unique real variable expressions of displacement and traction fundamental solutions covering all transversely isotropic elastic materials for 3d bem a general efficient and robust boundary element method bem formulation for the numerical solution of three dimensional linear elastic problems in transversely isotropic solids is developed in the present work the bem formulation is based on the closed form real variable expressions of the fundamental solution in displacements uik and in tractions tik originated by a unit point force valid for any combination of material properties and for any orientation of the radius vector between the source and field points a compact expression of this kind for uik was introduced by ting and lee q j mech appl math 1997 50 407 426 in terms of the stroh eigenvalues on the oblique plane normal to the radius vector working from this expression of uik and after a revision of their final formula a new approach based on the application of the rotational symmetry of the material for deducing the derivative kernel uik j and the corresponding stress kernel ijk and traction kernel tik has been developed in the present work these expressions of uik uik j ijk and tik do not suffer from the difficulties of some previous expressions obtained by other authors in different ways with complex valued functions appearing for some combinations of material parameters and or with division by zero for the radius vector at the rotational symmetry axis the expressions of uik uik j ijk and tik have been presented in a form suitable for an efficient computational implementation the correctness of these expressions and of their implementation in a three dimensional collocational bem code has been tested numerically by solving problems with known analytical solutions for different classes of transversely isotropic materials copyright 2007 john wiley sons ltd

computational modeling of uncertainty in time domain electromagnetics we discuss computationally efficient ways of accounting for the impact of uncertainty e g lack of detailed knowledge about sources materials shapes etc in computational time domain electromagnetics in contrast to classic statistical monte carlo based methods we explore a probabilistic approach based on high order accurate expansions of general stochastic processes we show this to be highly efficient and accurate on both one and two dimensional examples enabling the computation of global sensitivities of measures of interest e g radar cross sections rcs in scattering applications for a variety of types of uncertainties

on semi analytical probabilistic finite element method for homogenization of the periodic fiber reinforced composites the main aim of this paper is a development of the semi analytical probabilistic version of the finite element method fem related to the homogenization problem this approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method it originates from the generalized stochastic perturbation based fem where taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions the hybrid computational implementation of the system maple with homogenization oriented fem code mcceff is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber reinforced composites although numerical illustration deals with a homogenization of a composite with material properties defined as gaussian random variables other composite parameters as well as other probabilistic distributions may be taken into account the methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements finite differences or volumes as well as for meshless numerical strategies copyright 2011 john wiley sons ltd

extension of the certain generalized stresses method for the stochastic analysis of homogeneous and laminated shells abstract the paper presents an extension of the certain generalized stresses method cgsm for the static finite element analysis of homogeneous and laminated shells with variability the basic assumption is that the generalized stresses do not depend on input parameters perturbation the cgsm is a non intrusive method that requires only one finite element analysis with some load cases to calculate the variability of mechanical quantities of interest the uncertain input parameters are material and physical properties uniform random parameters as well as random fields are considered the displacements statistical results mean value standard deviation and distribution are obtained by monte carlo simulations using a semi analytical formula two examples are treated the scordelis lo shell roof and an automotive windscreen the method provides results of good quality and is very economical from a computational time point of view

modeling uncertainty in steady state diffusion problems via generalized polynomial chaos abstract we present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs in particular we focus on the solution of the poisson equation with random diffusivity forcing and boundary conditions the stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the askey scheme as a generalization of the original polynomial chaos idea of wiener amer j math 60 1938 897 a galerkin projection in random space is applied to derive the equations in the weak form the resulting set of deterministic equations for each random mode is solved iteratively by a block gauss seidel iteration technique both discrete and continuous random distributions are considered and convergence is verified in model problems and against monte carlo simulations

reduction of dimensions in random elastic soil medium abstract the paper deals with an application of the plane strain analysis in a stochastic three dimensional soil medium in a framework of random elasticity theory the geostatical state of stresses and the problem of a unit force acting in a statistically homogeneous half space are considered only the modulus of elasticity is considered to be random and is modelled as a three dimensional 3 d homogeneous random field as the result of imposed constrains due to the plane strain assumption the additional body and surface forces are induced in order to determine them additional equations must be introduced the equations in a form of constrain relations are proposed in this paper these equations are also valid for a case of uniformly distributed external loading first the two dimensional 2 d problem and its reduction to the uni axial strain state for the gravity forces and uniform unlimited surface loading is considered then it is generalised into a 2 d schematization of the 3 d state next the problem of a unit force acting in a statistically homogeneous half space is considered for a 3 d state of stress and strain the resulting stresses are compared with those for a 2 d state these stresses for the multidimensional state of strain and stress are presented as a sum of two components the first one reflects plane strain state stresses and is given in a form of a 3 d random field this term allows for incorporating a spatial 3 d soil variability into a two dimensional analysis the second component can be treated as a correction term and it represents the longitudinal influence of a 3 d analysis some numerical results are presented in this paper the proposed method can be regarded as a framework for further research aiming at application to a variety of geotechnical problems for which the plane strain state is assumed

