nonlinear analysis of reissner plates on an elastic foundation by the bem the fundamental solutions and the boundary element method for obtaining numerical solutions of nonlinear reissner plates on an elastic foundation are presented in the paper the derivation of the fundamental solutions is mainly based on two of hu s functions and the resolution method of differential operator an incremental form of the boundary integral equations is suggested to achieve linearization of the original nonlinear equations the plate may be moderately thick or sandwich plates with or without elastic foundation finally three examples are considered to illustrate the correctness and accuracy of the proposed method

anisotropic elastic plates with holes cracks inclusions subjected to out of plane bending moments the problems of anisotropic plates containing holes cracks and or inclusions have been studied extensively for two dimensional deformations although the correspondence between the two dimensional problems and the plate bending problems has been observed long time ago without clarifying the involved mathematical details one still cannot get the solutions of the plate bending problems directly from the solutions of the corresponding two dimensional problems based upon the correspondence relation recently we developed a stroh like formalism for the bending theory of anisotropic plates by this newly developed formalism most of the relations for bending problems can be organized into the forms for two dimensional problems thus by using the stroh like formalism the analytical solutions for problems of anisotropic plates with holes cracks inclusions subjected to out of plane bending moments can be obtained directly from the solutions of the corresponding two dimensional problems the stresses or resultant bending moments around the hole crack inclusion boundaries are also given explicitly in this paper since the explicit closed form solutions for the present cases have not been found in the literature comparison is made with some special cases of which the analytical solutions exist which shows that our solutions are exact simple and general

sextic formalism in anisotropic elasticity for almost non semisimple matrix n abstract the sextic formalism of stroh for anisotropic elasticity leads to the eigen relation n p in which n is a 6 6 real matrix the orthogonality and closure relations as well as many other relations involving the eigenvalues p and the eigenvectors x are based on the assumption that n is simple or semisimple so that the six eigenvectors span a six dimensional space problems arise when n is non semisimple in fact there are problems even when n is almost non semisimple we present a modified formalism which is valid regardless of whether n is simple almost non semisimple or non semisimple the modified formalism does not apply when n is semisimple

adjoint based optimal control using meshfree discretizations the paper at hand presents a combination of optimal control approaches for pdes with meshless discretizations applying a classical lagrangian type particle method to optimization problems with hyperbolic constraints several adjoint based strategies differing in the sequential order of optimization and discretization of the lagrangian or eulerian problem formulation are proposed and compared the numerical results confirm the theoretically predicted independence principle of the optimization approaches and show the expected convergence behavior moreover they exemplify the superiority of meshless methods over the conventional mesh based approaches for the numerical handling and optimization of problems with time dependent geometries and freely moving boundaries

fundamental solutions and boundary integral equations for reissner s plates on two parameter foundations abstract in this paper the fundamental solutions and boundary integral equations for reissner s plates on a two parameter foundation are presented the construction of the fundamental solutions and the numerical treatment of the boundary integral equations are described in detail some numerical examples are studied to demonstrate the correctness and accuracy of the formulation presented

buckling analysis of shear deformable plates by boundary element method in this paper the derivation and numerical implementation of boundary integral equations for the buckling analysis of shear deformable plates are presented plate buckling equations are derived as a standard eigenvalue problem the formulation is formed by coupling boundary element formulations of shear deformable plate and two dimensional plane stress elasticity the eigenvalue problem of plate buckling yields the critical load factor and buckling modes the domain integrals which appear in this formulation are treated in two different ways initially the integrals are evaluated using constant cells and next they are transformed into equivalent boundary integrals using the dual reciprocity method drm several examples with different geometry loading and boundary conditions are presented to demonstrate the accuracy of the formulation

