a computationally viable higher order theory for laminated composite plates abstract a variational higher order theory involving all transverse strain and stress components is proposed for the analysis of laminated composites plates derived from three dimensional elasticity with emphasis on developing a viable computational methodology the theory is well studied for finite element approximations as it incorporates both c0 and c 1 continuous kinematic fields and poisson boundary conditions from the theory a simple three node stretching bending finite element is developed and applied to the problem of cylindrical bending of a symmetric carbon epoxy laminate for which an exact solution is available both the analytic and finite element result were found to be in excellent agreement with the exact solution for a wide range of the length to thickness ratio the proposed higher order theory has the same computational advantages as first order shear deformable theories the present methodology however provides greater predictive capability especially for thick section composites

denseness of the generalized eigenvectors of an h s discrete operator let t be a closed densely defined linear operator in a hilbert space h and assume there exists 0 p t such that r 0 t is a hilbert schmidt operator the operator t is a special type of discrete operator a so called h s discrete operator which is shown to be a fredholm operator in h with fredholm set equal to the whole complex plane let t i i 1 where the operator t i has ascent mi let pi i 1 2 be the projection of h onto the generalized eigenspace n t i mi along r t i mi and let s and m be the subspaces of h consisting of all x h such that x i 1 pix and such that pix 0 for i 1 2 respectively sufficient conditions are introduced which guarantee that s h and m 0 these conditions require that r t be bounded on certain rays in the complex plane and r t 0 as on at least one of the rays but specific decay rates for r t are not necessary

on new symplectic approach for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported the symplectic geometry method is introduced for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported the basic equations for the plates are first transferred into hamilton canonical equations the whole state variables are then separated using the method of eigenfunction expansion in the symplectic geometry typical examples for plates with selected boundary conditions are solved and exact bending solutions obtained since only the basic elasticity equations of the plates are used this method eliminates the need to pre determine the deformation function and is hence more reasonable than conventional methods numerical results were presented to demonstrate the validity and accuracy of this approach as compared to those reported in other literatures

the non self adjointness of the radial momentum operator in n dimensions the non self adjointness of the radial momentum operator has been noted before by several authors but the various proofs are incorrect we give a rigorous proof that the n dimensional radial momentum operator is not self adjoint and has no self adjoint extensions the main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on l2 0 dr which is not self adjoint and has no self adjoint extensions

on an unconditional basis of generalized eigenvectors of the nonself adjoint gribov operator in bargmann space abstract in this article we prove that the system of generalized eigenvectors of the gribov operator is an unconditional basis in bargmann space we also give a generalized diagonalization in the abel sense of the semigroups respectively associated to this operator and to its square root finally some open problems are pointed out

free vibrations of plate using two variable refined plate theory the novelty of this paper is the use of two variable refined plate theory for free vibration analysis of plate unlike any other theory the theory is variationally consistent and gives two governing equations which are only inertially coupled and there is no elastic coupling at all number of unknown functions involved is only two as against three in case of mindlin s theory the theory has strong similarity with classical plate theory in many aspects the theory does not require shear correction factor and transverse shear stress variation is parabolic across the thickness simple variant of the theory is also presented

exact closed form frequency equations for thick circular plates using a third order shear deformation theory abstract this paper presents for the first time exact closed form frequency equations and transverse displacement for thick circular plates with free soft simply supported hard simply supported and clamped boundary conditions based on reddy s third order shear deformation theory hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate the new formulation is verified by comparing the results with their counterparts reported in open literature natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness radius ratios the results presented on the basis of exact closed form frequency equations are expected to serve as reliable benchmarks

stress analysis of flat plates with shear using explicit stiffness matrix an explicit expression for the stiffness matrix is worked out for a triangular plate bending element considering the effect of transverse shear deformation the element has twelve nodes on the sides and four nodes internal to it the formulation is displacement type and the use of area co ordinates makes it possible to obtain the shape functions explicitly separate polynomials are assumed for transverse displacement and rotations to obtain the element stiffness matrix no matrix inversion or numerical integration need be carried out and only a few matrix multiplications of low order are necessary the element which is initially of thirty five degrees of freedom can be reduced to a thirty degrees of freedom one by condensation of the internal nodes an interesting feature of the element developed is that the values of nodal moments computed at a node point considering different elements surrounding the node do not vary significantly thus the nodal moments can be obtained directly at node points also the element does not give rise to any inconvenience like locking even for very thin plates the straightforward approach in formation of the element stiffness will cut down the storage space considerably and will also call for less cpu time thus making the use of the element well suited to low capacity computers a number of plate bending problems have been worked out using the present element for different thickness to side ratios and a comparison has been made with the available results good accuracy has been observed in all cases even for a small number of elements

