough layer thickness in particular a three layer beam with the micro layer thickness has been investigated with respect to the classical theory of grigolyuk chulkov the derived boundary problem is of sixth order and can be solved analytically in the case of statics the carried out numerical experiments allowed to detect and explain size dependent effects exhibited by the micro beams the beam deflections and stress yielded by the employed couple stress model are less than those predicted by the classical grigolyuk chulkov theory while the estimated eigen frequencies are higher respectively it has been shown that the proposed model can be reduced to the classical three layer grigolyuk chulkov beam through increase of the layers thickness which validates our approach

a non classical mindlin plate model incorporating microstructure surface energy and foundation effects a non classical model for a mindlin plate resting on an elastic foundation is developed in a general form using a modified couple stress theory a surface elasticity theory and a two parameter winkler pasternak foundation model it includes all five kinematic variables possible for a mindlin plate the equations of motion and the complete boundary conditions are obtained simultaneously through a variational formulation based on hamilton s principle and the microstructure surface energy and foundation effects are treated in a unified manner the newly developed model contains one material length scale parameter to describe the microstructure effect three surface elastic constants to account for the surface energy effect and two foundation parameters to capture the foundation effect the current non classical plate model reduces to its classical elasticity based counterpart when the microstructure surface energy and foundation effects are all suppressed in addition the new model includes the mindlin plate models considering the microstructure dependence or the surface energy effect or the foundation influence alone as special cases recovers the kirchhoff plate model incorporating the microstructure surface energy and foundation effects and degenerates to the timoshenko beam model including the microstructure effect to illustrate the new mindlin plate model the static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulae derived

subgrid interaction and micro randomness novel invariance requirements in infinitesimal gradient elasticity abstract we present a micromechanically motivated form of the curvature energy in infinitesimal isotropic gradient elasticity the basis is a homogenization averaging scheme using a micro randomness assumption imposed on a directional higher gradient interaction term these directional interaction terms are matrix valued allowing to apply the standard orthogonal cartan lie algebra decomposition averaging over all subgrid directions leads to three quadratic curvature terms which are conformally invariant when neglecting volumetric effects restricted to rotational inhomogeneities we motivate thereby a symmetric couple stress tensor in the infinitesimal indeterminate couple stress model of koiter mindlin toupin type relations are established to a novel conformally invariant linear cosserat model

learning the variance of the reward to go in markov decision processes mdps the variance of the reward to go is a natural measure of uncertainty about the long term performance of a policy and is important in domains such as finance resource allocation and process control currently however there is no tractable procedure for calculating it in large scale mdps this is in contrast to the case of the expected reward to go also known as the value function for which effective simulation based algorithms are known and have been used successfully in various domains in this paper we extend temporal difference td learning algorithms to estimating the variance of the reward to go for a fixed policy we propose variants of both td 0 and lstd with linear function approximation prove their convergence and demonstrate their utility in an option pricing problem our results show a dramatic improvement in terms of sample efficiency over standard monte carlo methods which are currently the state of the art

optimal policy for minimizing risk models in markov decision processes we consider the minimizing risk problems in discounted markov decisions processes with countable state space and bounded general rewards we characterize optimal values for finite and infinite horizon cases and give two sufficient conditions for the existence of an optimal policy in an infinite horizon case these conditions are closely connected with lemma 3 in white 1993 which is not correct as wu and lin 1999 point out we obtain a condition for the lemma to be true under which we show that there is an optimal policy under another condition we show that an optimal value is a unique solution to some optimality equation and there is an optimal policy on a transient set

a new kirchhoff plate model based on a modified couple stress theory in this paper a new kirchhoff plate model is developed for the static analysis of isotropic micro plates with arbitrary shape based on a modified couple stress theory containing only one material length scale parameter which can capture the size effect the proposed model is capable of handling plates with complex geometries and boundary conditions from a detailed variational procedure the governing equilibrium equation of the micro plate and the most general boundary conditions are derived in terms of the deflection using the principle of minimum potential energy the resulting boundary value problem is of the fourth order instead of existing gradient theories which is of the sixth order and it is solved using the method of fundamental solutions mfs which is a boundary type meshless method several plates of various shapes aspect and poisson s ratios are analyzed to illustrate the applicability of the developed micro plate model and to reveal the differences between the current model and the classical plate model moreover useful conclusions are drawn from the micron scale response of this new kirchhoff plate model

