Explicit calculation of smoothed sensitivity coefficients for linear problems

A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary‐element and finite‐element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd.     

Completeness of corrective smoothed particle method for linear elastodynamics

 Two different solution algorithms of the corrective smoothed particle method (CSPM) are developed and examined with linear elastodynamic problems. One is to use the corrective first derivative approximations to solve the stress-based momentum equations, with stresses evaluated from the strains. This is an approach that has widely been adopted in smoothed particle hydrodynamics (SPH) methods. The other is new, in which the corrective second derivative approximations are used to directly solve the displacement-based Navier equations. The former satisfies the nodal completeness condition but lacks integrability; on the contrary, the latter is truly complete. Numerical tests show that the latter outperforms the former as well as other existing SPH methods, as expected. Received 1 April 1999     

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a “smooth + singular” decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.     

A contact analysis approach based on linear complementarity formulation using smoothed finite element methods

Based on the subdomain parametric variational principle (SPVP), a contact analysis approach is formulated in the incremental form for 2D solid mechanics problems discretized using only triangular elements. The present approach is implemented for the newly developed node-based smoothed finite element method (NS-FEM), the edge-based smoothed finite element method (ES-FEM) as well as standard FEM models. In the approach, the contact interface equations are discretized by contact point-pairs using a modified Coulomb frictional contact model. For strictly imposing the contact constraints, the global discretized system equations are transformed into a standard linear complementarity problem (LCP), which can be readily solved using the Lemke method. This approach can simulate different contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is conducted to investigate the effects of various parameters and validate the proposed method. The numerical results have demonstrated the validity and efficiency of the present contact analysis approach as well as the good performance of the ES-FEM method, which provides solutions of about 10 times better accuracy and higher convergence rate than the FEM and NS-FEM methods. The results also indicate that the NS-FEM provides upper-bound solutions in energy norm, relative to the fact that FEM provides lower-bound solutions.     

Recursive linear control of order release to manufacturing cells with random yield

One-piece flow job shop production environments in high labor turnover environments are oftentimes characterized by late shipments and incomplete orders due to random and variable yield. The problem addressed in this paper is that of determining an order release policy for a one-piece flow prototype production line in order to meet demand in an environment subject to random and variable yield induced by high labor turnover. This paper is motivated by a problem encountered in a facility that produces prototype parts. The problem at hand can be denned as that of determining a lot size to release into the line lo minimize deviations from the demand (i.e., target batch quota) for single-piece flow production in an environment characterized by random and variable yield. The objective of this research was to investigate the utility of recursive linear control as a mechanism for releasing parts into a single-piece flow production cell, and to develop a control algorithm using a Kalman filter. The methodology is evaluated via simulation using actual demand and yield data simulated from a distribution fit from historical data. Order release strategy and yield were found to be the dominant variables for complete and on-time orders without excess and shortages, and linear recursive control was found to be effective for tracking, monitoring and adjusting the release of parts into a single-piece flow job shop in an environment characterized by random and variable yield.     

Adaptive smoothed molecular dynamics for multiscale modeling

In the smoothed molecular dynamics (SMD), the high frequency modes are eliminated from the motion of atoms to enlarge the time step significantly. In some situations, however, rearrangements or atoms disorder may occur. Hence, it is desirable to use MD in localized regions to capture the interesting high frequency motion, while use SMD elsewhere to save the computational cost. In this paper, an adaptive smoothed molecular dynamics (ASMD) is developed. During the simulation process, if the high frequency motions of atoms are dominant in a region, the background grid in the region is refined hierarchically until it is able to capture the high frequency motion of the atoms.     

