variational asymptotic modeling of cosserat elastic plates one of the most important branches of applied mechanics is the theory of plates defined to be plane structural elements whose thickness is very small when compared to the two planar dimensions the

an enhancement of constraint feasibility in bpn based approximate optimization back propagation neural networks bpn have been extensively used as global approximation tools in the context of approximate optimization a traditional bpn is normally trained by minimizing the absolute difference between target outputs and approximate outputs when bpn is used as a meta model for inequality constraint function approximate optimal solutions are sometimes actually infeasible in a case where they are active at the constraint boundary the paper explores the development of the efficient bpn based meta model that enhances the constraint feasibility of approximate optimal solution the bpn based meta model is optimized via exterior penalty method to optimally determine interconnection weights between layers in the network the proposed approach is verified through a simple mathematical function and a ten bar planar truss problem for constrained approximate optimization design of rotor blade is conducted to support the proposed strategies

variational asymptotic method for unit cell homogenization of periodically heterogeneous materials a new micromechanics model namely the variational asymptotic method for unit cell homogenization vamuch is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields considering the periodicity as a small parameter we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional it is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories mht can be reproduced from this variational statement in comparison to other approaches vamuch does not rely on ad hoc assumptions has the same rigor as mht has a straightforward numerical implementation and can calculate the complete set of properties simultaneously without using multiple loadings this theory is implemented using the finite element method and an engineering program vamuch is developed for micromechanical analysis of unit cells many examples of binary composites fiber reinforced composites and particle reinforced composites are used to demonstrate the application power and accuracy of the theory and the code of vamuch

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

mathematical construction of a reissner mindlin plate theory for composite laminates abstract a reissner mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational asymptotic method instead of assuming a priori the distribution of three dimensional displacements in terms of two dimensional plate displacements as what is usually done in typical plate theories an exact intrinsic formulation has been achieved by introducing unknown three dimensional warping functions then the variational asymptotic method is applied to systematically decouple the original three dimensional problem into a one dimensional through the thickness analysis and a two dimensional plate analysis the resulting theory is an equivalent single layer reissner mindlin theory with an excellent accuracy comparable to that of higher order layer wise theories the present work is extended from the previous theory developed by the writer and his co workers with several sizable contributions a six more constants 33 in total are introduced to allow maximum freedom to transform the asymptotically correct energy into a reissner mindlin model b the semi definite programming technique is used to seek the optimum reissner mindlin model furthermore it is proved the first time that the recovered three dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces it is also shown that two of the equilibrium equations of three dimensional elasticity can be satisfied asymptotically and the third one can be satisfied approximately so that the difference between the reissner mindlin model and the second order asymptotical model can be minimized numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first order shear deformation theory demonstrating that the present theory has an excellent agreement with the exact solution

best strip beam properties derivable from classical lamination theory this paper presents a simple method to extract classical beam properties for composite strips with general anisotropy from an asymptotically correct classical lamination theory derived using the variational asymptotic method none of the ad hoc approximations common in the literature of beam theory are used rather this approach discovers the necessary and su cient engineering assumptions for obtaining the correct cross sectional constants and stress recovery relations for a strip numerical examples are provided to illustrate that the resulting theory resulting elastic constants agree well with those from well established methods of calculating cross sectional constants and the accuracy deteriorates as the strip thickness to width ratio increases

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

variational asymptotic micromechanics modeling of heterogeneous porous materials abstract this paper presents a numerical technique to predict the effective elastic properties of heterogeneous fluid filled porous media where the heterogeneity may result from dissimilar solid and fluid phase properties or due to mismatch in porous microstructure the technique is based on the variational asymptotic method of homogenization where finite element method is employed for discretization biot s theory of poroelasticity is used to describe porous media where both solid and fluid phase motions u u formulation are considered with associated strain measures the method estimates the poroelastic constitutive law in single analysis which makes it very efficient compared to other finite element based homogenization techniques the method is also general enough to compute all 28 elements of an anisotropic constitutive matrix other than estimating the effective properties the micro stress strain distribution is also obtained at no additional cost the method is successfully applied for homogenization of porous media fluid filled cavity and finally for effective property estimation of bone lamella in absence of any other direct method of porous media homogenization the present technique is compared with classical homogenization methods with fluid approximated as solid of very high poisson s ratio the suitability of this approximation and various other alternatives are also discussed it is shown that the present homogenization method can be an efficient tool for bone property estimation where fluid filled porous hierarchical micro nanostructure must be respected at all steps