an efficient computational approach for size dependent analysis of functionally graded nanoplates abstract in this paper an efficient computational approach based on refined plate theory rpt including the thickness stretching effect namely quasi 3d theory in conjunction with isogeometric formulation iga is proposed for the size dependent bending free vibration and buckling analysis of functionally graded nanoplate structures the present novel quasi 3d theory not only possesses 4 variables as refined plate theory but also accounts for both shear deformation and stretching effect without any requirement of shear correction factors scfs the size dependent effect is taken into account by nonlocal elasticity theory isogeometric analysis shows a great advantage in dealing with the high continuity and high order derivative requirements of the displacement fields used in quasi 3d and nonlocal theory the reliability and accuracy of the present method are ascertained by comparing the obtained results with other published ones numerical examples are also performed to show the significance of nonlocal effect material distribution profile aspect ratios and boundary conditions on the behaviour of fgm nanoplates

geometric material analogy for multiscale modelling of twisted plates abstract it is well known that the macroscopic behaviour of many engineering materials is strongly affected by the role of underlying microstructure currently though mathematical expressions linking behaviour of large scale structures to the geometry of their microscopic structure are largely lacking in this respect establishing quantitative links across different material lengthscales may offer new pathways for engineering design in the present work an analogy between cross sectional geometrical properties representing macrostructure and a material length parameter representing microstructure is presented the analogy is established through the study of a thin plate subject to axial loading undergoing finite displacements from two alternative perspectives first we consider a thin elastic plate with a pretwist about the loading axis where a warping term is introduced accounting for the out of plane deformation of the cross section the coupled governing differential equations and the corresponding coupled boundary conditions are explicitly derived employing a classical structural mechanics approach utilising an energy variational statement secondly an axially loaded thin flat plate i e with no pretwist is studied with strain gradient elasticity theory incorporating only one material length parameter representing the microstructure in addition to the two classical lame stiffness constants the ensuing analogy emerges by comparison of the governing equations of the two formulations which shows a mathematical expression can be identified which incorporates both geometric and material length variables that formalises the link between microscale and macroscale this mathematical expression which constitutes the kernel of the proposed multiscale approach admits a twofold interpretation depending on the assumed independent variable on the one hand the proposed multiscale modelling approach suggests that a plate with complex global geometry can be substituted by a structurally equivalent flat plate with constitutive relations given by a non local strain gradient theory on the other hand the material length parameter can be interpreted on a physical basis because for the first time it has been identified as a known function of geometrical features of the structure through simple algebraic relationships for various cross sectional profiles

minimizing risk models in markov decision processes with policies depending on target values abstract this paper studies the minimizing risk problems in markov decision processes with countable state space and reward set the objective is to find a policy which minimizes the probability risk that the total discounted rewards do not exceed a specified value target in this sort of model the decision made by the decision maker depends not only on system s states but also on his target values by introducing the decision maker s state we formulate a framework for minimizing risk models the policies discussed depend on target values and the rewards may be arbitrary real numbers for the finite horizon model the main results obtained are i the optimal value functions are distribution functions of the target ii there exists an optimal deterministic markov policy and iii a policy is optimal if and only if at each realizable state it always takes optimal action in addition we obtain a sufficient condition and a necessary condition for the existence of finite horizon optimal policy independent of targets and we give an algorithm computing finite horizon optimal policies and optimal value functions for an infinite horizon model we establish the optimality equation and we obtain the structure property of optimal policy we prove that the optimal value function is a distribution function of target and we present a new approximation formula which is the generalization of the nonnegative rewards cases an example which illustrates the mistakes of previous literature shows that the existence of optimal policy has not been proved really in this paper we give an existence condition which is a sufficient and necessary condition for the existence of an infinite horizon optimal policy independent of targets and we point out that whether there exists an optimal policy remains an open problem in the general case