diagonalization of non selfadjoint analytic semigroups and application to the shape memory alloys operator abstract to a densely defined but not necessarily selfadjoint operator a on a hilbert space h we consider on r h the following abstract elliptic problem of dirichlet type formula then in this paper we establish that for every t 0 the solution formula can be expanded into a series of generalized eigenvectors of the operator a provided that its resolvent belongs to carleman class c p for some p 0 1 2 a similar result holds for t large enough if the inverse a 1 belongs to carleman class c p for every p 1 2 see theorem 3 1 and theorem 3 2 furthermore we apply these obtained results to the shape memory alloys non selfadjoint operator formula and d n n x n when acting on an appropriate hilbert space e of functions on the interval 0 1 by establishing that the inverse c 1 belongs to the carleman class c p for every p 1 2 so that we get in this case more regularity in the sense that the operatorial series k 1 e tc p k converges strongly in e to the analytic semigroup e tc for every t 0 the p k are the projectors into the root subspaces of c a similar result holds for formula provided that t is large enough see theorem 4 1 and theorem 4 2 in section 4 for the precise result

thick levy plates re visited abstract this paper is concerned with the bending problem of levy plates which are simply supported on two opposite edges with any combination of simply supported clamped or free conditions at the remaining two edges this study attempts to solve thick levy plate problems in a novel way by establishing bending relationships that allow the prediction of mindlin plate results using the corresponding kirchhoff solutions based on the concept of load equivalence these relationships obviate the need for complicated thick plate analyses that involve significant computation time and effort numerical plate solutions are then determined from these relationships and the validity of these results is verified using other known results and those generated using the abaqus software it is through this study that the only analytical mindlin plate solutions by cooke and levinson int j mech sci 25 1983 207 are found to contain errors in this study it is found that there are important distinctions between the mindlin and reissner plate theories these differences will also be substantiated by numerical comparison

a semi analytical solution for laminated composite plates in hamiltonian system the mixed state hamiltonian canonical equation and a semi analytical solution are presented for analyzing the laminated composite plates the method accounts for the separation of variables the discrete element is employed in the plane of the lamina and the exact solution in the thick direction is derived by the state space approach furthermore in order to apply the transfer matrix method the continuity of interlaminar stresses and displacements is satisfied and the relational expression at the top and bottom plate surface is established no matter how many layers are considered by introducing the traction boundary condition at the top and bottom surface the final problem always leads to solve a set of algebraic equations of unknown joint displacements at the top surface the number of joint variables compared with the layer wise theory is 3 2q 3 in which q is the total layers the number of variables is greatly reduced the present solution is compared to those obtained using the classical theory and the higher theory

trotter kato product formula and operator norm convergence we find necessary and sufficient conditions for the operator norm convergence of the trotter kato product formula using them we prove that this convergence takes place i if the resolvent of one of the involved operators is compact either ii if one operator is relatively compact with respect to another one or iii if the product of resolvents of the involved operators is compact

analyse de scattering d un operateur cubique de heun dans l espace de bargmann the boundary conditions at infinity are used in a description of all maximal dissipative extensions in bargmann space of the minimal heun s operator the characteristic functions of the dissipative extensions are computed completeness theorems are obtained for the system of generalized eigenvectors

on an unconditional basis of generalized eigenvectors of an analytic operator and application to a problem of radiation of a vibrating structure in a light fluid abstract in this paper we prove that the system of generalized eigenvectors of the perturbed operator t e t 0 e t 1 e 2 t 2 e k t k forms an unconditional basis with parentheses in a separable hilbert space x where e c t 0 is a closed densely defined linear operator on x with domain d t 0 having compact resolvent while t 1 t 2 are linear operators on x with the same domain d d t 0 satisfying a specific growing inequality an application to a problem of radiation of a vibrating structure in a light fluid is presented

