a monte carlo based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type random set theory is a useful tool to quantify lower and upper bounds on the probability of the occurrence of events given uncertain information represented for example by possibility distributions probability boxes or dempster shafer structures among others in this paper it is shown that the belief and plausibility estimated by dempster shafer evidence theory are basically approximations by riemann stieltjes sums of the integrals of the lower and upper probability employed when using infinite random sets of indexable type in addition it is shown that the evaluation of the lower and upper probability is more efficient if it is done by pseudo monte carlo strategies this discourages the use of dempster shafer evidence theory and suggests the use of infinite random sets of indexable type specially in high dimensions not only because the initial discretization step of the basic variables is not required anymore but also because the evaluation of the lower and upper probability of events is much more efficient using the different techniques for multidimensional integration like monte carlo simulation

femoral strain during walking predicted with muscle forces from static and dynamic optimization mechanical strain plays an important role in skeletal health and the ability to accurately and noninvasively quantify bone strain in vivo may be used to develop preventive measures that improve bone quality and decrease fracture risk a non invasive estimation of bone strain requires combined musculoskeletal finite element modeling for which the applied muscle forces are usually obtained from static optimization so methods in this study we compared finite element predicted femoral strains in walking using muscle forces obtained from so to those obtained from forward dynamics fd simulation the general trends in strain distributions were similar between fd and so derived conditions and both agreed well with previously reported in vivo strain gage measurements on the other hand differences in peak maximum emax and minimum emin principal strain magnitudes were as high as 32 between fd emax emin 945 1271 e and so emax emin 752 859 e these large differences in strain magnitudes were observed during the first half of stance where so predicted lower gluteal muscle forces and virtually no co contraction of the hip adductors compared to fd the importance of these results will likely depend on the purpose application of the modeling procedure if the goal is to obtain a generalized strain distribution for adaptive bone remodeling algorithms then traditional so is likely sufficient in cases were strain magnitudes are critical as is the case with fracture risk assessment bone strain estimation may benefit by including muscle activation and contractile dynamics in so or by using fd when practical

comparison of dynamic response of structures with uncertain but bounded parameters using non probabilistic interval analysis method and probabilistic approach abstract now by combining the finite element analysis and interval mathematics a new non probabilistic set theoretical models that is interval analysis method is being developed in scientific and engineering communities to predict the variability or uncertainty resulting from the unavoidable scatter in structural parameters and the external excitations as an alternative to the classical probabilistic approaches interval analysis methods of uncertainty were developed for modeling uncertain parameters of structures in which bounds on the magnitude of uncertain parameters are only required not necessarily knowing the probabilistic distribution densities instead of conventional optimization studies where the minimum possible response is sought here an uncertainty modeling is developed as an anti optimization problem of finding the least favorable response and the most favorable response under the constraints within the set theoretical description in this study we presented the non probabilistic interval analysis method for the dynamical response of structures with uncertain but bounded parameters under the condition of the interval vector which contains the uncertain but bounded parameters determined from probabilistic statistical information or stochastic sample test through comparing between the non probabilistic interval analysis method and the probabilistic approach in the mathematical proof and the numerical examples we can see that the region of the dynamical response of structures with uncertain but bounded parameters obtained by the interval analysis method contains that produced by the probabilistic approach in other words the width of the maximum or upper and minimum or lower bounds on the dynamical responses yielded by the probabilistic approach is tighter than those produced by the interval analysis method this kind of results is coincident with the meaning of the probabilistic theory and interval mathematics

an exponential integrator for finite volume discretization of a reaction advection diffusion equation we consider the numerical approximation of a general second order semi linear parabolic partial differential equation equations of this type arise in many contexts such as transport in porous media using the finite volume with two point flux approximation on regular mesh combined with exponential time differencing of order one etd1 for temporal discretization we derive the l 2 estimate under the assumption that the non linear term is locally lipschitz numerical simulations to sustain the theoretical results are provided

finite element interval analysis of external loads identified by displacement input with uncertainty a finite element formulation is proposed for the interval estimation of the nodal forces identified by displacement input with uncertainty the stiffness matrix of the structural system in problem of linear elastic body under static loading is assumed to be known and determinate this assumption enables us to derive the governing equation of the nodal forces to be identified with respect to the nominal displacement input from the stiffness equation based on the moore penrose generalized inverse solution of the unknown remnant displacements we assume that the uncertain errors involved in the nodal displacements obtained somehow by measurement and used as input are confined in a convex hull the effect of the uncertainty on the identified nodal forces is evaluated by the sensitivity analysis of the forces with respect to the uncertain displacements how to estimate the scatter of the identified nodal forces corresponding to the uncertain displacements confined in the convex hull is devised by means of the lagrange multiplier method the validity of the proposed method for identification and interval estimation of the nodal forces is shown by the numerical example of an elastic square plate in the plane stress state and subject to in plane loading