achieving target state action frequencies in multichain average reward markov decision processes in this paper we address a basic problem that arises naturally in average reward markov decision processes with constraints and or nonstandard payoff criteria given a feasible state action frequency vector the target construct a policy whose state action frequencies match those of the target vector while it is well known that the solution to this problem cannot in general be found in the space of stationary randomized policies we construct a solution that has ultimately stationary structure it consists of two stationary policies where the first one is used initially and then the switch to the second one is made at a certain random switching time the computational effort required to construct this solution is minimal we also show that our problem can always be solved by a stationary policy if the original mdp is extended by adding certain states and actions the solution in the original mdp is obtained by mapping the solution in the extended mdp back to the original process

nonlinear thermo elastic bending behavior of graphene sheets embedded in an elastic medium based on nonlocal elasticity theory this paper investigates the large deflection behavior of orthotropic single layered graphene sheet slgs embedded in a winkler pasternak elastic medium under a uniform transverse load in thermal environments using the nonlocal differential constitutive relations of eringen the slgs is modeled as a nonlocal orthotropic plate using the principle of virtual work the coupled nonlinear equilibrium equations are obtained based on first order shear deformation theory fsdt and the von karman geometrical model the differential quadrature dq discretized form of the governing equations with clamped and simply supported boundary conditions is derived the newton raphson iterative scheme is used to solve the resulting system of nonlinear algebraic equations effects of small scale parameter thermal environment width to length elasticity ratio aspect ratio thickness elastic foundation load value and boundary conditions are considered in detail the results show that unlike the simply supported boundary conditions increase of small scale parameter plays a decreasing role in effect of thermal environment on the deflections of nanoplates with clamped edges it is also observed that increasing the plate thickness thermal load effects decline noticeably and depending on the small scale value the thermal loads do not have any significant effect on the results beyond a specified thickness

three dimensional vibration analysis of functionally graded material sandwich plates abstract free vibration of functionally graded material sandwich rectangular plates with simply supported and clamped edges is studied based on the three dimensional linear theory of elasticity two common types of fgm sandwich plates namely the sandwich with fgm facesheet and homogeneous core and the sandwich with homogeneous facesheet and fgm core are considered the three displacements of the plates are expanded by a series of chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions the natural frequencies are obtained by ritz method rapid convergence is observed in this study the natural frequencies of simply supported power law fgm sandwich plates are compared with results from different two dimensional plate theories parametric study is performed for varying volume fraction layer thickness ratios thickness length ratios and aspect ratios of the sandwich plates

global phase structure of the restricted isosceles three body problem with positive energy we study a restricted three body problem with special symmetries the restricted isosceles three body problem for positive energy the energy manifold is partially compactified by adding boundary manifolds corresponding to infinity and triple collision we use a new set of coordinates which are a variation on the mcgehee coordinates of celestial mechanics these boundary manifolds are used to study the global phase structure of this gradational system the orbits are classified by intersection number that is the number of times the infinitesimal body cross the line of syzygy before escaping to infinity

optimization models for the first arrival target distribution function in discrete time the study of expectation optimality criteria standard criteria has constituted most previous work in the area of markov decision processes mdps however the optimal policies obtained from such models are not reliable when considering a single or a few decision processes since only the average performance over many trials is guaranteed to be optimal in fact the expectation optimality criteria are insufficient to characterize the w x variability risk features of practical problems 1 5 a typical requirement for a long term application for example unmanned space flight and satellites is to have a 0 95 or greater probability of being operational at the end of a 10 year period whereas a typical requirement for space shuttle aircraft flight control and military systems is to have a reliability of 0 97 at the end of a 3 h time period likewise chemical reactions must

variational analysis of gradient elastic flexural plates under static loading gradient elastic flexural kirchhoff plates under static loading are considered their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case a variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions classical and non classical ones two circular gradient elastic plates clamped or simply supported at their boundaries are analyzed analytically and the gradient effect on their static response is assessed in detail a rectangular gradient elastic plate simply supported at its boundaries is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors finally a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple stress elasticity theories