highly convergent dynamic models obtained by modal synthesis with application to short wave pulse propagation a general approach for obtaining the matrices of a substructure ensuring minimum modal frequency errors of the whole structure is presented the mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of close to exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible the goal is achieved by formulating the minimization problem for the penalty type target function representing the cumulative relative modal frequency error of the joined sample domain and by applying the gradient descent minimization method after the optimum matrices of a component domain are obtained they can be used in any structure as higher order elements or super elements the well known generalized mass matrices obtained as a weighted sum of lumped and consistent components can be treated as a special case of the presented approach the obtained dynamic models are used for modelling short transient waves and wave pulses propagating in elastic or acoustic environments by using a only a few nodal points per pulse length copyright 2004 john wiley sons ltd

boundary element modelling of flat plate floors under vertical loading the present paper develops a boundary element model for flat plate floors the floor slab is modelled using the shear deformable plate bending theory internal columns or walls are treated using internal collocation technique where three interaction generalized forces are considered at the slab column connection two bending moments in two directions and shear force in the vertical direction such forces are considered to be constant over the column cross sections the present technique takes into account the realistic geometric modelling of the column cross sections the effect of considering such geometry in the analysis of the bending moments transferred from slab to columns is studied several examples including solution of practical building slab are presented the results are compared to those obtained from other numerical methods to demonstrate the accuracy and the reliability of the present formulation the present formulation can be considered as an accurate tool to predict moment transferred from the slab to the column copyright 2004 john wiley sons ltd

analysis of orthotropic thick plates by meshless local petrov galerkin mlpg method a meshless local petrov galerkin mlpg method is applied to solve static and dynamic problems of orthotropic plates described by the reissner mindlin theory analysis of a thick orthotropic plate resting on the winkler elastic foundation is given too a weak formulation for the set of governing equations in the reissner mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied the meshless approximation based on the moving least squares mls method is employed in the numerical implementation the present computational method is applicable also to plates with varying thickness numerical results for simply supported and clamped plates are presented copyright 2006 john wiley sons ltd

application of the boundary integral equation method to reissner s plate model numerical solution of reissner s model for the bending of elastic plates by an advanced boundary integral equation method is outlined construction of fundamental solutions and computational strategy is fully described implementation of the resulting one dimensional model is illustrated by two test problems including comparison to analytical solutions

a coupled element free galerkin boundary element method for stress analysis of two dimensional solids element free galerkin efg method is a newly developed meshless method for solving partial differential equations using moving least squares interpolants it is however computationally expensive for many problems a coupled efg boundary element be method is proposed in this paper to improve the solution efficiency a procedure is developed for the coupled efg be method so that the continuity and compatibility are preserved on the interface of the two domains where the efg and be methods are applied the present coupled efg be method has been coded in fortran the validity and efficiency of the efg be method are demonstrated through a number of examples it is found that the present method can take the full advantages of both efg and be methods it is very easy to implement and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains

analyzing sequentially randomized trials based on causal effect models for realistic individualized treatment rules in this paper we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials unlike a number of methods proposed previously this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified in addition it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously this is particularly useful if the number of such rules is large in which case an approach based on individual pairwise comparisons would be likely to suffer from too much sampling variability to provide an informative answer in addition such causal effect models represent an interesting alternative to methods previously proposed for selecting an optimal individualized treatment rule in that they immediately give the user a sense of how the optimal outcome is estimated to change in the neighborhood of the identified optimum we discuss an inverse probability of treatment weighted iptw estimator for these causal effect models which is straightforward to implement using standard statistical software and develop an approach for constructing valid asymptotic confidence intervals based on the influence curve of this estimator the methodology is illustrated in two simulation studies that are intended to mimic an hiv aids trial

two dimensional piezoelectricity part i eigensolutions of nondegenerate and degenerate materials abstract general solutions of two dimensional piezoelectricity which yield all solutions of 2 d boundary values problems are obtained by combining four complex conjugate pairs of independent eigensolutions each containing an arbitrary analytic function the forms of representation are fundamentally different for 14 different classes of nondegenerate and degenerate piezoelectric materials as determined by the multiplicity and types of eigenvalues degenerate materials possess high order eigensolutions in which the eigenvectors of equal and lower orders are intrinsically coupled such coupling is nonexistent in nondegenerate cases including the well known and analytically simple case with no multiple eigenvalues the present analysis is drastically simplified by using the compliance based formalism instead of the stiffness based extended eshelby stroh formalism explicit expressions are obtained for the eigensolutions the pseudometrics and the intrinsic tensors characterizing piezoelectric materials of every type