stochastic boundary elements for two dimensional potential flow in homogeneous domains abstract a stochastic boundary element formulation is presented for the analysis of two dimensional steady state potential flow through homogeneous domains the operator of the governing differential equation is assumed to be random and is described by a set of correlated random variables the perturbation method in conjunction with the boundary element method is employed to derive the systems of equations for the unknown boundary variables and their respective first and second order derivatives with respect to the random variables these quantities are then used to calculate the desired response statistics a general procedure is developed which is next applied for the specific cases of random geometric configuration and random material parameter the random geometric configuration is modeled using a finite set of correlated random variables the random material parameter is modeled as a homogeneous random field which allows the use of deterministic fundamental solutions and integral representations for homogeneous domains the random field is first discretized into a set of correlated random variables and then the general procedure is applied a transformation of the correlated random variables into an uncorrelated set is performed to reduce the number of numerical operations the results for the boundary variables are used to calculate the response statistics of internal potentials these calculations require the modeling of the interior of the domain under consideration several models for representing the interior of the domain are presented for both random configuration and random material parameter and their influence on the response statistics is analysed distributed sources are considered in the present study using the particular integral approach a number of numerical examples are presented to demonstrate the validity of the present formulations the results obtained from the present analyses are compared with those obtained from monte carlo simulations with 5000 samples and a good agreement of results is observed

computation of heat conduction in materials with random variable thermophysical properties a method for the direct computation of mean values and variances of the temperature in conduction heated objects with random variable thermophysical properties is presented this method is based on a taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive monte carlo method both steady state and transient problems are considered some example problems are solved and the results discussed the simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object this may have important consequences on the design of heating operations in food process engineering

boundary element method for thermoelastic analysis of three dimensional transversely isotropic solids abstract thermal effects are well known to manifest themselves as additional volume integral terms in the direct formulation of the boundary integral equation bie for linear elastic solids when using the boundary element method bem this domain integral has been successfully transformed in an exact manner to surface ones only in isotropy and in 2d anisotropy thereby restoring the bem as a truly boundary solution technique the difficulties with extending it to 3d general anisotropic solids lie in the mathematical complexity of the green s function and its derivatives for such materials these quantities are required items in the bem formulation in this paper the exact analytical transformation of the volume integral associated with thermal effects to surface ones is achieved for a transversely isotropic material using a similar approach which the authors have previously employed for the same task in bem for 2d general anisotropy a numerical scheme however needs to be employed to evaluate some of the new terms introduced in the surface integrals that arise from this process here the mathematical soundness of the formulation is demonstrated by a few examples the numerical results obtained are checked by alternative means including those obtained from the commercial fem code ansys

efficient computation of rcs from scatterers of uncertain shapes we propose a way of accounting for the lack of detailed knowledge about material shapes in computational time domain electromagnetics we use legendre gauss lobatto stroud 2 and stroud 3 quadrature formulas to solve the resulting stochastic equation and we show the efficiency of the proposed method over statistical monte carlo simulations we also show how the radar cross section rcs in scattering is affected by the uncertainty in shape of the objects and by the direction of the incident field

long duration response evaluation of linear structural system with random system properties using time dependent polynomial chaos abstract polynomial chaos pc is one of the popular methods for approximate evaluation of responses of stochastic structural mechanics problems in the case of a structural system under dynamic loading the pc method is combined with a time integration scheme the pc method with galerkin projection converts the stochastic pde to a set of simultaneous deterministic pde which can be solved using any standard time integration scheme however the convergence of responses is known to fail for long duration time integration problem due to the development of unacceptable error in calculated response the probability density functions of the responses are not of constant type as the time progresses however in the case of generalized pc gpc these are approximated using initially considered gpc thus loses its efficiency time dependent general polynomial chaos tdgpc can be considered to overcome these difficulties where polynomials are generated on the fly to match with the pdf of the responses the present study considered an investigation of structural mechanics responses with both gaussian and non gaussian random system properties under dynamic loading using tdgpc an adaptive updation scheme based on the rms value of the coefficients of pc expansion is investigated for a proper updation of pc expansion the curse of dimensionality of pc expansion is addressed by considering only the dominant components of the responses evaluated using kl expansion further starting with lower order pc the order of pc expansion is increased only after the first updation thus reducing computational complexities

boundary integral equation solution of three dimensional elastostatic problems in transversely isotropic solids using closed form displacement fundamental solutions the boundary integral equation method is used for the solution of three dimensional elastostatic problems in transversely isotropic solids using closed form fundamental solutions the previously published point force solutions for such solids were modified and are presented in a convenient form especially suitable for use in the boundary integral equation method the new presentations are used as a basis for accurate numerical computations of all green s functions necessary in the bem process without inaccuracy and redundant computations the validity of the new presentation is shown through three numerical examples copyright 2000 john wiley sons ltd