meet your expectations with guarantees beyond worst case synthesis in quantitative games abstract classical analysis of two player quantitative games involves an adversary modeling the environment of the system which is purely antagonistic and asks for strict guarantees while markov decision processes model systems facing a purely randomized environment the aim is then to optimize the expected payoff with no guarantee on individual outcomes we introduce the beyond worst case synthesis problem which is to construct strategies that guarantee some quantitative requirement in the worst case while providing a higher expected value against a particular stochastic model of the environment given as input we study the beyond worst case synthesis problem for two important quantitative settings the mean payoff and the shortest path in both cases we show how to decide the existence of finite memory strategies satisfying the problem and how to synthesize one if one exists we establish algorithms and we study complexity bounds and memory requirements

comment on nonlocal third order shear deformation plate theory with application to bending and vibration of plates by r aghababaei and j n reddy journal of sound and vibration 326 2009 277 289 abstract this paper aims to prove the inaccuracy of the navier solution presented by aghababaei and reddy 1 for the bending analysis of nanoplates based on the nonlocal theory of eringen according to the derived relations for bending of the nonlocal plate model the main cause of this inaccuracy is attributed to an incorrect approximation of the navier solution for a uniform transverse load of course this problem does not inherently occur for the navier solution in cases such as free vibration or the buckling of a nonlocal plate model in which the amount of transverse load is zero in order to obtain further verification the results reported based on the navier solution by aghababaei and reddy 2009 1 for the bending analysis of a nanoplate are compared with those computed by the differential quadrature dq and finite difference fd methods as shown the results obtained by both the fd and dq methods are consistently alike and unlike the solutions reported by aghababaei and reddy 2009 1 they are independent from small scale effect

large deflection of thermo mechanical loaded bilayer orthotropic graphene sheet in on polymer matrix based on nonlocal elasticity theory abstract in this paper large deflection behavior of a bilayer graphene sheet blgs is investigated under uniformly transverse load in thermal environment with various boundary conditions using the principle of virtual work the non linear formulations are derived based on first order shear deformation plate theory fsdt and large deflection von karman equations that includes the thermal effects differential quadrature dq method and the newton raphson iterative technique is employed to solve the system of nonlinear algebraic equations to study the effect of elastic foundation on the results two types of embedded in polymer matrix eipm and resting on polymer matrix ropm are considered besides the influences of temperature rise material properties boundary conditions small scale effect thickness to length ratio aspect ratio and polymer matrix properties are studied in detail

value iteration methods in risk minimizing stopping problems we consider an optimal stopping problem with a discrete time markov process where the criterion function is a threshold probability we give the fundamental properties of optimal values and optimal stopping times but the optimal value and the optimal stopping time depend upon the threshold value we also obtain the properties of optimal values with respect to the threshold value and a value iteration method is given

optimal threshold probability in undiscounted markov decision processes with a target set we consider risk minimizing problems in undiscounted markov decisions processes with a target set we formulate the problem as an infinite horizon case with a recurrent class we show that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy also we give several value iteration methods and a policy improvement method

on some fundamental misunderstandings in the indeterminate couple stress model a comment on recent papers of a r hadjesfandiari and g f dargush abstract in a series of papers which are either published hadjesfandiari a dargush g f 2011a couple stress theory for solids int j solids struct 48 18 2496 2510 hadjesfandiari a dargush g f 2013 fundamental solutions for isotropic size dependent couple stress elasticity int j solids struct 50 9 1253 1265 or available as preprints hadjesfandiari a dargush g f 2010 polar continuum mechanics preprint arxiv 1009 3252 hadjesfandiari a r dargush g f 2011b couple stress theory for solids int j solids struct 48 2496 2510 hadjesfandiari a r 2013 on the skew symmetric character of the couple stress tensor preprint arxiv 1303 3569 hadjesfandiari a r dargush g f 2015a evolution of generalized couple stress continuum theories a critical analysis preprint arxiv 1501 03112 hadjesfandiari a r dargush g f 2015b foundations of consistent couple stress theory preprint arxiv 1509 06299 hadjesfandiari and dargush have reconsidered the linear indeterminate couple stress model they are postulating a certain physically plausible split in the virtual work principle based on this postulate they claim that the second order couple stress tensor must always be skew symmetric since they do not consider that the set of boundary conditions intervening in the virtual work principle is not unique their statement is not tenable and leads to some misunderstandings in the indeterminate couple stress model this is shown by specifying their development to the isotropic case however their choice of constitutive parameters is mathematically possible and we show that it still yields a well posed boundary value problem