the fundamental solution of mindlin plates resting on an elastic foundation in the laplace domain and its applications abstract the aim of this study is to investigate the method of fundamental solution mfs applied to a shear deformable plate reissner mindlin s theories resting on the elastic foundation under either a static or a dynamic load the complete expressions for internal point kernels i e fundamental solutions by the boundary element method for the mindlin plate theory are derived in the laplace transform domain for the first time on employing the mfs the boundary conditions are satisfied at collocation points by applying point forces at source points outside the domain all variables in the time domain can be obtained by durbin s laplace transform inversion method numerical examples are presented to demonstrate the accuracy of the mfs and comparisons are made with other numerical solutions in addition the sensitivity and convergence of the method are discussed for a static problem the proposed mfs is shown to be simple to implement and gives satisfactory results for shear deformable plates under static and dynamic loads

frictional contact analysis of functionally graded materials with lagrange finite block method summary based on the one dimensional differential matrix derived from the lagrange series expansion the finite block method was recently developed to solve both the elasticity and transient heat conduction problems of anisotropic and functionally graded materials in this paper the formulation of the lagrange finite block method with boundary type in the strong form is presented and applied to non conforming contact problems for the functionally graded materials subjected to either static or dynamic loads the first order partial differential matrices are only needed both in the governing equations and in the neumann boundary condition by introducing the mapping technique a block of quadratic type is transformed from the cartesian coordinate of global system to the normalized coordinate with eight seeds time dependent partial differential equations are analyzed in the laplace transformed domain and the durbin s inversion method is applied to determine all the physical values in the time domain conforming and non conforming contacts are investigated by using the iterative algorithm with full load technique illustrative numerical examples are given and comparisons have been made with analytical solutions copyright 2015 john wiley sons ltd

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

dual boundary method for assembled plate structures undergoing large deflection summary in this paper the dual boundary element method is combined with a multiregion formulation to simulate plate assembly undergoing large deflection the incremental load approach is used to treat the geometrical nonlinearity and radial basis functions are used to approximate the derivatives of the large deflection terms the dual reciprocity method is used to transfer all the domain integrals to the boundary once the solution at the boundary is obtained for the assembly a j integral for large deflection is implemented to extract the fracture parameters copyright 2011 john wiley sons ltd

deconstructing plane anisotropic elasticity part ii stroh s formalism sans frills abstract eigensolutions for all types of anisotropic elastic materials are obtained in terms of the eigenvalues and the anisotropic elastic stiffness the generalized eigenvectors and eigensolutions in the degenerate and extra degenerate cases are obtained by the derivative rule a complete set of unnormlized eigenvectors now given in terms of the elastic moduli define the barnett lothe tensors by the same expressions irrespective of material degeneracy explicit expressions of the barnett lothe tensors are obtained in various forms depending on the multiplicity of eigenvalues these expressions complement the alternative expressions of part i in terms of the elastic compliances a new family of extra degenerate materials is found suggesting the superabundance of such materials a concise proof of the equivalence of the eigensystems of the compliance based and elasticity based formalisms is given eigenrelations applicable to all cases of material degeneracy are presented in both three dimensional and six dimensional matrix formalisms

augmented levy michell equations for flexural plates abstract a new sixth order isotropic elastic and flexural plate theory is presented based on the fourth order equations of levy 1877 and michell 1900 the lack of surface loading in these levy michell equations is overcome by including the dominant flexural component of dougall s 1904 solution for a point load on the surface of a three dimensional isotropic elastic layer the augmented plate equations are arranged to fit the form of a consistent sixth order system of isotropic plate equations which include the well known work of reissner and static equations of mindlin numerical applications to two three dimensional problems with analytical solutions show good comparative results