densite des vecteurs propres generalises d une classe d operateurs compacts non auto adjoints et applications we consider a closed densely defined linear operatort in a hilbert spacee and assume the existence of 0 t such thatk t 0i 1 is compact and the existence ofp 0 such thats n k o n 1 p wheres n k denotes the sequence of non zero eigenvalues of the compact hermitian operator sqrt k k in this work sufficient conditions announced in 1 are introduced to assure that the closed subspace ofe spanned by the generalized eigenvectors oft coincides withe these conditions are in particular verified by a family of non self adjoint operators arising in reggeon s field theory

trotter kato product formula and symmetrically normed ideals abstract it is proven that the trotter product formula converges in the norm of a symmetrically normed ideal of compact operators away from t0 0 if the kac operator the transfer matrix f t e tb 2e tae tb 2 belongs to this ideal for t t0 the result is generalized to the trotter kato product formula moreover if the perturbation b is small relative to a then error bounds for convergence are obtained the results apply to the dixmier trace

a two variable refined plate theory for orthotropic plate analysis a new theory which involves only two unknown functions and yet takes into account shear deformations is presented for orthotropic plate analysis unlike any other theory the theory presented gives rise to only two governing equations which are completely uncoupled for static analysis and are only inertially coupled i e no elastic coupling at all for dynamic analysis number of unknown functions involved is only two as against three in case of simple shear deformation theories of mindlin and reissner the theory presented is variationally consistent has strong similarity with classical plate theory in many aspects does not require shear correction factor gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions well studied examples available in literature are solved to validate the theory the results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the classical plate theory but are almost comparable to those obtained using higher order theories having more number of unknown functions

numerical analysis of thick plates bending behaviour of a rectangular plate is analysed with the help of a refined higher order theory the theory is based on a higher order displacement model and the three dimensional hooke s laws for plate material giving rise to a more realistic quadratic variation of the transverse shearing strains and linear variation of the transverse normal strain through the plate thickness it is shown that the segmentation method for the numerical analysis of plates simply supported on two opposite edges can be considered to be the most competitive method in terms of efficiency economy reliability and accuracy in such applications

the trotter kato product formula for gibbs semigroups the trace norm convergence of the trotter lie product formula has recently been proved for particular classes of gibbs semigroups in the present paper we prove it for the whole generality including generalization of the product formula proposed by kato

higher order piezoelectric plate theory derived from a three dimensional variational principle a three dimensional mixed variational principle is used toderive a kth order two dimensional lineartheory for an anisotropichomogeneouspiezoelectric pzt plate themechanicaldisplacements theelectricpotential theinplane components of the stress tensor and the in plane components of the electric displacement are expressed as a e niteseries of orderk inthethickness coordinate bytakinglegendrepolynomialsas thebasisfunctions however the transverse shear stress the transverse normal stress and the transverse electric displacement are expressed as a e nite series of order k 2 in the thickness coordinate the formulation accounts for the double forces without moments that may change the thickness of the plate results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1 normal tractions and 2 tangential tractions results are also computed for the bending of a cantilever thick pzt beam loaded by 1 a uniformly distributed charge density on the top and the bottom surfaces and 2 equal and opposite normal tractions distributed uniformly only on a part of the beam the seventh order plate theory captures well the boundary layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two also through the thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three dimensional elasticity equations the governing partial differential equations are second order so that lagrange basis functions can be used to solve the problem by the e nite element method

regularized trace formula of magic gribov operator on bargmann space abstract in this article we obtain a regularized trace formula for magic gribov operator h g h acting on bargmann space where g a 3 a 3 and h a a i a a a a here a and a are the standard bose annihilation and creation operators and in reggeon field theory the real parameters is the magic coupling of pomeron is pomeron intercept is the triple coupling of pomeron and i 2 1 by applying some abstract results of sadovnichii podol skii 2002 23 we give the number of corrections sufficient for the existence of finite formula of the trace of concrete magic gribov s operator

sur une valeur propre d un operateur the studied eigenvalue is the smallest one of the operator h mu mu a i lambda a a a a in the orthogonal complement of the vacuum wherea anda are the creation and annihilation operators call this eigenvaluee as attention is focused on the dependence on this eigenvalue exists and is a positive number for positive values of using the fact that the inverse ofh is a positive operator it is proved thate extends to a positive increasing analytic function on the whole real line in particular e 0 0 contrary to what might have been expected from the fact thata a a a is formally self adjoint