nodal high order methods on unstructured grids we present a convergent high order accurate scheme for the solution of linear conservation laws in geometrically complex domains as our main example we include a detailed development and analysis of a scheme for the time domain solution of maxwell s equations in a three dimensional domain the fully unstructured spatial discretization is made possible by the use of a high order nodal basis employing multivariate lagrange polynomials defined on the triangles and tetrahedra while the equations themselves are satisfied in a discontinuous galerkin form with the boundary conditions being enforced weakly through a penalty term accuracy stability and convergence of the semidiscrete approximation to maxwell s equations is established rigorously and bounds on the growth of the global divergence error are provided concerns related to efficient implementations are discussed in detail this sets the stage for the presentation of examples verifying the theoretical results and illustrating the versatility flexibility and robustness when solving two and three dimensional benchmark problems in computational electromagnetics pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated

high order collocation methods for differential equations with random inputs recently there has been a growing interest in designing efficient methods for the solution of ordinary partial differential equations with random inputs to this end stochastic galerkin methods appear to be superior to other nonsampling methods and in many cases to several sampling methods however when the governing equations take complicated forms numerical implementations of stochastic galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations on the other hand the traditional sampling methods e g monte carlo methods are straightforward to implement but they do not offer convergence as fast as stochastic galerkin methods in this paper a high order stochastic collocation approach is proposed similar to stochastic galerkin methods the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence however the numerical implementation of stochastic collocation is trivial as it requires only repetitive runs of an existing deterministic solver similar to monte carlo methods the computational cost of the collocation methods depends on the choice of the collocation points and we present several feasible constructions one particular choice based on sparse grids depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods

stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion this paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates specifically the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated the uncertain moduli eigen frequencies and eigen modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis the expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen frequencies and the eigen modes distribution functions of the uncertain moduli are derived from experimental data where the pearson model is used to identify the type of density functions this realization then is employed to construct random orthogonal basis for each uncertain parameter because of available experimental modal analysis data this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results

an efficient technique based on polynomial chaos to model the uncertainty in the resonance frequency of textile antennas due to bending the generalized polynomial chaos theory is combined with a dedicated cavity model for curved textile antennas to statistically quantify variations in the antenna s resonance frequency under randomly varying bending conditions the nonintrusive stochastic method solves the dispersion relation for the resonance frequencies of a set of radius of curvature realizations corresponding to the gauss quadrature points belonging to the orthogonal polynomials having the probability density function of the random variable as a weighting function the formalism is applied to different distributions for the radius of curvature either using a priori known or on the fly constructed sets of orthogonal polynomials numerical and experimental validation shows that the new approach is at least as accurate as monte carlo simulations while being at least 100 times faster this makes the method especially suited as a design tool to account for performance variability when textile antennas are deployed on persons with varying body morphology

random field finite elements the probabilistic finite element method pfem is formulated for linear and non linear continua with inhomogeneous random fields analogous to the discretization of the displacement field in finite element methods the random field is also discretized the formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization furthermore it is shown that a reduced set of the uncorrelated variables is sufficient for the second moment analysis based on the linear formulation of the pfem the method is then extended to transient analysis in non linear continua the accuracy and efficiency of the method is demonstrated by application to a one dimensional elastic plastic wave propagation problem and a two dimensional plane stress beam bending problem the moments calculated compare favourably with those obtained by monte carlo simulation also the procedure is amenable to implementation in deterministic fem based computer programs

on the use of the auto bispectral density for detecting quadratic nonlinearity in structural systems abstract higher order spectra appear often in the analysis and identification of nonlinear systems the auto bispectral density is one example of a higher order spectrum and may be used in the analysis of stationary structural response data to detect the presence of certain types of structural nonlinearities in this work a closed form expression for the auto bispectral density derived previously by the authors is used to find the bispectral frequency most sensitive to the nonlinearity the properties of nonlinearity detectors based on estimates of the magnitude of the auto bispectral density at this frequency are then explored estimates of the auto bispectral density are obtained using the direct method based on the discrete fourier transform the bias associated with this estimator is derived here and combined with previously derived expressions for the estimator variance to give both type i and type ii errors for the detector detector performance is quantified using a receiver operating characteristic roc curve illustrating the trade off between false positives type i error and power of detection 1 0 type ii error theoretically derived roc curves are compared to those obtained via numerical simulation and show excellent agreement results are presented for different levels of nonlinearity in both the stiffness and damping terms for a spring mass system possible consequences are discussed with regard to the detection of damage induced nonlinearities in structures

a perturbation method for stochastic meshless analysis in elastostatics a stochastic meshless method is presented for solving boundary value problems in linear elasticity that involves random material properties the material property was modelled as a homogeneous random field a meshless formulation was developed to predict stochastic structural response unlike the finite element method the meshless method requires no structured mesh since only a scattered set of nodal points is required in the domain of interest there is no need for fixed connectivities between nodes in conjunction with the meshless equations classical perturbation expansions were derived to predict second moment characteristics of response numerical examples based on one and two dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method a good agreement is obtained between the results of the proposed method and monte carlo simulation since mesh generation of complex structures can be a far more time consuming and costly effort than the solution of a discrete set of equations the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems copyright 2001 john wiley sons ltd