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

dual boundary element formulation for fracture mechanics analysis of shear deformable shells this paper presents a new boundary element formulation for fracture mechanics analysis of shear deformable shells hyper singular boundary integral equations for shear deformable shells are derived dual boundary element formulations are constructed by using traction integral equations on one side of the crack surface and displacement integral equations on the other side of the crack surface and all other boundaries five stress intensity factors two for membrane behaviour and three for shear and bending are computed several crack configurations are analysed to demonstrate the efficiency and accuracy of the proposed formulation

the general fundamental solution of the sixth order reissner and mindlin plate bending models revisited abstract the sixth order differential equation system of the reissner and mindlin plate bending models describe mathematically the plate problem where lines normal to the mid plane before deformation remain straight and inextensible in the deformed configuration but not necessarily normal to the reference plane anymore the non normality condition is due to the consideration of transverse shearing strains disregarded in the classical bi harmonic kirchhoff plate model as the plate thickness is reduced and or the transverse shear modulus is increased the deformed configuration is less dependent of the transverse shear strains and in the limit as the plate thickness approaches zero and or the transverse shear modulus approaches the transverse shear strain effects vanish and the problem is exactly that described by the classical plate model in this paper we investigate the fundamental solutions of both the fourth order kirchhoff and the sixth order reissner and mindlin plate models we consider a transversely isotropic material and show that the fundamental solution of the bi harmonic problem can be obtained directly from the general fundamental solution of the sixth order plate problem in the limit as the plate thickness approaches zero and or the transverse shear modulus approaches this solution is in agreement with the analytical solution of an infinite thin clamped circular plate submitted to a unitary concentrated load acting at its center

efg approximation with discontinuous derivatives a technique for incorporating discontinuities in derivatives into meshless methods is presented the technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives the special shape functions have compact support which results in banded matrix equations the technique is described in element free galerkin context but is easily applicable to other meshless methods and projections numerical results for problems in one and two dimensions are reported 1998 john wiley sons ltd

boundary element frequency domain formulation for dynamic analysis of mindlin plates a new boundary element formulation for analysis of shear deformable plates subjected to dynamic loading is presented fundamental solutions for the mindlin plate theory are derived in the laplace transform domain the characteristics of the three flextural waves are studied in the time domain it is shown that the new fundamental solutions exhibit the same strong singularity as in the static case two numerical examples are presented to demonstrate the accuracy of the boundary element method and comparisons are made with the finite element method copyright 2006 john wiley sons ltd

simply supported plates by the boundary integral equation method plates governed by kirchhoff s equation have been analysed by the boundary integral equation method using the fundamental solution of the biharmonic equation in the case of supported plates the boundary conditions permit the uncoupling of the field equation into two harmonic equations that originate due to the nature of the fundamental solution easier integration kernels and a simpler system of equations the calculation of bending and twisting moments and transverse shear force can be formed combining derivatives of the integral equation which defines the expression of the deflection on any point of the plate the uncoupling of the biharmonic equation into two poisson s equations involves the discretization of the domain of the studied problems nevertheless the unknown quantity of the problem does not appear in the domain integrations for which a refined discretization is unnecessary in the paper however a numerical alternative is considered to express the domain integral by means of boundary integrals in this way we need only discretize the boundary of the plate making it necessary to solve a supplementary system of equations in order to calculate the coefficients of the approximation carried out

meshless local petrov galerkin mlpg method for reissner mindlin plates under dynamic load abstract a meshless local petrov galerkin mlpg method is applied to solve dynamic plate bending problems described by the reissner mindlin theory both harmonic and impact loads are considered the laplace transform is used to eliminate the time dependence of the variables for transient problems a weak formulation for the set of governing equations in the reissner mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied the meshless approximation based on the moving least squares mls method is employed for the implementation unknown laplace transformed quantities are computed from the local boundary integral equations the time dependent values are obtained by the stehfest s inversion technique