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

stochastic optimization of forward recursive functions this note solves a finite horizon stochastic optimization problem with forward recursive criterion through dynamic programming the forward recursive criterion is wide it includes additive discounted multiplicative discounted risk sensitive minimum and terminal criteria the basic idea is to apply invariant imbedding method for the stochastic optimization the method incorporates recursive accumulation process into dynamics by expanding the original state space

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

markov decision processes with sample path constraints the communicating case we consider time average markov decision processes mdps which accumulate a reward and cost at each decision epoch a policy meets the sample path constraint if the time average cost is below a specified value with probability one the optimization problem is to maximize the expected average reward over all policies that meet the sample path constraint the sample path constraint is compared with the more commonly studied constraint of requiring the average expected cost to be less than a specified value although the two criteria are equivalent for certain classes of mdps their feasible and optimal policies differ for many nontrivial problems in general there does not exist optimal or nearly optimal stationary policies when the expected average cost constraint is employed assuming that a policy exists that meets the sample path constraint we establish that there exist nearly optimal stationary policies for communicating mdps a parametric linear programming algorithm is given to construct nearly optimal stationary policies the discussion relies on well known results from the theory of stochastic processes and linear programming the techniques lead to simple proofs of the existence of optimal and nearly optimal stationary policies for unichain and deterministic mdps respectively

inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems abstract at small length scales and or in presence of large field gradients the implicit long wavelength assumption of classical elasticity breaks down postulating a form of second gradient elasticity with couple stresses as a suitable phenomenological model for small scale elastic phenomena we herein extend eshelby s classical formulation for inclusions and inhomogeneities while the modified size dependent eshelby s tensor and hence the complete elastic state of inclusions containing transformation strains or eigenstrains is explicitly derived the corresponding inhomogeneity problem leads to integrals equations which do not appear to have closed form solutions to that end eshelby s equivalent inclusion method is extended to the present framework in form of a perturbation series that then can be used to approximate the elastic state of inhomogeneities the approximate scheme for inhomogeneities also serves as the basis for establishing expressions for the effective properties of composites in second gradient elasticity with couple stresses the present work is expected to find application towards nano inclusions and certain types of composites in addition to being the basis for subsequent non linear homogenization schemes

percentile optimization for markov decision processes with parameter uncertainty markov decision processes are an effective tool in modeling decision making in uncertain dynamic environments because the parameters of these models typically are estimated from data or learned from experience it is not surprising that the actual performance of a chosen strategy often differs significantly from the designer s initial expectations due to unavoidable modeling ambiguity in this paper we present a set of percentile criteria that are conceptually natural and representative of the trade off between optimistic and pessimistic views of the question we study the use of these criteria under different forms of uncertainty for both the rewards and the transitions some forms are shown to be efficiently solvable and others highly intractable in each case we outline solution concepts that take parametric uncertainty into account in the process of decision making

implementation of clamped and simply supported boundary conditions in the gdq free vibration analysis of beams and plates abstract in this paper a new methodology for implementing the clamped and simply supported boundary conditions is presented for the free vibration analysis of beams and plates using the generalized differential quadrature gdq method the proposed approach directly substitutes the boundary conditions into the governing equations and is referred to as sbcge approach the sbcge approach is presented to overcome the drawbacks of previous approaches in treating the boundary conditions a comparison of the sbcge approach with the method of modifying weighting coefficient matrices mwcm is made by their application to the vibration analysis of beams and plates with combinations of simply supported and clamped boundary conditions some details of the gdq method are also described in the paper