asymptotically optimal truncated multivariate gaussian hypothesis testing with application to consensus algorithms in the interest of complexity reduction or to facilitate efficient distributed computation using consensus truncated versions of the optimal hypothesis test are considered for a canonical multivariate gaussian problem with l observations the truncated tests employ correlation terms involving any given observation the focus is on cases with a large l such that significant efficiency results with a truncation rule k as a function of l which increases very slowly with l a key result provides sufficient conditions on truncation rules and sequences of hypothesis testing problems which provide no loss in deflection performance as l approaches infinity when compared to the optimal detector the set of asymptotically optimal truncation rules satisfying these sufficient conditions varies with the scaling behavior of the difficulty of the hypothesis testing problem with l several popular classes of system and process models including observations from wide sense stationary limiting processes as l after the mean is subtracted are used as illustrative classes of examples to demonstrate the sufficient conditions are not overly restrictive in these examples significant truncation can be employed even when the difficulty of the hypothesis testing problem scales in the least favorable manner putting the most stringent conditions on the truncation rule in all the cases considered numerical results imply the fixed false alarm rate detection probability of the truncated detector converges to the detection probability of the optimal detector for our asymptotically optimal truncation in terms of deflection

a small perturbation automatic differentiation method for determining uncertainty in computational electromagnetics a new methodology for approximating uncertainties in computational electromagnetics cem solutions is discussed the proposed method involves the use of a taylor series expansion to account for small perturbations uncertainty in the input parameters and subsequent use of an automatic differentiation technique throughout the numerical calculation chain this approach is denoted as small perturbation automatic differentiation spad method and provides certain benefits over other cem uncertainty methods available in the literature the method is illustrated in a couple of examples involving a moment method solution of the electric field integral equation

scattering from two dimensional objects of varying shape combining the method of moments with the stochastic galerkin method in this communication the combined field integral equation for perfect electrically conducting scatterers is combined with the stochastic galerkin method sgm to model the impact of stochastic variations of the shape of the scatterer on the radar cross section and on the induced current distribution the sgm is compared to the stochastic collocation method scm and it is shown that for a modest number of random variables the sgm is a good alternative to the scm

stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness abstract the paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties the isogeometric analysis method is employed in the new stochastic analysis scheme which is called stochastic isogeometric analysis siga the elastic modulus and mass density are modeled as homogeneous gaussian random fields along the plane of structure the governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues in order to verify proposed method the brute force monte carlo simulation is employed the mean variance and cov coefficient of variation predicted by siga and those predicted by monte carlo simulation show good agreement the numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates the correlation between elastic modulus and mass density is also observed to have significant effect on the response cov of eigenvalue

stochastic boundary elements for two dimensional potential flow in non homogeneous media abstract a stochastic boundary element formulation is presented for the treatment of two dimensional problems of steady state potential flow in non homogeneous media that involve a random operator in the governing differential equation the randomness is introduced through the material parameter of the domain which is described as a non homogeneous random field the random field is discretized into a set of correlated random variables and a perturbation is applied to the differential equation of the problem this leads to differential equations for the unknown potential and its first and second order derivatives respectively evaluated at the mathematical expectations of the random variables resulting from the discretization of the random field an approximate method is applied for the solution of these equations by expressing the potential and its derivatives as a sum of functions of descending order these solutions are introduced into the differential equations and upon equating similar order terms a sequence of poisson s equations is obtained for each order a transformation of the correlated random variables into an uncorrelated set is performed to reduce the number of numerical operations by retaining a small number of transformed random variables the resulting equations are solved using the boundary element method to obtain the unknown boundary values of the potentials and their respective first and second order derivatives which are then used to compute the desired response statistics quadratic conforming boundary elements are used in the boundary integration and four node quadrilateral cells are used in the domain integration strongly singular terms of the boundary element matrices are obtained indirectly by applying a state of uniform unit potential over the entire contour of the object the singular domain integrals are calculated analytically direct solution techniques are used to calculate the response variables and their derivatives respectively a number of example problems are presented and the results are compared with those obtained from monte carlo simulations a good agreement of the results is observed

3d bem for general anisotropic elasticity abstract a new method for computing the system matrices g and h of the three dimensional boundary element method is presented for the elastostatic problems of general anisotropy green s functions expressed by the line integrals over a semi circle have a simple structure that allows analytical integration over the boundary elements the computation for the system matrices g and h is reduced to numerical integration of regular line integrals over the unit semi circle the proposed method has been implemented and tested with numerical examples

stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains we present stochastic projection schemes for approximating the solution of a class of deterministic linear elliptic partial differential equations defined on random domains the key idea is to carry out spatial discretization using a combination of finite element methods and stochastic mesh representations we prove a result to establish the conditions that the input uncertainty model must satisfy to ensure the validity of the stochastic mesh representation and hence the well posedness of the problem finite element spatial discretization of the governing equations using a stochastic mesh representation results in a linear random algebraic system of equations in a polynomial chaos basis whose coefficients of expansion can be non intrusively computed either at the element or the global level the resulting randomly parametrized algebraic equations are solved using stochastic projection schemes to approximate the response statistics the proposed approach is demonstrated for modeling diffusion in a square domain with a rough wall and heat transfer analysis of a three dimensional gas turbine blade model with uncertainty in the cooling core geometry the numerical results are compared against monte carlo simulations and it is shown that the proposed approach provides high quality approximations for the first two statistical moments at modest computational effort