robust estimation of optimal dynamic treatment regimes for sequential treatment decisions a dynamic treatment regime is a list of sequential decision rules for assigning treatment based on a patient s history q and a learning are two main approaches for estimating the optimal regime i e that yielding the most beneficial outcome in the patient population using data from a clinical trial or observational study q learning requires postulated regression models for the outcome while a learning involves models for that part of the outcome regression representing treatment contrasts and for treatment assignment we propose an alternative to q and a learning that maximizes a doubly robust augmented inverse probability weighted estimator for population mean outcome over a restricted class of regimes simulations demonstrate the method s performance and robustness to model misspecification which is a key concern

three dimensional analysis of functionally graded plates based on the state space formalism a three dimensional analysis is presented for orthotropic functionally graded rectangular plates with simply supported edges under static and dynamic loads the material properties are assumed to be variable through the thickness the governing equations for the functionally graded material fgm are developed on the state space approach in the laplace transform domain assuming constant material properties we derive the analytical solutions that can be used to validate any numerical methods for fgm plates the numerical solutions are obtained by the use of radial basis function method three examples are presented for the fgms and laminated composite the accuracy of the proposed numerical technique has been compared with the exact solutions copyright 2011 john wiley sons ltd

interactive model building for q learning evidence based rules for optimal treatment allocation are key components in the quest for efficient effective health care delivery q learning an approximate dynamic programming algorithm is a popular method for estimating optimal sequential decision rules from data q learning requires the modeling of nonsmooth nonmonotone transformations of the data complicating the search for adequately expressive yet parsimonious statistical models the default q learning working model is multiple linear regression which is not only provably misspecified under most data generating models but also results in nonregular regression estimators complicating inference we propose an alternative strategy for estimating optimal sequential decision rules for which the requisite statistical modeling does not depend on nonsmooth nonmonotone transformed data does not result in nonregular regression estimators is consistent under a broader array of data generation models than q learning results in estimated sequential decision rules that have better sampling properties and is amenable to established statistical approaches for exploratory data analysis model building and validation we derive the new method iq learning via an interchange in the order of certain steps in q learning in simulated experiments iq learning improves on q learning in terms of integrated mean squared error and power the method is illustrated using data from a study of major depressive disorder

two dimensional piezoelectricity part ii general solution green s function and interface cracks abstract the complete solution space of a piezoelectric material is the direct sum of several orthogonal eigenspaces one for each distinct eigenvalue each one of the 14 different classes of piezoelectric materials has a distinct form of the general solution expressed in terms of the eigenvectors of the zeroth and higher orders and a kernel matrix containing analytic functions when these functions are chosen to be logarithmic one obtains in a unified way green s function of the infinite space as a single 8 8 matrix function g for the various load cases of concentrated line forces dislocations and a line charge this expression of green s function is valid for all classes of nondegenerate and degenerate materials with an appropriate choice of the parameters it reduces to the solution of a half space with concentrated line forces at a boundary point and with dislocations in the displacements as another application eigenvalues and eigensolutions are obtained for the bimaterial interface crack problem

meshless formulations for simply supported and clamped plate problems in this paper simply supported and clamped thin elastic plates are analysed the biharmonic differential equation representing the basis of the kirchhoff theory is decomposed into two poisson equations local boundary integral equations are derived for this system of equations the meshless approximation based on the moving least squares method is employed for the implementation in the case of simply supported plates it is sufficient to use the local boundary integral equations for the case of clamped plates we propose to use a combination of the local boundary integral equations and the global ones then two groups of nodal unknowns are computed separately this leads to a reduced system of algebraic equations copyright 2002 john wiley sons ltd

a boundary element method for dynamic plate bending problems abstract in this paper the fundamental solution for kirchhoff plate in the laplace transform domain is deduced and the boundary element formulation is established to study plate bending problem by use of the moment integral equation the dual boundary element equation is developed to solve the cracked plate problem subjected to dynamic loads durbin s laplace transform inversion method is used and the dynamic stress intensity factors are determined by equivalent stress technique an infinite plate containing an isolated crack or two cracks or one set of parallel cracks under heaviside load on the crack surfaces is studied the numerical results obtained demonstrate the efficiency and accuracy of the proposed formulation