variability sensitive markov decision processes considered are time average markov decision processes mdps with finite state and action spaces two definitions of variability are introduced namely the expected time average variability and time average expected variability the two criteria are in general different although they can both be employed to penalize for variance in the stream of rewards for communicating mdps we construct a randomized stationary policy that is e optimal for both criteria the policy is optimal and pure for a specific variability function for general multichain mdps a state space decomposition leads to a similar result for the expected time average variability we also consider the problem of the decision maker choosing the initial state along with the policy

a refined nonconforming quadrilateral element for couple stress strain gradient elasticity c0 1 patch test int j numer meth engng 2004 61 433 454 proposed by soh and chen is a reliable method to ensure convergence of nonconforming finite element for the couple stress strain gradient elasticity the c0 1 patch test function is a complete quadratic polynomial that satisfies the equilibrium equations to pass the c0 1 patch test the element displacement functions used to calculate strains must satisfy c0 continuity or weak c0 continuity and quadratic completeness in this paper a 24 dof degrees of freedom quadrilateral element cq12 rdkq for the couple stress strain gradient elasticity is developed by combining the refined thin plate element rdkq and the nonconforming element cq12 the element rdkq which satisfies weak c1 continuity is used to calculate strain gradients whereas strains are computed by the element cq12 which is established based on an extended variational functional and satisfies weak c0 continuity and quadratic completeness numerical examples show that the element cq12 rdkq passes the c0 1 patch test and it is also more efficient than the existing available triangular and quadrilateral elements in stress concentration problems with size effects copyright 2010 john wiley sons ltd

percentile performance criteria for limiting average markov decision processes addresses the following basic feasibility problem for infinite horizon markov decision processes mdps can a policy be found that achieves a specified value target of the long run limiting average reward at a specified probability level percentile related optimization problems of maximizing the target for a specified percentile and vice versa are also considered the authors present a complete and discrete classification of both the maximal achievable target levels and of their corresponding percentiles the authors also provide an algorithm for computing a deterministic policy corresponding to any feasible target percentile pair next the authors consider similar problems for an mdp with multiple rewards and or constraints this case presents some difficulties and leads to several open problems an lp based formulation provides constructive solutions for most cases

thermo mechanical vibration of fgm sandwich beam under variable elastic foundations using differential quadrature method thermo mechanical vibration analysis of functionally graded fg beams and functionally graded sandwich fgsw beams are presented the functionally graded material fgm beams are considered to be resting on variable i winkler foundation and ii two parameter elastic foundation the material properties of these beams are assumed to be varying in the thickness direction the governing differential equations for beam vibration are being solved using the modified differential quadrature method mdqm the applied kinematic boundary conditions are implemented using the modified weighting coefficient matrix mwcm the weighting coefficients are generated from the chebyshev basis function present results for the vibration of isotropic beam with variable winkler foundation are in good agreement with those reported in the literature parametric study on the vibration response of fg beams and fgsw beams are being investigated these parameters include i temperature distributions ii power law index iii variable winkler foundation modulus iv two parameter elastic foundation modulus and v normalized core thickness of fgsw beams

non local elastic plate theories a non local plate model is proposed based on eringen s theory of non local continuum mechanics the basic equations for the non local kirchhoff and the mindlin plate theories are derived these non local plate theories allow for the small scale effect which becomes significant when dealing with micro nanoscale plate like structures as illustrative examples the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non local solutions are discussed in relation to their corresponding local solutions

nonlocal third order shear deformation plate theory with application to bending and vibration of plates abstract the third order shear deformation plate theory of reddy a simple higher order theory for laminated composite plates j appl mech 51 1984 745 752 is reformulated using the nonlocal linear elasticity theory of eringen this theory has ability to capture the both small scale effects and quadratic variation of shear strain and consequently shear stress through the plate thickness analytical solutions of bending and free vibration of a simply supported rectangular plate are presented using this theory to illustrate the effect of nonlocal theory on deflection and natural frequency of the plates finally the relations between nonlocal third order first order and classical theories are discussed by numerical results