correlation analysis of non probabilistic convex model and corresponding structural reliability technique compared with the probability approach the non probabilistic convex model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters and whereby makes the reliability analysis very convenient and economical in this paper we attempt to propose and create a correlation analysis technique mathematically for the non probabilistic convex model and based on it develop an effective method to construct the multidimensional ellipsoids on the uncertainty a marginal convex model is defined to describe the variation range of each uncertain parameter and a covariance is defined to represent the correlation degree of two uncertain parameters for a multidimensional problem the covariance matrix and correlation matrix can be created through all marginal convex models and covariances based on which the required ellipsoid on the uncertainty can be conveniently achieved by combining the correlation analysis technique and the reliability index approach a non probabilistic reliability analysis method is also developed for uncertain structures six numerical examples are presented to demonstrate the effectiveness of the present method

a meshless method for solving the cauchy problem in three dimensional elastostatics the application of the method of fundamental solutions to the cauchy problem in three dimensional isotropic linear elasticity is investigated the resulting system of linear algebraic equations is ill conditioned and therefore its solution is regularized by employing the first order tikhonov functional while the choice of the regularization parameter is based on the l curve method numerical results are presented for both under and equally determined cauchy problems in a piece wise smooth geometry the convergence accuracy and stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain and decreasing the amount of noise added into the input data respectively are analysed

remediation of contaminated groundwater by meshless local weak forms in this paper four meshless local weak form methods such as direct meshless local petrovgalerkin method dmlpg meshless local petrovgalerkin method mlpg local weak radial point interpolation method lwrpim and local weak moving kriging method lwmk are applied to find the numerical solution of coupled non linear advectiondiffusionreaction system arising in the prevention of groundwater contamination problem a comparison between these methods is done from the perspective of accuracy and computational efficiency an efficient fourth order exponential time differencing rungekutta method is utilized for the time discretization the computational efficiency is the most significant advantage of the dmlpg method in comparison with the other meshless local weak form methods because dmlpg reduces the computational costs significantly this is due to the fact that dmlpg shifts the numerical integrations over low degree polynomials rather than over complicated shape functions the main aim of this paper is to show that the meshless local weak form methods can be used for solving the system of non linear partial differential equations especially coupled non linear advectiondiffusionreaction system the numerical results confirm the good efficiency of the proposed methods for solving our model

error estimates for the interpolating moving least squares method in this paper the interpolating moving least squares imls method presented by lancaster and salkauskas is discussed in details the advantage of the imls method is that the meshless method which is constructed based on the imls method can apply the essential boundary conditions directly and easily a simpler expression of the approximation function of the imls method is obtained then the error estimate of the approximation function and its first and second order derivatives of the imls method are presented in one dimensional case in this paper the theoretical results show that if the order of the polynomial basis functions is big enough and the original function is sufficiently smooth then the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes for the purpose of demonstration some selected numerical examples are given to prove the theories in this paper

the complex variable interpolating moving least squares method abstract in this paper a new method for deriving the moving least squares mls approximation is presented first considering the unclear physical meaning of the functional in the existing complex variable moving least squares cvmls approximation an improved cvmls approximation is presented by constructing a new functional with an explicit physical meaning based on the improved cvmls approximation the complex variable interpolating moving least squares cvimls method is presented and the interpolating property of the corresponding shape function of the cvimls method is proved

coupled nonlinear advection diffusion reaction system for prevention of groundwater contamination by modified upwind finite volume element method the coupled advection dominated diffusion reaction equations arising in the prevention of groundwater contamination problem are approximated by the modified upwind finite volume element method in order to solve the resulting nonlinear system efficiently we use a two grid algorithm to decompose the nonlinear system into a small nonlinear system on a coarse grid with mesh size h and a linear system on a fine grid with mesh size h it is shown that the approximation still achieves asymptotically optimal as long as the mesh sizes satisfy h o h 1 3 numerical examples are presented to illustrate efficiency and accuracy of the proposed method

analysis of ciarlet raviart mixed finite element methods for solving damped boussinesq equation abstract in this paper we consider the numerical solution of damped boussinesq equation using ciarlet raviart mixed finite element method an implicit finite difference scheme is used for the time discretization a priori error estimates are analyzed and stability analysis of the method is shown we obtain an optimal error estimate in l 2 norm with quadratic or higher order element for both semi and fully discrete finite element approximations finally numerical examples are given to verify the theoretical results