high order theory of homogeneous plate flexure the need for higher order models to obtain accurate estimates to transverse shear and normal stresses and strains is well known in this paper a higher order shear deformation theory with provision for cubic variation of in plane displacements and parabolic variation of the normal displacement has been considered for detailed study numerical results have been obtained for infinite plate strip simply supported on opposite edges and infinitely long in the other direction subjected to sinusoidal static load displacements strains and stresses are compared with the exact solution results by the classical plate theory levinson s theory and a higher order theory based on partial deflections are also included this study shows that the present model can predict all displacements strains and stresses reasonably accurately further it is also noted that the statically equivalent estimates to transverse stresses from classical theory and the corresponding strains also agree closely with the exact solution

the hierarchical lattices of a finite machine the concept of dynamical consistency is introduced to define a high level transition function for an arbitrary partition of the state space of a finite input state machine m the existence of a dynamically consistent transition from a partition member xi to a member xj corresponds to the existence for every state x in xi of some x dependent control sequence which takes that state directly into xj this paper analyses what are termed in block controllable partition machines and between block controllable partition machines and establishes the existence of the associated in block controllable hierarchical lattice ibcp m it is shown that any partition machine in ibcp m is between block controllable if and only if the base machine m is controllable this setting allows the specification of state to state control trajectories of m to be decomposed into high level and low level components

quelques nouvelles proprietes de regularite de l operateur de gribov in this work we establish new regularity properties for gribov s operator h a a i a a a a 2 wherea anda are the creation and annihilation operators particularly we prove that for all e 0 h 1 is in the class of carleman s operatorl1 e

the hierarchical control of st finite state machines this paper follows caines and wei 1995 where a new notion of state aggregation for finite machines was introduced via the concept of the dynamical consistency dc relation between the blocks of states in any given state space partition this formulation results in a definition of high level dynamics on the finite partition machine m whose states correspond to the given partition elements this paper treats the more general case of st systems where there is a preferred sense of flow from a set of source states s to a set of target states t which is to be achieved by hierarchical control a generalisation of the theory of caines and wei to st systems is given which includes the generalisation of the notions of dynamical consistency in block controllability and hierarchical feedback control on the associated hierarchical lattices

refined global local higher order theory and finite element for laminated plates based on completely three dimensional elasticity theory a refined global local higher order theory is presented as enhanced version of the classical global local theory proposed by li and liu int j numer meth engng 1997 40 1197 1212 in which the effect of transverse normal deformation is enhanced compared with the previous higher order theory the refined theory offers some valuable improvements these are able to predict accurately response of laminated plates subjected to thermal loading of uniform temperature however the previous higher order theory will encounter difficulty for this problem a refined three noded triangular element satisfied the requirement of c1 weak continuity conditions in the inter element is also presented the results of numerical examples of moderately thick laminated plates and even thick plates with span thickness ratios l h 2 are given to show that in plane stresses and transverse shear stresses can be reasonably predicted by the direct constitutive equation approach without smooth technique in order to accurately obtain transverse normal stresses the local equilibrium equation approach in one element is employed herein copyright 2006 john wiley sons ltd

on the existence of hybrid models for finite state machines abstract within the framework of the hierarchical hybrid control theory presented in caines and wei ieee trans automat control 43 4 1988 501 508 one may pose the following hybrid modelling problem for a given finite state machine m find a state space d a state space partition and a controlled ode system s on d such that the associated hierarchical hybrid partition machine m is a hybrid in block controllable machine which is isomorphic to m in this paper a constructive solution is given to this problem for all finite machines m

hierarchical hybrid control systems a lattice theoretic formulation the notion of dynamical consistency is extended to hybrid systems so as to define the set of dynamically consistent hybrid partition machines associated with a continuous system s following the formulation of the notions of between block and in block controllable hybrid partition machines the lattice hibc s of hybrid in block controllable partition machines is defined and investigated based on these constructions the definition and properties of hierarchical hybrid control systems are presented together with an example

