Characterising plastic collapse of pipe bend structures

Two recently proposed design by analysis criteria of plastic collapse based on plastic work concepts, the plastic work (PW) criterion and the plastic work curvature (PWC) criterion, are applied to a strain hardening pipe bend arrangement subject to combined pressure and in-plane moment loading. Calculated plastic pressure-moment interaction surfaces are compared with limit surfaces, large deformation analysis instability surfaces and plastic load surfaces given by the ASME Twice Elastic Slope criterion and the tangent intersection criterion. The results show that both large deformation theory and material strain hardening have a significant effect on the elastic-plastic response and calculated static strength of the component. The PW criterion is relatively simple to apply in practice and gives plastic load values similar to the tangent intersection criterion. The PWC criterion is more subjective to apply in practice but it allows the designer to follow the development of the gross plastic deformation mechanism in more detail. The PWC criterion indicates a more significant strain hardening strength enhancement effect than the other criteria considered, leading to a higher calculated plastic load

Stochastic equations, flows and measure-valued processes

We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming--Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatments of three kinds of flows in Bertoin and Le Gall [Ann. Inst. H. Poincar\'{e} Probab. Statist. 41 (2005) 307--333]. Two scaling limit theorems for the generalized Fleming--Viot flows are proved, which lead to sub-critical branching immigration superprocesses. From those theorems we derive easily a generalization of the limit theorem for finite point motions of the flows in Bertoin and Le Gall [Illinois J. Math. 50 (2006) 147--181].Comment: Published in at http://dx.doi.org/10.1214/10-AOP629 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiphysics models for friction stir welding simulation

Purpose: The Friction Stir Welding (FSW) process comprises of several highly coupled (and non-linear) physical phenomena: large plastic deformation, material flow transportation, mechanical stirring of the tool, tool-workpiece surface interaction, dynamic structural evolution, heat generation from friction and plastic deformation, etc. In this paper, an advanced Finite Element (FE) model encapsulating this complex behavior is presented and various aspects associated with the FE model such as contact modeling, material model and meshing techniques are discussed in detail. Methodology: The numerical model is continuum solid mechanics-based, fully thermomechanically coupled and has successfully simulated the friction stir welding process including plunging, dwelling and welding stages. Findings: The development of several field variables are quantified by the model: temperature, stress, strain, etc. Material movement is visualized by defining tracer particles at the locations of interest. The numerically computed material flow patterns are in very good agreement with the general findings from experiments. Value: The model is, to the best of the authors’ knowledge, the most advanced simulation of FSW published in the literature

Asymptotic Theory of Rerandomization in Treatment-Control Experiments

Although complete randomization ensures covariate balance on average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. To supplement existing results, we develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and a truncated Gaussian random variable. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We also demonstrate that, compared to complete randomization, rerandomization reduces the asymptotic sampling variances and quantile ranges of the difference-in-means estimator. Moreover, our work allows the construction of accurate large-sample confidence intervals for the average causal effect, thereby revealing further advantages of rerandomization over complete randomization