determination of interior point stresses in two dimensional bem thermoelastic analysis of anisotropic bodies abstract in conventional boundary element method bem analysis the displacements and stresses at an interior point of an elastic body are obtained using the respective somigliana s identities after the boundary solutions for the displacements and tractions have been solved for this paper presents the derivation of somigliana s identity for the strains at any interior point of an anisotropic domain subjected to thermal effects from these strains the corresponding stresses at the interior point may be calculated directly using the duhamel neumann relation this identity is obtained in terms of integrals over the boundary of the solution domain only difficulties arising from the exact transformation of the volume integral term associated with thermal loading in bem analysis into surface integrals in the anisotropic case are discussed and the procedures to overcome them are described three numerical examples are presented to demonstrate the veracity of the formulations developed

beyond the limitations of perturbation methods for real random eigenvalue problems using exceptional points and analytic continuation a numerical method is proposed to approximate the solution of parametric eigenvalue problem when the variability of the parameters exceed the radius of convergence of low order perturbation methods the radius of convergence of eigenvalue perturbation methods based on taylor series is known to decrease when eigenvalues are getting closer to each other this phenomenon knwon as veering in structural dynamics is a direct consequence of the existence of branch point singularity in the complex plane of the varying parameters where some eigenvalues are defective when this degeneracy referred to as exceptional point ep is close to the real axis the veering becomes stronger the main idea of the proposed approach is to combined a pair of eigenvalues to remove this singularity to do so two analytic auxiliary functions are introduced and are computed through high order derivatives of the eigenvalue pair with respect to the parameter this yields a new robust eigenvalue reconstruction scheme which is compared to taylor and puiseux series in all cases theoretical bounds are established and all approximations are compared numerically on a three degrees of freedom toy model this system illustrate the ability of the method to handle the vibrations of a structure with a randomly varying parameter computationally efficient the proposed algorithm could also be relevant for actual numerical models of large size arising from other applications involving parametric eigenvalue problems e g waveguides rotating machinery or instability problems such as squeal or flutter

nonlinear free vibration analysis of composite plates with material uncertainties a monte carlo simulation approach abstract in this paper the effects of dispersion in material properties on free vibration response of composite plates with geometric nonlinearity in von karman sense are investigated the higher order shear deformation theory is employed for the study reported here an efficient c0 finite element formulation is developed for the analysis using monte carlo simulation the second order statistics i e mean and standard deviation of the nonlinear free vibration response of the composite laminates are obtained for different thickness and amplitude ratios the input statistics mean and variance of the material property are assumed to be known as a priori the computed results demonstrate the influence of the variations in the material properties and amplitudes on the nonlinear free vibration response of the composite plates the results are compared with those available in the literature

stochastic galerkin methods for elliptic interface problems with random input in this work we consider random elliptic interface problems namely the media in elliptic equations have both randomness and interfaces a galerkin method using bi orthogonal polynomials is used to convert the random problem into an uncoupled system of deterministic interface problems a principle on how to choose the orders of the approximated polynomial spaces is given based on the sensitivity analysis in random spaces with which the total degree of freedom can be significantly reduced then immersed finite element methods are introduced to solve the resulting system convergence results are given both theoretically and numerically

index set expressions can represent temporal logic formulas abstract in temporal logic tl a well formed formula is generally formed by applying rules of its syntax finitely many times however under some circumstances although formulas such as ones expressed by index set expressions are constructed via applying rules of the syntax infinitely many times they are possibly still well formed since their equivalent concise syntax formulas can be found with this motivation this paper investigates the relationship between formulas specified by index set expressions and concise syntax by means of fixed point approach firstly we present two kinds of formulas namely i n 0 i q and i n 0 q i and prove they are indeed well formed by proving they are equivalent to formulas q and q respectively further we generalize i n 0 i q to i n 0 p i i q and explore the least and greatest fixed points of an abstract equation x q p x based on these some well formed special instances of i n 0 p i i q are obtained besides with the index set expression technique we equivalently represent u strong until and w weak until constructs of propositional linear temporal logic ltl within propositional projection temporal logic pptl

the bispectrum and bicoherence for quadratically nonlinear systems subject to non gaussian inputs in the analysis of data from nonlinear systems both the bispectrum and the bicoherence have emerged as useful tools both are frequently used to detect the influence of a nonlinear system on the joint probability distribution of the system input previous work has provided an analytical expression for the bispectrum of a quadratically nonlinear system output if the input is stationary jointly gaussian distributed this work significantly generalizes the previous analysis by providing an analytical expression for the bispectrum of the response of quadratically nonlinear systems subject to stationary jointly non gaussian inputs possessing arbitrary auto correlation function the expression is then used to determine the optimal input probability density function for detecting a quadratic nonlinearity in a second order system it is also shown how the expression can be used to design an optimal nonlinear filter for detecting deviations from normality in the probability density of a signal