approximation of the semigroup generated by the hamiltonian of reggeon field theory in bargmann space abstract the reggeon field theory is governed by a non self adjoint operator constructed as a polynomial in a a the standard bose annihilation and creation operators in zero transverse dimension this hamiltonian acting in bargmann space is defined by h a 2 a 2 a a i a a a a where i 2 1 and are real numbers and the operators a a satisfy the commutation relation a a i as the quantum mechanical system described by h has a velocity dependent potential containing powers of momentum up to the fourth the problem of existence of hamiltonian path integral for the evolution operator e t h of this theory is of interest on its own in particular can we express e t h as a limit of integral operators in this article one considerably reduces the difficulty by studying the trotter product formula of h to reach two objectives the first objective is to prove a very specific error estimate for the error in a trotter product formula in trace norm for h viewed as the sum of the operators a 2 a 2 and a a i a a a a the second objective of this work is to give a approximation of the semigroup generated by h when h is split in the sum of a 2 a 2 a a and i a a a a we note that this case is entirely different in fact the usual trotter product formula is not defined because the interaction operator a a a a is not the infinitesimal generator of a semigroup on bargmann space for 0 and 0 we choose an approximation operator i i a a a a e a 2 a 2 a a and we give a connection between and e h this choice allows us to give in a intissar note on the path integral formulation of reggeon field theory preprint a generalized trotter product formula for t a a i a a a a i e for limit case as 0 and answers to the above question

efficient formulation of robust hybrid elements using orthogonal stress strain interpolants and admissible matrix formulation this paper presents an investigation of using orthogonal constant and higher order stress modes in formulating efficient hybrid elements by equipping the primary idea of bergan and hanssen two sample elements modified from pian sumihara 5 plane and pian tong 18 hexahedral assumed contravariant stress elements are derived with the suggested admissible simplifications of the flexibility matrices incorporated into the two new elements new plane and hexahedral elements requiring respectively no and a negligible amount of computing efforts for inverting the flexibility matrices are formed all proposed elements are stable invariant contain no empirically determined factor and strictly pass the patch test popular benchmark problems are studied and the accuracy of the proposed elements is close to their parent models

an exact symplectic geometry solution for the static and dynamic analysis of reissner plates from the mixed variational principle by selection of the variables and its dual variables the hamiltonian canonical equation for the statics and dynamics analysis of reissner plates is derived so it leads the problem to the mathematical frame of symplectic geometry and its algorithms and the exact solution for the arbitary boundary conditions is also derived by the adjoint ortho normalized symplectic expansion method

a symplectic method for approximating all the eigenvalues of a hamiltonian matrix a fast method for computing all the eigenvalues of a hamiltonian matrix m is given the method relies on orthogonal symplectic similarity transformations which preserve structure and have desirable numerical properties the algorithm is about four times faster than the standard q r algorithm the computed eigenvalues are shown to be the exact eigenvalues of a matrix m e where vert e vert depends on the square root of the machine precision the accuracy of a computed eigenvalue depends on its condition and its magnitude larger eigenvalues typically being more accurate

exact solution for thermoelastic deformations of functionally graded thick rectangular plates an exact solution is obtained for three dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and or bottom surfaces suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate which are then solved by employing the power series method the exact solution is applicable to both thick and thin plates results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistentschemes exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory thee rst ordershear deformation theory and athird order shear deformation theory for functionally graded plates results are alsocomputed for a functionally graded plate with material properties derived by the mori tanaka method the self consistent scheme and a combination of these two methods

on the riesz basis of a family of analytic operators in the sense of kato and application to the problem of radiation of a vibrating structure in a light fluid abstract in this paper we prove that the system formed by some of generalized eigenvectors of the operator t 0 e t 1 e 2 t 2 which are analytic on e forms a riesz basis of the separable hilbert space h where e c and t 0 t 1 t 2 some linear transformations on h which have the same domain d h after that we give an application for a problem concerning the radiation of a vibrating structure in a light fluid

vibrations of unsymmetrically laminated plates analyzed by using a higher order theory with a c finite element formulation recently developed shear deformation theory is used to analyze vibrations of laminated composite and sandwich plates in conjunction with a c isoparametric finite element formulation the present theory is based on a higher order displacement model and the three dimensional hooke s laws for plate material giving rise to a more realistic representation of the cross sectional deformation the theory does not require the usual shear correction coefficients generally associated with reissner mindlin theories a special mass lumping procedure is used in the dynamic equilibrium equations the numerical examples presented are compared with 3 d elasticity analytical and mindlin s plate solutions and it is demonstrated that the present model predicts the frequencies more accurately when compared with the first order shear deformation theories and classical plate theories