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

hypersingular boundary element formulation for reissner plates in this work the hypersingular boundary element formulation for plate bending analysis based on reissner theory is presented first order taylor expansion are used to deal with the strong singularity o 1 r whereas rigid body considerations together with the taylor expansion are used to compute the hypersingular kernels o l r2 the plate boundary is discretised into quadratic isoparametric discontinuous boundary elements to satisfy the continuity requirements for the boundary unknowns several examples are tested including thin and thick plates the results show a good agreement with both the analytical solutions and the corresponding results for the standard displacement boundary element formulation 1998 elsevier science ltd all rights reserved

bi expansion approximation of the bessel functions applied to analytical integration based bem for reissner plates the paper deals with the boundary element analysis of plates modeled by the reissner theory the integral equations are obtained in standard fashion by boundary collocation the fundamental solution is expressed in terms of modified bessel functions using different series expansions for small and large arguments the transition from one to the other form is regulated by an error based criterion for selecting the number of terms which have to be used in the series expansion attention is paid to the computational aspects influencing the accuracy of the numerical model the boundary variables are described by using a quadratic b spline interpolation and the evaluation of the boundary integrals is developed almost entirely in analytical form some numerical experiments test and compare the performances of the numerical model in particular the solution within the boundary layer is studied

a boundary element formulation for geometrically nonlinear analysis of shear deformable shells abstract a new boundary element method to solve geometrically nonlinear deflection problems of shear deformable shallow shells having quadratic mid surface is presented the displacement integral equations have been derived to obtain five integral equations in term of displacements two rotations one out of plane displacement and two in plane displacements the boundary is discretised into quadratic isoparametric elements and the domain is transferred to the boundary using the dual reciprocity technique a simple yet efficient load incremental technique is developed to solve the nonlinear problem several examples are presented and the results are in good agreement with the finite element method

a modified lekhnitskii formalism a la stroh for anisotropic elasticity and classifications of the 6 6 matrix n the stroh formalism for two dimensional deformations of anisotropic elastic materials computes the eigenvalue p and the eigenvector a from an eigenrelation the vector b is then determined from a depending on the number of repeated eigenvalues p and the number of independent eigenvectors a b the system has it can be classified into six groups the lekhnitskii formalism has no eigenrelation to speak of we present a modified lekhnitskii formalism that computes the eigenvalue p and the eigenvector b from an eigenrelation the vector a is then determined from b thus the modified lekhnitskii formalism is a dual to the stroh formalism not only does the modified formalism enable us to do the classifications it is much simpler than using the stroh formalism the six groups are the sp ss d1 d2 ed and es groups the es group does not exist for a real material the ss group that has p 1 p 2 p 3 and the d2 group that has p 1 p 2 p 3 can be identified without computing the eigenvalues p and the eigenvectors a b we show that the repeated eigenvalue p 1 p 2 in the ss and d2 groups is simply a root of the quadratic equation l 2 0 we present an explicit expression of p 3 for the ss group the ed group that has three identical p can also be identified without computing p and a b however we do present an explicit expression of p we show that monoclinic materials with the symmetry plane at x 3 0 cannot belong to the ed group the identification of the sp and d1 groups is the only one that requires computation of p but not a b for special classes of materials however they can be identified without computing p in all cases the eigenvectors and the generalized eigenvectors are obtained explicitly

causal inference on quantiles with an obstetric application the current statistical literature on causal inference is primarily concerned with population means of potential outcomes while the current statistical practice also involves other meaningful quantities such as quantiles motivated by the consortium on safe labor csl a large observational study of obstetric labor progression we propose and compare methods for estimating marginal quantiles of potential outcomes as well as quantiles among the treated by adapting existing methods and techniques we derive estimators based on outcome regression or inverse probability weighting and stratification as well as a doubly robust dr estimator by incorporating stratification into the dr estimator we further develop a hybrid estimator with enhanced numerical stability at the expense of a slight bias under misspecification of the or model the proposed methods are illustrated with the csl data and evaluated in simulation experiments mimicking the csl