numerical methods for second order shape sensitivity analysis with applications to heat conduction problems in this paper two finite element based schemes for second order shape sensitivity analysis are presented in the first formulation the av dd method the first order shape sensitivity equation is derived and expressed in terms of state and adjoint variables the resultant equation is then directly differentiated to obtain the second order shape sensitivity equation in the second formulation the dd av method the functional of concern is differentiated twice to yield the second order sensitivity equation in which the second order shape derivatives can be eliminated by introducing a proper adjoint equation a thermal fin problem and a thermal insulation layer problem have been studied to validate the proposed schemes it is shown that both methods yield identical results though the dd av method is computationally more efficient

an isserlis theorem for mixed gaussian variables application to the auto bispectral density this work derives a version of isserlis theorem for the specific case of four mixed gaussian random variables the theorem is then used to derive an expression for the auto bispectral density for quadratically nonlinear systems driven with mixed gaussian iid noise

robust design of structures using optimization methods the robust design of structures with stochastic parameters is studied using optimization techniques the first two statistical moments of the stochastic parameters including design variables are considered in conjunction with the second order perturbation method for the approximation of mean value and variance of the structural response in this framework the sensitivities of the mean values and variances of the structural performance function with respect to the design variables are calculated for use in the optimization task the robust design of structures is formulated as a multi criteria optimization problem in which both the expected value and the standard deviation of the objective function are to be minimized the robustness of the feasibility is also taken into account by involving the variability of the structural response in the constraints the two criteria optimization problem is converted into a scalar one and is then solved by a gradient based optimization algorithm to demonstrate the applicability of the presented method numerical examples are given involving static and dynamic response

karhunen loeve decomposition of random fields based on a hierarchical matrix approach summary the simulation of the behavior of structures with uncertain properties is a challenging issue because it requires suitable probabilistic models and adequate numerical tools nowadays it is possible to perform probabilistic investigations of the structural performance which take into account a space variant uncertainty characterization of the structures given a structural solver and the probabilistic models the reliability analysis of the structural response depends on the continuous random fields approximation which is carried out by means of a finite set of random variables the paper analyzes the main aspects of discretization in the case of 2d problems the combination of the well known karhunen loeve series expansion the finite element method and the hierarchical matrices approach is proposed in the paper copyright 2013 john wiley sons ltd

a canonical form based decision procedure and model checking approach for propositional projection temporal logic this paper proposes a canonical form cf for chop formulas of propositional projection temporal logic pptl based on cf an improved algorithm for constructing labeled normal form graph lnfg of a pptl formula is presented this improvement leads to a better decision procedure for pptl with infinite models in addition a transformation from lnfgs to generalized buchi automata gba and then buchi automata ba is formalized thus a spin based model checking approach is generalized for pptl to illustrate how these algorithms work several examples are given

an efficient 3d stochastic finite element method real life structural systems are characterized by their inherent or externally induced uncertainties in the design parameters this study proposes a stochastic finite element tool efficient to take account of these uncertainties here uncertain structural parameter is modeled as homogeneous gaussian stochastic field and commonly used two dimensional 2d local averaging technique is extended and generalized for 3d random field this is followed by cholesky decomposition of respective covariance matrix for digital simulation by expanding uncertain stiffness matrix about its reference value the neumann expansion method is introduced blended with direct monte carlo simulation this approach involves decomposition of stiffness matrix only once for the entire simulated structure thus substantial saving of cpu time and also the scope of tackling several stochastic fields simultaneously are the basic advantages of the proposed algorithm accuracy and efficiency of this method with reference to example problem is also studied here and numerical results validate its superiority over direct simulation method or first order perturbation approach

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

stress based topology optimization of continuum structures under uncertainties abstract this work addresses the use of the topology optimization approach to the design of continuum structures with failure constraints under the hypothesis of uncertainties in the spatial distribution of young s modulus to this end the first order perturbation approach is used to model the response of the structure and the midpoint discretization technique is used to represent the random field the objective is the minimization of the amount of material used in the design subjected to local stress constraints under uncertainties the probability of failure is bounded by the one sided chebychev inequality since the exact probability distribution function of the stress constraints is not known in advance the effective probability of failure of the obtained optimal designs is validated with the use of the monte carlo simulation approach indicating that the probability of failures of the topologies obtained with the stochastic approach is within the bounds provided by the one sided chebychev inequality the optimization problem is solved by means of the augmented lagrangian method in order to address the large number of constraints associated to this kind of formulation it is shown that the correlation length and the number of standard deviations considered in the formulation play an important role in both the obtained topology and effective probability of failure

a practical decision procedure for propositional projection temporal logic with infinite models this paper presents a practical decision procedure for propositional projection temporal logic with infinite models first a set prop l of labels l i 0 i n n 0 is used to mark nodes of an lnfg of a formula and a node with l i is treated as an accepting state as in an automaton further the generalized buchi accepting condition for automata is employed to identify a path resulting a word in an lnfg as a model of the formula in addition the implementation details of the decision procedure and relevant algorithms including pre processing lnfg circle finding algorithms are presented as a matter of fact all algorithms are implemented by c programs