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

interpolating stabilized moving least squares mls approximation for 2d elliptic interface problems abstract the main aim of the current paper is to propose a new truly meshless numerical technique to solve the one and two dimensional elliptic interface problems the employed meshless approach is based on a new class of mls approximation the numerical procedure is based on the interpolating stabilized mls ismls approximation the new shape functions that have been made by the ismls technique have the kronecker property thus the dirichlet boundary conditions can be applied directly in the current investigation we propose a meshless collocation method for solving elliptic interface problems based on the shape functions of ismls technique several test problems with sufficient complexity have been studied to check the accuracy and efficiency of the new numerical procedure moreover test problems show the acceptable accuracy and efficiency of the proposed scheme

an emg driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo this paper examined if an electromyography emg driven musculoskeletal model of the human knee could be used to predict knee moments calculated using inverse dynamics across a varied range of dynamic contractile conditions muscle tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three dimensional anatomical model of the lower limb muscle activation was determined using a second order discrete non linear model using rectified and lowpass filtered emg as input a modified hill type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs the model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion extension fe muscle moment with those measured by inverse dynamics the model was calibrated for each subject using 5 different tasks including passive and active fe in an isokinetic dynamometer running and cutting manoeuvres recorded using three dimensional motion analysis once calibrated the model was used to predict the fe moments estimated via inverse dynamics from over 200 isokinetic dynamometer running and sidestepping tasks the inverse dynamics joint moments were predicted with an average r 2 of 0 91 and mean residual error of b12 nm a re calibration of only the emg to activation parameters revealed fe moments prediction across weeks of similar accuracy changing the muscle model to one that is more physiologically correct produced better predictions the modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks r 2003 elsevier science ltd all rights reserved

maximum voluntary joint torque as a function of joint angle and angular velocity model development and application to the lower limb measurements of human strength can be important during analyses of physical activities such measurements have often taken the form of the maximum voluntary torque at a single joint angle and angular velocity however the available strength varies substantially with joint position and velocity when examining dynamic activities strength measurements should account for these variations a model is presented of maximum voluntary joint torque as a function of joint angle and angular velocity the model is based on well known physiological relationships between muscle force and length and between muscle force and velocity and was tested by fitting it to maximum voluntary joint torque data from six different exertions in the lower limb isometric concentric and eccentric maximum voluntary contractions were collected during hip extension hip flexion knee extension knee flexion ankle plantar flexion and dorsiflexion model parameters are reported for each of these exertion directions by gender and age group this model provides an efficient method by which strength variations with joint angle and angular velocity may be incorporated into comparisons between joint torques calculated by inverse dynamics and the maximum available joint torques

a strategy to identify exciting forces acting on structures the strategy for identifying the external forces acting on structures sketched by turco comput method appl mech eng 1998 165 291 306 is extended to the dynamic case starting from the measurement of the stress or strain history in a suitable number of points of the structure the exciting forces are reconstructed this inverse problem is tackled in the frequency domain by using the standard tools of computational mechanics along with a classical approach to treat ill conditioned problems some numerical results relating to pin jointed trusses are discussed in order to validate the proposed strategy copyright 2005 john wiley sons ltd

lattice boltzmann method for groundwater flow in non orthogonal structured lattices the efficiency of the lattice boltzmann method lbm in modeling isotropic groundwater flow in domains of arbitrary geometry has been investigated the poisson equation was transformed in general curvilinear coordinates the corresponding equilibrium function for the d2q9 square lattice based on metric function between the physical and the computational domain has been established the resulting lbm was checked on examples having higher generality flows in confined and unconfined aquifers in vertical and horizontal plane have been considered in addition the phreatic water table representing upper boundary in the vertical plane was determined by the dynamic stretching approach not requiring complex concepts for dealing with the free surface like the volume of fluid method the accuracy and stability of the model is controlled by the adaptive mesh concept this allows application of higher density grid in critical areas with high pressure and velocity gradients and vice versa the number of computation points is significantly reduced without loosing accuracy the basic characteristics of the lbm including features like parallelization and simplicity are maintained the advantages of the proposed curvilinear lbm in modeling groundwater flow in domains of complex shape over the former published methods is demonstrated by three examples

reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering the localization and the magnitude of acting steady states forces resulting from the dynamic response of a cylindrical shell are investigated the derivatives present in the equation of motion are expressed in terms of displacements using finite difference schemes displacements of the structure are introduced into the equation of motion in order to calculate the distribution of these forces numerical simulations show that when the force distribution is calculated using well defined displacements the exact position of the force is easily determined however when the displacements are mixed with uncertainties noise appears and the real force is relatively inaccurate in order to handle this instability in the inverse problem a regularization method based on signal processing techniques such as windowing and filtering in the spatial wavenumber domain should be performed numerical examples that illustrate the regularization process show that when the local filtering is applied to the force distribution calculated from noisy data reasonable results are obtained experiments are performed on a cylindrical shell in order to measure its velocities unfortunately using the displacements derived from measured velocities high sensitivity to the noise in the measurements is observed overall the experimental identification gives also good results when the same technique of filtering is applied to the force distribution

reliability analysis of structures with interval uncertainties under stationary stochastic excitations reliability analysis of linear discretized structural systems with interval uncertainties subjected to stationary gaussian random excitation is addressed under the assumption of independent up crossings of a specified threshold an efficient procedure for the evaluation of the bounds of the interval reliability function of the generic response process is presented the first step of the proposed approach is to derive approximate expressions of the interval mean value and spectral moments of the response along with the associated bounds to this aim the improved interval analysis via extra unitaryinterval is applied in conjunction with a novel series expansion of the inverse of an interval matrix with modifications called interval rational series expansion irse then the lower bound and upper bounds of the interval reliability function are readily evaluated by properly combining the bounds of the interval mean value and spectral moments of the response two numerical examples are provided to demonstrate the accuracy of the proposed procedure and its usefulness in view of decision making in engineering practice

comparing different approaches for determining joint torque parameters from isovelocity dynamometer measurements strength or maximum joint torque is a fundamental factor governing human movement and is regularly assessed for clinical and rehabilitative purposes as well as for research into human performance this study aimed to identify the most appropriate protocol for fitting a maximum voluntary torque function to experimental joint torque data three participants performed maximum isometric and concentric eccentric knee extension trials on an isovelocity dynamometer and a separate experimental protocol was used to estimate maximum knee extension angular velocity a nine parameter maximum voluntary torque function which included angle angular velocity and neural inhibition effects was fitted to the experimental torque data and three aspects of this fitting protocol were investigated using an independent experimental estimate of maximum knee extension angular velocity gave lower variability in the high concentric velocity region of the maximum torque function compared to using dynamometer measurements alone a weighted root mean square difference rmsd score function that forced the majority 73 92 of experimental data beneath the maximum torque function was found to best account for the one sided noise in experimental torques resulting from sub maximal effort by the participants the suggested protocol an appropriately weighted rmsd score function and an independent estimate of maximum knee extension angular velocity gave a weighted rmsd of between 11 and 13 nm 4 5 of maximum isometric torque it is recommended that this protocol be used in generating maximum voluntary joint torque functions in all torque based modelling of dynamic human movement

the improved complex variable element free galerkin method for two dimensional schrodinger equation abstract a numerical study of two dimensional schrodinger equation is carried out using the improved complex variable element free galerkin icvefg method the icvefg method involves employment of the improved complex variable moving least squares icvmls in the element free galerkin efg procedure for numerical approximation the icvmls is used to construct trial functions for the two dimensional schrodinger equation in the form of one dimensional basis function that effectively reduces the number of unknown coefficients in this study the applicability of the icvefg method is examined through a number of numerical example problems convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases the stability and accuracy of the icvefg method are validated by comparing the computed results with the exact solutions

proper orthogonal decomposition variational multiscale element free galerkin pod vmefg meshless method for solving incompressible navier stokes equation abstract recently because of simplicity of meshless methods they have been employed for solving many partial differential equations one of the meshless methods is element free galerkin technique the element free galerkin is very similar to the finite element method with this difference that the test and trial spaces of efg procedure are shape functions of moving least squares approximation using the mentioned shape functions solving a problem on a complex domain is very simple some researchers proposed several modifications and enriched approaches for improving the element free galerkin method that one of them is variational multiscale element free galerkin procedure up to the best of authors knowledge the element free galerkin method based on the shape functions of moving least squares approximation needs more cpu time than the element free galerkin method based on the shape functions of moving kriging interpolation thus in the current paper we employ the variational multiscale element free galerkin based on the shape functions of moving kriging interpolation also for reducing the cpu time of the presented numerical scheme we use the proper orthogonal decomposition pod approach therefore in the current paper we propose the proper orthogonal decomposition variational multiscale element free galerkin pod vmefg method for solving time dependent incompressible navier stokes equation moreover several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme

the relation between the resultant moments at a joint and the moments measured by an isokinetic dynamometer isokinetic dynamometers have frequently been used to determine in vivo properties of human skeletal muscles in these investigations the moments recorded by the dynamometer were often implicitly assumed to be the same as the joint moments produced by muscles this assumption may have contributed to the conflicting results about in vivo muscle properties of human skeletal muscles that are reported in the literature the purpose of this paper is to present a method for calculating the resultant joint moments from the moments recorded using a cybex ii dynamometer and to determine the differences between these two moments for some typical exercise conditions the differences between these these moments are shown to be due to a gravitational effects b inertial effects and c non rigidity of the cybex arm shank foot system the results obtained suggest that the moments recorded using the dynamometer should not be used to derive muscle properties without taking into account the relationship between the resultant joint moments and the moments measured using an isokinetic dynamometer

contrasting probabilistic and anti optimization approaches in an applied mechanics problem probabilistic and non probabilistic anti optimization analyses of uncertainty are contrasted in this study specifically the comparison of these two competing approaches is conducted for an uniform column with initial geometric imperfection subjected to an impact axial load the reliability of the column is derived for the cases when the initial imperfections posses either a uniform probability density b truncated exponential density or c generic truncated probability density the problem is also analyzed in the context of an interval analysis it is shown that in the most important near unity reliability range these two approaches tend to each other since the interval analysis constitutes a much simpler procedure than the probabilistic approach it is argued that the former is advantageous over the latter in some circumstances

a comparison of muscle energy models for simulating human walking in three dimensions the popular hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions these extended models differ considerably in their approach to computing energy expenditure particularly in their treatment of active lengthening and eccentric work but their predictive abilities have never been compared in this study we compared the predictions of five different hill based muscle energy models in 3d forward dynamics simulations of normal human walking in a data tracking simulation that minimized muscle fatigue the energy models predicted metabolic costs that varied over a three fold range 2 45 7 15 j m kg with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate in predictive simulations that optimized neuromuscular control to minimize the metabolic cost all five models predicted similar speeds step lengths and stance phase durations however some of the models predicted a hip circumduction strategy to minimize metabolic cost while others did not and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used the results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3d musculoskeletal model the potential for using such models to predict energetically optimal gait modifications and the room for improvement in existing muscle energy models and locomotion simulation frameworks

the encounter of interval and probabilistic approaches to structural reliability at the design point abstract the consideration of uncertainties in structural analysis has traditionally been made in the field of structural reliability within the framework of classical probability theory in many cases however there is no sufficient probabilistic information to substantiate such an approach in recent years several non probabilistic methods have been proposed as alternatives one of them is the interval analysis oriented to estimate the range of variation of output structural variables given the ranges of the input ones the method however requires the use of special arithmetics which renders its application unpractical for structural analysis based on finite elements or other numerical techniques in this paper a monte carlo method that can be applied to probabilistic as well as to interval approaches to reliability analysis is proposed it is based on the optimal properties of the classical design point of probabilistic structural reliability in particular it is shown that the order statistics of the output variable is concealed in a plot defined by the design point vector this facilitates the selection of the relevant samples for either interval or probability based analysis the examples show that the desired interval of the response or the failure probability can be accurately estimated on such a basis the paper also discusses the use of monte carlo methods for both reliability and interval analysis from the point of view of the proposed representation

probabilistic interval reliability of structural systems the probabilistic reliability approach is the most widely used method for reliability analysis the recent research shows that the reliabilities of structural systems strongly depend on the parameters of the probability model it is possible that the little error in the estimation of the parameters may lead to the remarkable error of the resulting probability in this study we introduce the interval approach into the conventional reliability theory we present a novel approach which allows us to obtain the system failure probability interval from the statistical parameter intervals of the basic variables this approach is a combination of the two techniques namely the classical reliability theory and the interval analysis in the end of this paper we show the feasibility of the proposed approach through two examples of the truss systems

convex models and interval analysis method to predict the effect of uncertain but bounded parameters on the buckling of composite structures a new non probabilistic set theoretical models that is interval analysis method is developed in this study to predict the variability or uncertainty in buckling loads of composite structures resulting from the unavoidable scatter in structural parameters by mathematically analyzing and proving the width of the upper and lower bounds on the critical buckling loads calculated by the interval analysis method is sharper than those that are obtained by convex models method moreover the interval analysis method has less computational cost than convex models method comparison between convex models and interval analysis method is performanced through numerical examples for the specific cases considered the results of numerical examples indicate that uncertainties in structural parameters have significant effect on the critical buckling loads of composite structures