on the numerical green s function technique for cracks in reissner s plates abstract the numerical green s function ngf technique previously proposed by the present authors is here extended to fracture mechanics problems involving reissner s plate theory the technique numerically produces a plate bending fundamental green s function that automatically includes embedded cracks to be used in the classical boundary element method bem to solve this class of problems the applications discussed include torsion bending moment and shear force loadings in addition also presented is a series of numerical results computed in terms of normalized stress intensity factors to illustrate the good accuracy of the procedure

boundary domain element method for free vibration of moderately thick laminated orthotropic shallow shells in this paper an integral equation formulation of free vibration of moderately thick laminated orthotropic shallow shells has been established by using the method of weighted residuals and taking the static fundamental solution as the weighted function in the present formulation there are not only boundary unknowns but also domain unknowns the integral equations presented are reduced to a standard algebraic eigenvalue problem by means of the boundary domain element in the numerical implementation two kinds of different matrix formulation are presented by using two kinds of different domain elements some numerical results are presented and compared with the exact solutions in order to demonstrate the correctness and the accuracy of the present method

fracture mechanics analysis of curved stiffened panels using bem abstract a dual boundary element method is developed for a analysis of reinforced cracked shallow shells boundary integral equations are derived from the betti s reciprocal theorem for a cracked shallow shell with transverse frames and longitudinal stiffeners the effect of frames and stiffeners are treated as a distribution of line body forces the radial basis function is used to transform domain integrals to boundary integrals stress intensity factors are evaluated from crack opening displacements the effect of curvature on the stress intensity factors is illustrated by numerical examples three examples are presented to demonstrate the accuracy of this method compared with solutions obtained using the finite element method

interactive q learning for quantiles abstracta dynamic treatment regime is a sequence of decision rules each of which recommends treatment based on features of patient medical history such as past treatments and outcomes existing methods for estimating optimal dynamic treatment regimes from data optimize the mean of a response variable however the mean may not always be the most appropriate summary of performance we derive estimators of decision rules for optimizing probabilities and quantiles computed with respect to the response distribution for two stage binary treatment settings this enables estimation of dynamic treatment regimes that optimize the cumulative distribution function of the response at a prespecified point or a prespecified quantile of the response distribution such as the median the proposed methods perform favorably in simulation experiments we illustrate our approach with data from a sequentially randomized trial where the primary outcome is remission of depression symptoms supplementary materials for this arti

a state space formalism for anisotropic elasticity part i rectilinear anisotropy a state space formalism for anisotropic elasticity including the thermal effect is developed a salient feature of the formalism is that it bridges the compliance based and stiffness based formalisms in a natural way the displacement and stress components and the thermoelastic constants of a general anisotropic elastic material appear explicitly in the formulation yet it is simple and clear this is achieved by using the matrix notation to express the basic equations and grouping the stress in such a way that it enables us to cast neatly the three dimensional equations of anisotropic elasticity into a compact state equation and an output equation the homogeneous solution to the state equation for the generalized plane problem leads naturally to the eigen relation and the sextic equation of stroh extension twisting bending temperature change and body forces are accounted for through the particular solution based on the formalism the general solution for generalized plane strain and generalized torsion of an anisotropic elastic body are determined in an elegant manner

a bem based domain meshless method for the analysis of mindlin plates with general boundary conditions abstract in this paper a bem based domain meshless method is developed for the analysis of moderately thick plates modeled by mindlin s theory which permits the satisfaction of three physical conditions along the plate boundary the presented method is achieved using the concept of the analog equation of katsikadelis according to this concept the original governing differential equations are replaced by three uncoupled poisson s equations with fictitious sources under the same boundary conditions the fictitious sources are established using a technique based on bem and approximated by radial basis functions series the solution of the actual problem is obtained from the known integral representation of the potential problem thus the kernels of the boundary integral equations are conveniently established and evaluated the presented method has the advantages of the bem in the sense that the discretization and integration are performed only on the boundary and consequently mindlin plates with general boundary conditions can be analyzed without difficulty to illustrate the effectiveness applicability as well as accuracy of the method numerical results of various example problems are presented