an iterative polynomial chaos approach for solution of structural mechanics problem with gaussian material property abstract a new approach for solution of stochastic structural mechanics problem with random coefficient in the framework of polynomial chaos pc expansion is proposed the basic strategy of the proposed method is to iteratively construct a pc expansion with reduced numbers of unknown coefficients the method is based on orthogonal expansion of stochastic responses and generation of an iterative pc based on the responses of the previous iteration the polynomials are evaluated using gram schmidt orthogonalization process the number of random variables in pc expansion is reduced by considering only the dominant components of the response characteristics which is evaluated using karhunen loeve kl expansion in case of random material field problem kl expansion is used to discretize the random field the usefulness of the proposed method in terms of accuracy and computational efficiency is examined the results of linear static structural mechanics problems are compared with mcs and pc method the proposed method is observed to be computationally more efficient and accurate than pc method

electromagnetic uncertainty analysis using stochastic fdfd method this paper presents a novel stochastic finite difference frequency domain s fdfd method that incorporates the statistical variations of electrical properties directly into the fdfd algorithm by using the delta method approximation the method is validated through two examples a 1 d bioelectromagnetic layered model and specific absorption rate in a 2 d slice of a human head model comparisons between the single run s fdfd results and those of the monte carlo method the benchmark in statistical simulations show that the s fdfd method can predict the mean and variance of electromagnetic fields with a fair degree of accuracy in a computationally efficient way our numerical experiment also shows that the accuracy is highly dependent on the approximation for the correlation coefficients of the variance equations

a decision procedure and complete axiomatization for projection temporal logic abstract to specify and verify the concurrent and reactive systems with the theorem proving approach a complete axiomatization is formalized for first order projection temporal logic ptl with both finite and infinite time to this end ptl is restricted to a finite domain and the syntax semantics as well as the axiomatization of ptl are presented further the techniques of labeled normal form and labeled normal form graph of ptl formulas are introduced respectively with which a decision procedure for quantifier free ptl qfptl formulas is given moreover a generalized labeled normal form graph is defined and employed to transform a quantified ptl formula into its equivalent qfptl formula finally a decision procedure for ptl is formalized and the completeness of the axiomatic system is proved based on the decidability of ptl formulas

derivatives of the three dimensional green s functions for anisotropic materials abstract a concise formulation is presented for the derivatives of green s functions of three dimensional generally anisotropic elastic materials direct calculation for derivatives of the green s function on the cartesian coordinate system is a common practice which however usually leads to a complicated course in this paper the green s function derived by ting and lee ting t c t lee v g 1997 the three dimensional elastostatic green s function for general anisotropic linear elastic solids the quarterly journal of mechanics and applied mathematics 50 3 407 426 is extended to obtain the derivatives using a spherical coordinate system the green s function can be shown as the composition of two independent functions one depends only on the radial distance of the field point to the origin and the other is in spherical angles the method of derivation is based on the total differential scheme and then takes its partial differentiation accordingly with the application of cauchy residue theorem the contour integral can be evaluated in terms of the stroh eigenvalues of a sextic equation for the degenerate case evaluation of residues at multiple poles is also given applications of the present result are made to examine the green s functions and stress components for isotropic and transversely isotropic materials the results are in exact agreement with existing solutions

analytical transformation of the volume integral in the boundary integral equation for 3d anisotropic elastostatics involving body force abstract in the boundary element method bem it is well known that the presence of body force shall give rise to an additional volume integral that conventionally requires domain discretization for numerical computations to restore the bem s distinctive notion of boundary discretization the present work analytically transforms the volume integral to surface ones for the body force effect in the 3d anisotropic elasticity on applying green s theorem new fundamental solutions with explicit forms of fourier series are introduced to facilitate the volume to surface transformation the coefficients of the fourier series representations are determined by solving a banded matrix formulated from integrations of the constrained equation of no doubt such an approach has fully restored the boundary element method as a truly boundary solution technique for analyzing 3d anisotropic elasticity involving body force at the end numerical verifications of the volume to surface integral transformation are presented also such an approach has been implemented in an existing bem code for demonstrating the implementation numerical examples are presented with comparisons with ansys analysis to the author s knowledge this is the first work in the open literature that reports the successful transformation for 3d anisotropic elasticity

stochastic finite elements of discretely parameterized random systems on domains with boundary uncertainty the problem of representing random fields describing the material and boundary properties of the physical system at discrete points of the spatial domain is studied in the context of linear stochastic finite element method a randomly parameterized diffusion system with a set of independent identically distributed stochastic variables is considered the discretized parametric fields are interpolated within each element with multidimensional lagrange polynomials and integrated into the weak formulation the proposed discretized random field representation has been utilized to express the random fluctuations of the domain boundary with nodal position coordinates and a set of random variables the description of the boundary perturbation has been incorporated into the weak stochastic finite element formulation using a stochastic isoparametric mapping of the random domain to a deterministic master domain a method for obtaining the linear system of equations under the proposed mapping using generic finite element weak formulation and the stochastic spectral galerkin framework is studied in detail the treatment presents a unified way of handling the parametric uncertainty and random boundary fluctuations for dynamic systems the convergence behavior of the proposed methodologies has been demonstrated with numerical examples to establish the validity of the numerical scheme

