Hybrid-trefftz six-node triangular finite element models for helmholtz problem

In this paper, six-node hybrid-Trefftz triangular finite element models which can readily be incorporated into the standard finite element program framework in the form of additional element subroutines are devised via a hybrid variational principle for Helmholtz problem. In these elements, domain and boundary variables are independently assumed. The former is truncated from the Trefftz solution sets and the latter is obtained by the standard polynomial-based nodal interpolation. The equality of the two variables are enforced along the element boundary. Both the plane-wave solutions and Bessel solutions are employed to construct the domain variable. For full rankness of the element matrix, a minimal of six domain modes are required. By using local coordinates and directions, rank sufficient and invariant elements with six plane-wave modes, six Bessel solution modes and seven Bessel solution modes are devised. Numerical studies indicate that the hybrid-Trefftz elements are typically 50% less erroneous than their continuous Galerkin element counterpart.published_or_final_versionSpringer Open Choice, 01 Dec 201

Axisymmetric quadrilateral elements for large deformation hyperelastic analysis

In this paper, axisymmetric 8-node and 9-node quadrilateral elements for large deformation hyperelastic analysis are devised. To alleviate the volumetric locking which may be encountered in nearly incompressible materials, a volumetric enhanced assumed strain (EAS) mode is incorporated in the eight-node and nine-node uniformly reduced-integrated (URI) elements. To control the compatible spurious zero energy mode in the 9-node element, a stabilization matrix is attained by using a hybrid-strain formulation and, after some simplification, the matrix can be programmed in the element subroutine without resorting to numerical integration. Numerical examples show the relative efficacy of the proposed elements and other popular eight-node elements. In view of the constraint index count, the two elements are analogous to the Q8/3P and Q9/3P elements based on the u-p hybrid/mixed formulation. However, the former elements are more straight forward than the latter elements in both formulation and programming implementation. © 2010 Springer Science+Business Media, B.V.preprin

Discrimination and Telomere Length Among Older Adults in the United States

Abstract Objectives: Chronic stress from experiencing discrimination can lead to long-term changes in psychological and physiologic responses, including shorter leukocyte telomere length. We examined the association between leukocyte telomere length and variations in the association by race or type of discrimination. Methods: Our study consisted of 3868 US-born non-Hispanic black (hereinafter, black) and non-Hispanic white (hereinafter, white) adult participants from the 2008 Health and Retirement Study biomarker sample with complete sociodemographic and discrimination information. We examined major lifetime unfair treatment and everyday discrimination. Coarsened exact matching matched exposed and unexposed participants on several sociodemographic factors. Coarsened exact matching creates analytic weights for the matched data sets. We applied weighted linear regression to the matched data sets. We conducted 2 subanalyses in which we matched on potential mediators—physical activity, smoking status, and obesity—and examined if racism was associated with shorter telomere length compared with other attributes. All analyses were stratified by race. Results: We found no difference in telomere length for black and white participants reporting major lifetime unfair treatment (β = 0.09; 95% CI, –0.33 to 0.15) or everyday discrimination (β = 0.04; 95% CI, –0.12 to 0.40). Everyday discrimination was associated with shorter leukocyte telomere length among black people (β = –0.23; 95% CI, –0.44 to –0.01) but not among white people (β = 0.05; 95% CI, –0.01 to 0.10). Matching on potential mediators generally decreased the effect estimate among black people. Conclusions: Experiencing everyday discrimination was associated with shortened telomere length among older black adults. Further research is needed to understand the adverse physiologic effects of discrimination to create effective interventions

Popular benchmark problems for geometric nonlinear analysis of shells

In most, if not all, of the previous work on finite element formulation and nonlinear solution procedures, results of geometric nonlinear benchmark problems of shells are presented in the form of load-deflection curves. In this paper, eight sets of popularly employed benchmark problems are identified and their detailed reference solutions are obtained and tabulated. It is hoped that these solutions will form a convenient basis for subsequent comparison and that the tedious yet inaccurate task of reconstructing data points by graphical measurement of previously reported load-deflection curves can be avoided. Moreover, the relative convergent difficulty of the problems are revealed by the number of load increments and the total number of iterations required by an automatic load incrementation scheme for attaining the converged solutions under the maximum loads. © 2003 Elsevier B.V. All rights reserved.postprin

Spherical-wave based triangular finite element models for axial symmetric Helmholtz problems