numerical models for 2d free boundary analysis of groundwater in slopes stabilized by drain trenches a numerical model for 2d free boundary analysis of groundwater in slopes stabilized by drain trenches has been developed it consists of a front tracking method based on an original way of adapting the space derivatives very effective in saving calculation time respect to classical fix grid methods the method analyses the trenches effect inside slopes in which the soils above the water table are partially saturated for which a boundary can be recognized between the saturated domain water table and the unsaturated one above the water table in this case pore pressure lowering due to trenches can be analyzed considering the progressively reduction of the saturated domain this approach efficiently solves the problem of fixing hydraulic boundary conditions on the sides of the trenches results have been compared with those obtained by a fix grid method observing difference less than 0 14 applying the method the capability of drain trenches to control the effect of heavy rainfalls has been investigated calculating during the transient process of water table lowering limit values of water recharge for which water table keeps on constant

complex variable boundary element free method for two dimensional elastodynamic problems abstract we proposed a new direct meshless boundary integral equation technique the complex variable boundary element free method cvbefm based on the complex variable moving least squares cvmls approximation and the boundary element free method befm to study the two dimensional elastodynamic problems with the cvmls approximation the trial function of a two dimensional problem is formed with a one dimensional basis function the number of unknown coefficients in the trial function of the cvmls approximation is less than that in the trial function of the moving least squares mls approximation therefore it requires fewer nodes in the meshless method which formed from the cvmls approximation than that formed from the mls approximation with no lose of precision the laplace transform is used to formulate the boundary integral equations of the two dimensional elastodynamics and then the formulae of the cvbefm for two dimensional elastodynamic problems are derived the cvbefm is a direct numerical method in which the basic unknown quantities are the real solutions of the nodal variables moreover in the cvbefm the boundary conditions can be applied directly and easily that leads to a greater computational precision in this paper we selected a few numerical examples to illustrate the applicability of the cvbefm

a generalized moving least square reproducing kernel method a generalization of moving least square reproducing kernel method is presented in this work the moving least square reproducing kernel method is obtained by using a moving least square scheme but not in the discrete version the resulted scheme provides a continuous basis which is able to reproduce any m th order polynomial and prepares a scheme that can approximate smooth functions with an optimal accuracy on the other hand considering the power of moving least square scheme in meshless approximation for the numerical solution of partial differential equations the generalized moving least square approximation is able to approximate l u just in terms of node values where l is an arbitrary linear operator in this paper a generalization of moving least square reproducing kernel method is presented which employs the generalized version of moving least square method the method approximates a test functional based on the values of nodes the convergence rate of the method is measured in terms of dilation parameter of window function the method is simpler and faster to implement than the classical ones where it does not use the shape function numerical tests are presented to confirm the theoretical results the numerical results establish the efficiency of the proposed method

investigation of regularization parameters and error estimating in inverse elasticity problems the method of tarantola1 based on bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in schnur and zabaras 2 it is shown that when normal gaussian distributions are assumed and the error in the data is uncorrelated the bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in schnur and zabaras 2 as such the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution

on computing the forces from the noisy displacement data of an elastic body this study is concerned with the accurate computation of the unknown forces applied on the boundary of an elastic body using its measured displacement data with noise vision based minimally intrusive force sensing using elastically deformable grasping tools is the motivation for undertaking this problem since this problem involves incomplete and inconsistent displacement force of ail elastic body it leads to an ill posed problem known as cauchy s problem in elasticity vision based displacement measurement necessitates large displacements of the elastic body for reasonable accuracy therefore we use geometrically non linear modelling of the elastic body which was not considered by others who attempted to solve cauchy s elasticity problem before we present two methods to solve the problem the first method uses the pseudo inverse of an over constrained system of equations this method is shown to be not effective when the noise in the measured displacement data is high we attribute this to the appearance of spurious forces at regions where there should not be any forces the second method focuses on minimizing the spurious forces by varying the measured displacements within the known accuracy of the measurement technique both continuum and frame elements are used in the finite element modelling of the elastic bodies considered in the numerical examples the performance of the two methods is compared using seven numerical examples all of which show that the second method estimates the forces with an error that is not more than the noise in the measured displacements an experiment was also conducted to demonstrate the effectiveness of the second method in accurately estimating the applied forces