enhanced first order theory based on mixed formulation and transverse normal effect abstract an accurate prediction of displacements and stresses for laminated and sandwich plates is presented using an enhanced first order plate theory based on the mixed variational theorem efsdtm developed in this paper in the mixed formulation transverse shear stresses based on an efficient higher order plate theory ehopt developed by cho and parmerter cho m parmerter r r 1993 efficient higher order composite plate theory for general lamination configurations aiaa journal 31 1299 1306 are utilized and modified to satisfy prescribed lateral conditions and displacements are assumed to be those of a first order shear deformation theory fsdt relationships between the modified ehopt and the fsdt are systematically derived via both the mixed variational theorem and the least square approximation of difference between in plane stresses including the transverse normal stress effect it is shown that the transverse normal stress effect should be considered in predicting the in plane stresses when the poisson effect is dominant the developed efsdtm preserves the computational advantage of the classical fsdt while allowing for important local through the thickness variations of displacements and stresses through the recovery procedure the accuracy and efficiency of the present theory are assessed by comparing its results with various plate models as well as the three dimensional exact solutions for thick laminated and sandwich plates

variational asymptotic analysis for plates of variable thickness abstract it is a common assumption in plate theory that the effect of varying thickness on plate elastic constants can be simply accounted for by incorporating the thickness distribution in the formulae obtained for a plate of uniform thickness for plates whose thickness varies linearly in the global directions the variation described by a set of taper parameters a plate theory has been developed using the variational asymptotic method in a first of its kind development both the 8 8 stiffness matrix and the 3d stress and strain recovery are shown to contain these taper parameters explicitly as opposed to their merely being present by virtue of the varying plate thickness furthermore terms such as bending shear and twist shear coupling are shown to be present which are typically disregarded in published works on tapered plates it is later clearly demonstrated using the full 3d finite element solutions from a test case that an analysis of this kind is needed to accurately determine the complete stress distribution in conclusion merely changing the thickness distributions in results for uniform plates may work for some problems but it is clearly not sufficient in general nor can it guarantee good agreement with all aspects of plate analysis this is because these kinds of approximations are not in tune with the mechanics of such a problem as they disregard the tilt of the outward directed normals in the boundary conditions for top and bottom surfaces furthermore as always a theory developed using the variational asymptotic method does not make any assumptions regarding the deformation and is generally well suited for capturing such effects without fundamental changes in the procedure

fibonacci and galois representations of feedback with carry shift registers a feedback with carry shift register fcsr with fibonacci architecture is a shift register provided with a small amount of memory which is used in the feedback algorithm like the linear feedback shift register lfsr the fcsr provides a simple and predictable method for the fast generation of pseudorandom sequences with good statistical properties and large periods in this paper we describe and analyze an alternative architecture for the fcsr which is similar to the galois architecture for the lfsr the galois architecture is more efficient than the fibonacci architecture because the feedback computations are performed in parallel we also describe the output sequences generated by the d fcsr a slight modification of the fibonacci fcsr architecture in which the feedback bit is delayed for d clock cycles before being returned to the first cell of the shift register we explain how these devices may be configured so as to generate sequences with large periods we show that the d fcsr also admits a more efficient galois architecture

nonlinear bending analysis of radial stiffened annular laminated sector plates with dynamic relaxation method in this paper the nonlinear bending of laminated stiffened annular sector plates under mechanical loading with various boundary conditions is investigated the plates are made of layers with orthotropic properties and different fiber orientations which the aforementioned fibers are placed in a cartesian coordinate system based on first order shear deformation plate theory fsdt and von karman relations for large deflection nonlinear equilibrium equations are developed dynamic relaxation dr numerical method combined with the finite difference discretization technique is used to solve the plate nonlinear partial differential equations and fortran program is developed to generate the numerical results effects of the plate thickness to radius ratio boundary condition stiffener depth plate lay ups and the sector angle are discussed

on asymptotically correct linear laminated plate theory abstract the focus of this paper is the development of asymptotically correct theories for laminated plates the material properties of which vary through the thickness and for which each lamina is orthotropic this work is based on the variational asymptotical method a mathematical technique by which the three dimensional analysis of plate deformation can be split into two separate analyses a one dimensional through the thickness analysis and a two dimensional plate analysis the through the thickness analysis includes elastic constants for use in the plate theory and approximate closed form recovering relations for all three dimensional field variables expressed in terms of plate variables in general the specific type of plate theory that results from this procedure is determined by the procedure itself however in this paper only reissner like plate theories are considered often called first order shear deformation theories this paper makes three main contributions first it is shown that construction of an asymptotically correct reissner like theory for laminated plates of the type considered is not possible in general second a new point of view on the variational asymptotical method is presented leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible third numerical results from such an optimum reissner like theory are presented these results include comparisons of plate displacement as well as of three dimensional field variables and are the best of all extant reissner like theories indeed they even surpass results from theories that carry many more generalized displacement variables