In this paper, six-node hybrid triangular finite element models are devised for axial symmetric Helmholtz problems. In the formulation, boundary and domain approximations to the Helmholtz field are defined for each element. While the boundary approximation is constructed by nodal interpolation, the domain approximation satisfies the Helmholtz equation and is composed of spherical waves with source points located along the axis of symmetry. To formulate rank sufficient six-node elements, a minimal of six wave modes from three source points are required. Two methods of selecting the source points are attempted. In the first method, the directions of the waves passing through the element are essentially parallel to the three lines connecting the parametric center of the element and its three corner (or side) nodes. In the second method, the directions are essentially equally spaced at 2π/3 interval in the rz-plane. For the attempted examples, the average error ratios of the proposed elements and the conventional element are around 50%. © 2010 Elsevier B.V. All rights reserved.postprin

Hybrid quadrilateral finite element models for axial symmetric Helmholtz problem

This paper is a continuation of the previous work in which six-node triangular finite element models for the axial symmetric Helmholtz problem are devised by using a hybrid functional and the spherical-wave modes [1]. The six-node models can readily be incorporated into the standard finite element program framework and are typically ∼50% less erroneous than their conventional or, equivalently, continuous Galerkin counterpart. In this paper, four-node and eight-node quadrilateral models are devised. Two ways of selecting the spherical-wave modes are attempted. In the first way, a spherical-wave pole is selected such that it is equal-distant from an opposing pair of element nodes. In the second way, the directions of the spherical-waves passing through the element origin are equal-spaced with one of the directions bisecting the two parametric axes of the element. Examples show that both ways lead to elements that yield very similar predictions. Furthermore, four-node and eight-node hybrid elements are typically ∼50% and ∼70% less erroneous than their conventional counterparts, respectively. © 2011 Elsevier B.V. All rights reserved.postprin

Four- and eight-node hybrid-Trefftz quadrilateral finite element models for helmholtz problem

In this paper, four- and eight-node quadrilateral finite element models which can readily be incorporated into the standard finite element program framework are devised for plane Helmholtz problems. In these models, frame (boundary) and domain approximations are defined. The former is obtained by nodal interpolation and the latter is truncated from Trefftz solution sets. The equality of the two approximations are enforced along the element boundary. Both the Bessel and plane wave solutions are employed to construct the domain approximation. For full rankness, a minimal of four and eight domain modes are required for the four- and eight-node elements, respectively. By using local coordinates and directions, rank sufficient and invariant elements with minimal and close to minimal numbers of domain approximation modes are devised. In most tests, the proposed hybrid-Trefftz elements with the same number of nodes yield close solutions. In absolute majority of the tests, the proposed elements are considerably more accurate than their single-field counterparts. © 2009 Elsevier B.V. All rights reserved.postprin

Multi-field three-node triangular finite element model for helmholtz problem

In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples. © 2011 IMACS.postprin

Residential Modifications and Decline in Physical Function Among Community-Dwelling Older Ad

Purpose: The purpose of this study is to quantify the effect of residential modification on decreasing the risk of physical function decline in 2 years. Design: Cohort study using propensity scores method to control for baseline differences between individuals with residential modifications and those without residential modifications. Participants: Participants (N = 9,447) were from the Second Longitudinal Study on Aging, a nationally representative sample of the civilian noninstitutionalized population, aged 70 years and older in the United States at the time of baseline interview in 1994-1995. Methods: Participants self-reported residential modifications at baseline (e.g., railings, bathroom modifications). The decline in physical functioning was measured by comparing self-reported activities of daily living at baseline and at 2-year follow-up. Results: Compared with individuals without baseline modifications, a higher proportion of those with baseline modifications were aged 85 years and older (16% vs. 10%), used special aides (36% vs. 14%), and lived alone (40% vs. 31%). Using a weighted propensity score method, we found a modest decrease in risk of decline at Wave 2 for those with baseline modifications (risk difference = 3.1%). Respondents with a baseline residential modification were less likely to experience a subsequent decline in functional ability (adjusted odds ratio = 0.88, 95% confidence interval = 0.79-0.97) after adjusting for quintile of the propensity score in a survey-weighted regression model. Implications: Baseline modifications may be associated with reduced risk of decline among a nationally representative sample of older community-dwelling adults. Widespread adoption of residential modifications may reduce the overall population estimates of decline