SPC scheme to monitor linear predictors embedded in nonlinear profiles

Response Modeling Methodology (RMM) is a general platform to model monotone convex relationships. In this article, RMM is combined with linear regression analysis to model and estimate linear predictors (LPs) embedded in a nonlinear profile. A regression‐adjusted statistical process control scheme is then implemented to monitor the LP's residuals. To model and estimate the LP, RMM defines a Taylor series expansion of an unknown response transformation and then use canonical correlation analysis to estimate the LP. A possible hindrance to the implementation of the new scheme is possible occurrence of nonnormal errors (in violation of the linear regression model). Reasons for the occurrence of this phenomenon are explored and remedies offered. The effectiveness of the new scheme is demonstrated for data generated via Monte Carlo simulation. Results from hypothesis testing clearly indicate that the type of the response distribution, its skewness and the sample size, do not affect the effectiveness of the new approach. A detailed implementation routine is expounded, accompanied by a numerical example. When interest is solely focused on the stability of the LP, and the nonlinear profile per se is of little interest, the new general RMM‐based statistical process control scheme delivers an effective platform for process monitoring. Copyright © 2015 John Wiley & Sons, Ltd.     

Interpolated smoothed pseudo Wigner-Ville distribution for accuratespectrum analysis

This paper deals with a new application of the time-domain windowed (smoothed version) of the pseudo Wigner-Ville distribution (PWD), that can be easily implemented in a dedicate digital instrument to be used as a spectral analyzer for time-frequency analysis of nonstationary signals. New computational algorithms are studied and developed to attain high time-frequency resolution, accuracy, flexibility and computational efficiency. Particularly, to reduce the negative effects due to leakage during frequency changes, a new interpolation formula is derived by using the windowing theory. The suggested technique allows the users to perform optimal evaluations of the instantaneous amplitudes and frequencies of analyzed signals     

A corrective smoothed particle method for transient elastoplastic dynamics

 An incremental approach is presented to model transient, elastoplastic dynamic problems using the corrective smoothed particle method. It uses the corrective first- and second-derivative approximations to solve the nonlinear momentum equations, which is described in terms of displacement increments entirely. This algorithm not only satisfies the nodal completeness condition but also exhibits no integrablity problem. Several 2D examples, including forced vibration, stress wave propagation, and rigid wall impact, are investigated to demonstrate the numerical stability and accuracy of the proposed method. Received 2 May 2000     

An improvement for tensile instability in smoothed particle hydrodynamics

A corrective Smoothed-Particle Method (CSPM) is proposed to address the tensile instability and, boundary deficiency problems that have hampered full exploitation of standard smoothed particle hydrodynamics (SPH). The results from applying this algorithm to the 1-D bar and 2-D plane stress problems are promising. In addition to the advantage of being a gridless Lagrangian approach, improving the above two major obstacles in standard SPH makes it attractive for applications in computational mechanics.     

Temporal stabilization of the node-based smoothed finite element method and solution bound of linear elastostatics and vibration problems

A stabilization procedure for curing temporal instability of node-based smoothed finite element method (NS-FEM) is proposed for dynamic problems using linear triangular element. A stabilization term is added into the smoothed potential energy functional of the original NS-FEM, consisting of squared-residual of equilibrium equation. A gradient smoothing operation on second order derivatives is applied to relax the requirement of shape function, so that the squared-residual can be evaluated using linear elements. Numerical examples demonstrate that stabilization parameter can “tune” NS-FEM from being “overly soft” to “overly stiff”, so that eigenvalue solutions can be stabilized. Numerical tests provide an empirical value range of stabilization parameter, within which the stabilized NS-FEM can still produce upper bound solutions in strain energy to the exact solution of force-driven elastostatics problems, as well as lower bound natural frequencies for free vibration problems.     