reanalysis of linear and nonlinear structures using iterated shanks transformation reanalysis of structures is a common task in two important fields of structural engineering namely optimization and reliability it implies the solution of the kinematic equations for each new set of data in order to simplify this task several approximate methods have been developed in this paper a simple method for reanalysis applicable to either linear or nonlinear structures is proposed it is based on the improvement of the neumann resolvent series which diverges beyond a certain radius by means of the iterated shanks transformation the method is compared with two relevant proposals intended to improve the convergence of the neumann series namely the pade series and the scaled approximation methods the accuracy and simplicity of the proposed method is demonstrated through some examples concerning linear and nonlinear structures

a local radial basis function method for advection diffusion reaction equations on complexly shaped domains abstract time dependent advection diffusion reaction and diffusion reaction equations are used as models in biology chemistry physics and engineering as representative examples we focus on a chemotaxis model and a turing system from biology and apply a local radial basis function method to numerically approximate the solutions the numerical method can efficiently approximate large scale problems in complexly shaped domains

hybrid high dimensional model representation for reliability analysis abstract this paper presents a new probabilistic method based on hybrid high dimensional model representation hhdmr for predicting the failure probability of structural and mechanical systems subject to random loads material properties and geometry high dimensional model representation hdmr is a general set of quantitative model assessment and analysis tools for capturing the high dimensional relationships between sets of input and output model variables it is a very efficient formulation of the system response if higher order variable cooperative effects are weak and if the response function is dominantly of additive nature allowing the physical model to be captured by the first few lower order terms but if multiplicative nature of the response function is dominant then all right hand side components of hdmr must be used to be able to obtain the best result however if hdmr requires all components which means 2 n number of components to get a desired accuracy making the method very expensive in practice then factorized hdmr fhdmr can be used but in most cases the limit state performance function has neither additive nor multiplicative nature rather it has an intermediate nature this paper presents a new hhdmr based approximation for the limit state performance functions having an intermediate nature the proposed approximation of an implicit limit state performance function includes both hdmr and fhdmr expansions through a hybridity parameter as an alternative to the conventional methods for reliability analysis which are very computationally demanding when applied in conjunction with complex finite element models this study aims to assess how accurately and efficiently hhdmr technique can capture complex model output uncertainty once the approximate form of the original implicit limit state performance function is defined the failure probability can be obtained by statistical simulation results of six numerical examples involving mathematical functions and structural solid mechanics problems indicate that the failure probability obtained using hhdmr based approximation of an implicit limit state performance function provides significant accuracy when compared with the conventional monte carlo method while requiring fewer original model simulations

hybrid uncertain static analysis with random and interval fields abstract uncertain static analysis of an engineering structure with diverse type of non deterministic system parameter is investigated in this study unlike the traditional hybrid uncertain static analysis involving random and interval variables the concept of random and interval fields has been implemented to model the spatially dependent uncertainties associated with the system inputs a novel computational approach namely the extended unified interval stochastic sampling x uiss method is proposed to calculate the statistical characteristics i e mean and standard deviation of the extreme bounds i e lower and upper bounds of the concerned responses e g displacement and stress of engineering structure involving hybrid spatially dependent uncertainties subsequently by utilizing either parametric or nonparametric statistical analysis the probability density functions pdfs as well as the cumulative distribution functions cdfs of the extreme bounds of the concerned structural responses can be effectively established consequently the upper and lower bounds of either the concerned responses of the engineering structure at any particular percentile of probability or the structural reliability against any specified capacities can be effectively secured the applicability and effectiveness of the proposed computational analysis framework are illustrated through the numerical investigations on various examples

a novel complex variable element free galerkin method for two dimensional large deformation problems abstract based on complex variable theory and moving least squares mls approximation the improved complex variable moving least squares icvmls approximation is discussed in this paper compared with complex variable moving least squares cvmls approximation the function in the icvmls approximation has an explicit physics meaning by using a new basis function the icvmls approximation can obtain greater precision and computational efficiency based on the icvmls approximation an improved complex variable element free galerkin icvefg method which belongs to a novel element free galerkin efg method is presented for two dimensional large deformation problems the galerkin weak form is employed to obtain the equations while the penalty method is used to apply the essential boundary conditions then the corresponding formulae of the icvefg method for two dimensional large deformation problems are obtained compared with the efg method the icvefg method has greater precision and efficiency