source identification in time domain electromagnetics in this paper we introduce two numerical methods to get an electric source that gives a specified electromagnetic field some time after the source starts emitting the first one is called the time reversal method trm and originates from acoustics and the second one is called linear combination of configuration fields lccf and consists in constructing and solving a linear problem in order to find a possible required source in this paper we show on 1d and 2d examples that the last method gives lower relative errors when compared with the time reversal method

free vibration of laminated spherical panels with random material properties randomness in the material properties is inherent in all engineering materials composites exhibit a greater scatter compared to conventional materials because of the larger number of parameters associated with its fabrication and manufacturing for accurate prediction of its behavior the composite material properties have been modelled as random variables in the present study higher order shear deformation theory including rotatory inertia effects has been employed in developing the system equations and first order perturbation technique has been adopted for the solution an approach has been presented for obtaining the analytical solution for generalized eigenvalue problem associated with free vibrations mean and variance of the natural frequency have been obtained for cross ply spherical laminates projected in rectangular plan form with different boundary conditions

computational uncertainty analysis in multiresolution materials via stochastic constitutive theory abstract a stochastic constitutive theory is proposed in this work to propagate microstructure uncertainties in computational multiscale continuum models to bulk multiresolution material behavior ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized in detail and this research transmits these uncertainties to coarser material resolutions by introducing a stochastic constitutive theory deduced from volume element simulations to implement the stochastic upscaling process two advanced uncertainty quantification methods are examined statistical copula functions and random process polynomial chaos expansion both methods confront the mathematical difficulty in randomizing constitutive laws by capturing the marked correlation among constitutive parameters seen in complex materials thus the results proffer a more accurate probabilistic estimation of constitutive material behavior the contribution of this work is twofold uncertainty is propagated from heterogeneous material structure to material property via the stochastic constitutive theory and rigorous data driven mathematics are formalized to represent complicated dependence structures in multivariate statistical distributions to the authors knowledge this is the first work in multiresolution mechanics that presents an approach to computationally derive correlation functions from numerical experiments as opposed for instance to assuming one a priori the method put forth in this research though quite general is applied to a mathematical example and plastic high strength steel alloy for demonstration results include stochastic constitutive curve confidence intervals for the material stress strain response and qualitative comparisons of the two stochastic methods detailed herein

stochastic analysis of scattered field by building facades using polynomial chaos this paper presents a statistical assessment of scattered field from a building facade having rando m physical and geometrical parameters a simple inhomogeneous model is considered for the building and the calculation met hod is based on green s functions the basis of polynomial chaos expansion method is explained and applied to estimate the sca ttered electric field from a building facade having 8 random parameters in specular and non specular scenarios uncertainty analysis and total output distribution are discussed in differen t diffraction zones of the building ireless communications particularly mobile networks experienced a great expansion worldwide these networks are very dense in urban areas and th e electromagnetic field distribution is highly depend ent on city structures it is essential to have predictive tool s to assess as accurately as possible the distribution of electrom agnetic fields in order to enable optimized implementation of base stations and respect the constraints regarding huma n exposure wave propagation simulators are based on different models of urban environment with different assumptions on the building architectural details given the adopted model the y incorporate appropriate calculation methods we can mention empirical statistical theoretical site specific models or a combination of them to generate a hybrid model 1 empirical models 2 are based on the extensive measurement campaigns and are highly related to the structure of the city statistical models 3 are also based on measurements and are u sed to give wide band multipath model of the environment theoretical physical 4 models are obtained by i mposing some general idealized conditions on the geometry they usually use physical optics with or without diffrac tion phenomena site specific models 5 depend on a lar ge number of parameters which are related to a given s ite and their computing time depending on the complexity o f the environment can be long these models usually employ ray

explicit solution to the stochastic system of linear algebraic equations α1a1 α2a2 αmam x b abstract this paper presents a novel solution strategy to the stochastic system of linear algebraic equations 1 a 1 2 a 2 m a m x b arising from stochastic finite element modelling in computational mechanics in which i i 1 m denote random variables a i i 1 m real symmetric deterministic matrices b a deterministic random vector and x the unknown random vector to be solved the system is first decoupled by simultaneously diagonalizing all the matrices a i via a similarity transformation and then it is trivial to invert the sum of the diagonalized stochastic matrices to obtain the explicit solution of the stochastic equation system unless all the matrices a i share exactly the same eigen structure the joint diagonalization can only be approximately achieved hence the solution is approximate and corresponds to a particular average eigen structure of the matrix family specifically the classical jacobi algorithm for the computation of eigenvalues of a single matrix is modified to accommodate multiple matrices and the resulting jacobi like joint diagonalization algorithm preserves the fundamental properties of the original version including its convergence and an explicit solution for the optimal givens rotation angle three numerical examples are provided to illustrate the performance of the method