密度函数递归核估计的Bootstrap逼近

设X1，X2，…xn是从分布密度函数为f（x）的总体中抽取的独立同分布的样本，f（x）的递归核估计fn（x），本文讨论了fn（x）的渐近正态性以及Bootstrap逼近问题．     

An edge-based smoothed XFEM for fracture in composite materials

In this work, an edge-based smoothed extended finite element method (ES-XFEM) is extended to fracture analysis in composite materials. This method, in which the edge-based smoothing technique is married with enrichment in XFEM, shows advantages of both the extended finite element method (XFEM) and the edge-based smoothed finite element method (ES-FEM). The crack tip enrichment functions are specially derived to represent the characteristic of the displacement field around the crack tip in composite materials. Due to the strain smoothing, the necessity of integrating the singular derivatives of the crack tip enrichment functions is eliminated by transforming area integration into path integration, which is an obvious advantage compared with XFEM. Two examples are presented to testify the accuracy and convergence rate of the ES-XFEM.     

Recursive distribution method for probabilistic fracture mechanics

This paper proposes a new method for Probabilistic Fracture Mechanics (PFM). The present method gives a recursive formula for a joint probability distribution function of crack geometry, which is obtained from random variables of the initial crack geometry and a deterministic time-evolution law of the variables. A numerical example of Light Water Reactor (LWR)'s piping is solved by the present method, and the results are compared with those of the Monte Carlo (MC) method. It is clearly shown that both results agree sufficiently well, while CPU time of the present method is remarkably short.     

A smoothed radial point interpolation method for application in porodynamics

A meshfree numerical method for the dynamic analysis of porous media is presented. The u,?p form of Biot’s theory is adopted to mathematically model the dynamic interaction of the solid and the fluid phase within the porous media. The obtained partial differential equations (PDEs) are discretized by the generalized smoothed Galerkin weak form, which is established based on smoothed strains and fluxes. Therefore, edge-based and cell-based smoothing domains are used and a T3-scheme is employed for the selection of support nodes. The shape functions are generated by the radial point interpolation method. The focus of this work lies on the spatial integration of the mass/compressibility and coupling terms of the discrete PDE system. A new algorithm is introduced, which reuses the shape function values that are needed for the construction of the stiffness/permeability matrix to keep the computational effort at a minimum. Numerical problems are analyzed in order to test the algorithm regarding accuracy and efficiency.     

On computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method

Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this paper, the smoothed finite element method (SFEM) is used for finding upper and lower bounds on the local quantities of interest that are outputs of the displacement field for linear elasticity problems, based on bounds on strain energy in both the primal and dual problems. One important feature of SFEM is that it bounds the strain energy of the structure from above without needing the solutions of different subproblems that are based on elements or patches but only requires the direct finite element computation. Upper and lower bounds on two linear outputs and one quadratic output related with elasticity—the local reaction, the local displacement and the J‐integral—are computed by the proposed method in two different examples. Some issues with SFEM that remain to be resolved are also discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Recursive parameter estimation for categorical process control

Statistical process adjustment (SPA) is utilised prevalently in novel manufacturing scenarios. When quality characteristics rather than internal process variables are inspected for the purpose of quality control, data with different resolutions may be collected. This paper proposes a Bayesian framework for parameter estimation when only categorical observations are available. The proposed method incorporates categorical information recursively and updates parameter estimates in real time. Simulation results show that the framework is effective in utilising low-resolution information in parameter estimation, model building and process control.     

Development of smoothed particle hydrodynamics method for modeling active nematics

This article proposes a novel graphics processing unit-based active nematic flow solver based on the smoothed particle hydrodynamics (SPH) method. Nematohydrodynamics equations are discretized using the SPH algorithm. Flow behavior, nematic ordering, topological defects, and vorticity correlation are calculated and discussed in detail. The spectrum of the kinetic energy with respect to the wavenumber is calculated at high particle resolution, and its slope at the different length scales is discussed. To exploit the SPH capabilities, pathlines of nematic particles are evaluated during the simulation. Finally, the mixing behavior of the active nematics is calculated as well and described qualitatively. The effects of two important parameters, namely, activity and elastic constant are investigated. It is shown that the activity intensifies the chaotic mixing nature of the active nematics, while the elastic constant behaves oppositely.