symmetric galerkin bem for shear deformable plates a symmetric galerkin boundary element formulation is developed for shear deformable plates a mixed strategy is used for the integration process i e partial regularization using simple solutions followed by a singularity subtraction technique for the shear equation full regularization is achieved using new kernel relationships found through a constant shear mode of deformation some of the strong singular integrals are avoided altogether by using a modified traction obtained through a very simple variable change appropriate boundary conditions are defined details of the implementation are given and several example problems solved to verify the accuracy of the proposed formulation copyright 2003 john wiley sons ltd

a coupled interpolating meshfree method for computing sound radiation in infinite domain summary in this paper the coupling of the improved interpolating element free galerkin iiefg method and the variable order infinite acoustic wave envelope element wee method is studied a coupled iiefg wee method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages the coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the iiefg and wee domains in the iiefg domain the improved interpolating moving least squares iimls method is employed to form the shape functions satisfying the kronecker delta condition while nonsingular weight functions can be used the impacts of the size of the influence domain and the shape parameter on the performance of this coupled method are investigated the numerical results show that the coupled iiefg wee method can take full advantage of both the iiefg and wee methods and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the wee the experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain this article is protected by copyright all rights reserved

a novel meshless scheme for solving surface integral equations with flat integral domains numerical solutions for electromagnetic em integral equations rely on the discretization of integral domains and the use of meshes for geometric description meshing geometries is very tedious especially for complicated structures with many details tiny parts and geometric discontinuities corners or edges and remeshing could be required in many scenarios to reduce the costs of generating quality meshes meshless or mesh free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in em community the meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally in this work we first address the traditional meshless scheme for solving em integral equations based on the moving least square mls approximation for unknown currents and the use of background meshes for integrations and then develop a novel meshless scheme by applying the green s lemma to the em surface integral equations with flat domains the novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain since only the domain boundaries are discretized and no background meshes are needed the scheme is truly meshless numerical examples for em scattering by flat surface objects are presented to demonstrate the effectiveness of the novel scheme

meshless local petrov galerkin mlpg approximation to the two dimensional sine gordon equation during the past few years the idea of using meshless methods for numerical solution of partial differential equations pdes has received much attention throughout the scientific community and remarkable progress has been achieved on meshless methods the meshless local petrov galerkin mlpg method is one of the truly meshless methods since it does not require any background integration cells the integrations are carried out locally over small sub domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions in this paper the mlpg method for numerically solving the non linear two dimensional sine gordon sg equation is developed a time stepping method is employed to deal with the time derivative and a simple predictor corrector scheme is performed to eliminate the non linearity a brief discussion is outlined for numerical integrations in the proposed algorithm some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped sg equation is investigated the final numerical results confirm the ability of proposed method to deal with the unsteady non linear problems in large domains

q learning with censored data we develop methodology for a multistage decision problem with flexible number of stages in which the rewards are survival times that are subject to censoring we present a novel q learning algorithm that is adjusted for censored data and allows a flexible number of stages we provide finite sample bounds on the generalization error of the policy learned by the algorithm and show that when the optimal q function belongs to the approximation space the expected survival time for policies obtained by the algorithm converges to that of the optimal policy we simulate a multistage clinical trial with flexible number of stages and apply the proposed censored q learning algorithm to find individualized treatment regimens the methodology presented in this paper has implications in the design of personalized medicine trials in cancer and in other life threatening diseases

optimal dynamic treatment regimes summary a dynamic treatment regime is a list of decision rules one per time interval for how the level of treatment will be tailored through time to an individual s changing status the goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response to explicate our objective and to state the assumptions we use the potential outcomes model the method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules we illustrate the methodology proposed via a small simulation