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

zeroth order shear deformation micro mechanical model for composite plates with in plane heterogeneity abstract this article introduces a new model for investigating the mechanical behavior of heterogeneous plates which are composed of periodically repeated microstructures along the in plane directions we first formulate the original three dimensional problem in an intrinsic form for implementation into a single unified formulation and application to geometrically nonlinear problem taking advantage of smallness of the plate thickness to length parameter and heterogeneity and performing homogenization along dimensional reduction simultaneously the variational asymptotic method is used to rigorously construct an effective zeroth order plate model which is similar to a generalized reissner mindlin model the first order shear deformation model capable of capturing the transverse shear deformations but still carries out the zeroth order approximation which can maximize simplicity and promote efficiency this present approach is incorporated into a commercial analysis package for the purpose of dealing with realistic and complex geometries and constituent materials at the microscopic level a few examples available in literature are used to demonstrate the consistence and efficiency of this new model especially for the structures in which the effects of transverse shear deformations are significant

an asymptotic method based composite plate model considering imperfect interfaces abstract this paper presents an asymptotic method based analysis of composite laminates having interfacial imperfections in general imperfect interfaces are simply modeled by introducing a linear spring layer model which empirically assumes that the displacement jumps that occur at the weakened interface are proportional to the transverse shear stresses of interface positions in this study we propose a composite plate model derived by using asymptotic expansion that does not make any assumptions other than the scaling of coordinate systems within the framework of the asymptotic analysis the spring layer model is introduced to describe the effect of weakened interfaces which is realized by the separation of domains in the through the thickness direction and the integration of piecewise continuous warping functions as a result we newly define a spring parameter that is exactly the same as the stiffness of a spring therefore a set of spring elements are added to the through the thickness modeling of the microscopic analysis and the plate equations derived in the macroscopic problem are the same as those of the perfectly bonded laminates as a consequence we also derive the proposed plate model with the mathematical rigor that the previous asymptotic models contain we provide some numerical results verifying that the proposed method shows good agreement with the elasticity and 3d fem solutions

distribution properties of multiply with carry random number generators we study the multiply with carry family of generators proposed by marsaglia as a generalization of previous add with carry families we define for them an infinite state space and focus our attention on the finite subset of recurrent states this subset will in turn split into possibly several subgenerators we discuss the uniformity of the d dimensional distribution of the output of these subgenerators over their full period in order to improve this uniformity for higher dimensions we propose a method for finding good parameters in terms of the spectral test our results are stated in a general context and are applied to a related complementary multiply with carry family of generators

geometrically exact intrinsic theory for dynamics of moving composite plates a geometrically exact and fully intrinsic theory is presented for dynamics of composite plates undergoing large deformation to say that the formulation is intrinsic means that it is without displacement and rotation variables although the equations are geometrically exact the highest degree nonlinearities are quadratic there are no singularities associated with finite rotation methods for posing problems in this framework along with advantages of the formulation are discussed

homogenization and dimensional reduction of composite plates with in plane heterogeneity the variational asymptotic method is used to construct a new model for composite plates which could have in plane heterogeneity due to both geometry and material we first formulate the original three dimensional problem in an intrinsic form which is suitable for geometrically nonlinear analysis taking advantage of smallness of the plate thickness and heterogeneity we use the variational asymptotic method to rigorously construct an effective plate model unifying a homogenization process and a dimensional reduction process this approach is implemented in the computer code vapas using the finite element technique for the purpose of dealing with realistic heterogeneous plates a few examples are used to demonstrate the capability of this new model

reconstruction of first order shear deformation shell theory for laminated and sandwich shells a first order shear deformation shell theory fsdt based on general curvilinear coordinates has been reconstructed through a strain energy transformation based on the definition of the mean displacements the transverse shear strains that are constant through the thickness are improved to vary through the thickness it is assumed that the displacements and in surface strains of three dimensional theory are approximated by those of fsdt relationship between fsdt and three dimensional theory has been systematically established in the averaged least square sense this relationship provides the closed form recovering relations for three dimensional variables expressed in terms of fsdt relations the present approach has been applied to a higher order zigzag shell theory comparisons of displacements and stresses of laminated and sandwich shells using the present theory are made with the original fsdt and three dimensional exact solutions

boundary conditions and defect lines in the abelian sandpile model we add a defect line of dissipation or crack to the abelian sandpile model we find that the defect line renormalizes to separate the two dimensional plane into two half planes with open boundary conditions we also show that varying the amount of dissipation at a boundary of the abelian sandpile model does not affect the universality class of the boundary condition we demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions

invariant finite element model for composite structures the generalized unified formulation the generalized unified formulation presented here is a modern approach for the finite element analysis of sandwich plates and in general multilayered structures a large variety of types of theories with any combination of orders of expansion for the different displacement variables can be obtained from the expansion of six 1 x 1 arrays the kernels or fundamental nuclei of the generalized unified formulation each of the displacement variables is independently treated and different orders of expansions for the different unknowns can be chosen because infinite combinations can be freely chosen for the displacements the generalized unified formulation allows the user to write 3 higher order shear deformation theories 3 zig zag theories and 3 layerwise theories with a single invariant formulation implemented in a single finite element method code the six independent fundamental nuclei are formally invariant with respect to the order used for the expansion or with respect to the type of theory the generalized unified formulation can be also adopted for mixed variational statements in such cases the number of independent kernels would be different but their size would still be 1 x 1 arrays this paper assesses bending of sandwich structures analytical and elasticity solution are compared the effect of the zig zag form of the displacement is discussed