a non local asymptotic theory for thin elastic plates the three dimensional dynamic non local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size the integral constitutive relations incorporating the variation of an exponential non local kernel across the thickness are adopted long wave low frequency approximations are derived for both bending and extensional motions boundary layers specific for non local behaviour are revealed near the plate faces it is established that the effect of the boundary layers leads to the first order corrections to the bending and extensional stiffness in the classical two dimensional plate equations

the existence of noncollision singularities in newtonian systems in this paper we solve a long standing problem in celestial mechanics proposed by painleve and poincare in the last century the problem which concerns the nature of the singularities in the n body problem asks whether there exists a noncollision singularity in the newtonian n body problem here we give an affirmative answer to this problem by proving the existence of noncollision singularities in the 5 body problem we consider n point masses moving in a euclidean space w3 let the mass of the ith particle be mi 0 let its position be qj e r3 and let 4i e 3 be its velocity according to newton s law

reply to the comments of m e golmakani and j rezatalab comment on nonlocal third order shear deformation plate theory with application to bending and vibration of plates by r aghababaei and j n reddy journal of sound and vibration 326 2009 277 289 journal of sound vibration 333 2014 3831 3835 abstract golmakani and rezatalab 1 suggested in their paper that the deflection of a simply supported nonlocal elastic plate under uniform load is not affected by the small length scale terms they based their proof on the use of navier s method using a sinusoidal based deflection solution this insensitivity of the deflection solution of a simply supported nonlocal elastic plate with respect to the small length terms of eringen s model is not correct as already detailed in the literature for example see 2 for beam problems in fact the deflection of the nonlocal plate in the eringen sense is larger than the one of the local case as shown in many papers available in the literature we prove in this reply to the authors that the navier s method has to be correctly applied for highlighting the specific sensitivity phenomenon of the deflection solution as compared to exact analytical solution the problem is exactly the same as for the bending of a beam

threshold probability of non terminal type in finite horizon markov decision processes abstract we consider a class of problems concerned with maximizing probabilities given stage wise targets which generalizes the standard threshold probability problem in markov decision processes the objective function is the probability that at all stages the associatively combined accumulation of rewards earned up to that point takes its value in a specified stage wise interval it is shown that this class reduces to the case of the nonnegative valued multiplicative criterion through an invariant imbedding technique we derive a recursive formula for the optimal value function and an effective method for obtaining the optimal policies

triangular mindlin microplate element in this article based on the most general form of strain gradient theory mgsgt a novel extended triangular mindlin plate element is proposed to accomplish this aim first the quadratic form of energy functional is obtained by vectorizing the higher order tensors of energy pairs from which the stiffness and mass matrices of the element are readily derived in comparison with the standard mindlin plate element the new element needs three additional nodal degrees of freedom dof including derivatives of lateral deflection and rotations which means a total of nine dofs per node also as compared to the standard mindlin plate element which requires only c0 shape functions the present one requires c1 continuous smooth shape functions due to second derivatives of deflection and rotations hence cubic polynomials are used to interpolate the displacement components the new element can be reduced to that based on the modified strain gradient theory msgt and the modified couple stress theory mcst moreover the standard mindlin plate element is recovered when the gradient based material parameters tend to zero the mindlin microplates with different boundary conditions are considered as the problem under study whose free vibration and bending are analyzed the results are compared with the exact solutions and excellent agreement is achieved

the principle of optimality in dynamic programming with returns in partially ordered sets a general sequential model is defined where returns are in a partially ordered set a distinction is made between maximal nondominated returns and greatest returns we show that bellman s principle of optimality is valid with respect to maximal returns and it leads to an algorithm to approximate these returns we argue that significantly greater effort is needed to apply this algorithm to maximal returns than to greatest returns

on the minimizing triple collision orbits in the planar newtonian three body problem in this paper we study the minimizing triple collision orbits in the planar newtonian three body problem with arbitrary masses we show that for a given non collinear initial configuration the minimizing triple collision orbit is collision free until a simultaneous collision and its limiting configuration is the lagrangian configuration with the same orientation as the initial configuration for the collinear initial configuration under a certain technical assumption there exist two minimizing orbits the limiting configurations of these orbits are the two opposite lagrangian configurations