interval analysis of structures with uncertain but bounded axial stiffness abstract a method to evaluate the static response of structures with interval axial stiffnesses is proposed the procedure overcomes the drawbacks arising in traditional interval analysis due to dependency phenomenon the inversion of the interval stiffness matrix is pursued by means of a novel approximate relationship based on an interval valued sherman morrison woodbury formula numerical results on truss and frame structures evidence the accuracy and the effectiveness of the proposed approach to evaluate bounds of displacements and internal forces

steady heat conduction analyses using an interpolating element free galerkin scaled boundary method abstract through use of the improved interpolating moving least squares iimls shape functions in the circumferential direction of the scaled boundary method based on the galerkin approach an interpolating element free galerkin scaled boundary method iefg sbm is developed in this paper for analyzing steady heat conduction problems which weakens the governing differential equations in the circumferential direction and seeks analytical solutions in the radial direction the iimls method exhibits some advantages over the moving least squares approximation and the interpolating moving least squares method because its shape functions possess the delta function property and the involved weight function is nonsingular in the iefg sbm only a nodal data structure on the boundary is required and the primary unknown quantities are real solutions of nodal variables higher accuracy and faster convergence are obtained due to the increased smoothness and continuity of shape functions based on the iefg sbm the steady heat conduction problems with thermal singularities and unbounded domains can be ideally modeled some numerical examples are presented to validate the availability and accuracy of the present method for steady heat conduction analysis

interval fields to represent uncertainty on the output side of a static fe analysis abstract intervals have been used extensively for the representation of parametric uncertainty in finite element models when the available information is insufficient to build representative probabilistic models although the complexity of the interval concept is rather limited the numerical problem arising at the core of the interval finite element method was proven to be non trivial many research activities have focussed on this problem over the last decade still one of the principal shortcomings of the current interval finite element procedures is that they are intrinsically not capable of representing dependencies among uncertain input and or output quantities this poses important limitations on the applicability of the interval concept in non deterministic finite element analysis these limits arise in the model definition phase as well as in the post processing phase in order to cope with this problem this paper introduces the concept of interval fields the focus in this work is on the static analysis of mechanical structures with interval uncertainties in the context of the finite element method however the presented methodology is generic and can be readily extended to any kind of finite element problem including interval uncertainties in the first part of the paper the theoretical background of the concept is presented and it is shown how explicit and implicit interval fields can be used to represent dependent uncertain parameters in the model definition phase and in the post processing phase furthermore the applicability and accuracy of both types of interval fields are studied by means of a numerical validation example

analysis and application of the interpolating element free galerkin iefg method to simulate the prevention of groundwater contamination with application in fluid flow abstract we develop a meshless numerical procedure to simulate the groundwater equation gwe the used technique is based on the interpolating element free galerkin iefg method the interpolating moving least squares imls approximation produces a set of functions such that they are well known as shape functions the iefg technique employs the shape functions of imls approximation the shape functions of imls approximation vanish on the boundary and also they satisfy the property of the kronecker delta function thus dirichlet boundary conditions can be exactly imposed in this paper we check the unconditional stability and convergence of the proposed numerical scheme based on the energy method the numerical results confirm the theoretical analysis

an effective algorithm for reconstructing boundary conditions in elastic solids this paper discusses the reconstruction of boundary conditions for linear elastic solids when there are not enough known boundary conditions but the stress tensor is known in a sufficient number of internal points starting with a refined boundary elements discretization of the elastic solid an iterative strategy based on the conjugate gradient method is presented this iterative strategy uses a monte carlo simulation of the generalized cross validation criterion to select the optimal solution the proposed algorithm possesses some advantages with respect to direct approaches indeed it furnishes almost as accurate results but at a low computational cost some numerical results allow an analysis of the algorithm s performance

error analysis of interpolating element free galerkin method to solve non linear extended fisher kolmogorov equation abstract nonlinear partial differential equations pdes play an important role in the modeling of the natural phenomena as they have great significance in real world applications this investigation proposes a new algorithm to find the numerical solution of the non linear extended fisher kolmogorov equation firstly the time variable is discretized by a second order finite difference scheme the rate of convergence and stability of the semi discrete formulation are studied by the energy method the existence and uniqueness of the solution of the weak form based on the proposed technique have been proved in detail furthermore the interpolating element free galerkin approach based on the interpolation moving least squares approximation is employed to derive a fully discrete scheme finally the error estimate of the full discrete plan is proposed and its convergence order is o 2 m 1 in which and m denote the time step the radius of the weight function and smoothness of the exact solution of the main problem respectively