Flora Farago, Kay Sanders and Larissa Gaias
This chapter draws on developmental intergroup theory, parental ethnic-racial socialization literature, anti-bias curricula, and prejudice intervention studies to address the…
Abstract
This chapter draws on developmental intergroup theory, parental ethnic-racial socialization literature, anti-bias curricula, and prejudice intervention studies to address the appropriateness of discussing race and racism in early childhood settings. Existing literature about teacher discussions surrounding race and racism is reviewed, best practices are shared, and the need for more research in this area is highlighted. The construct of parental ethnic-racial socialization is mapped onto early childhood anti-bias classroom practices. The chapter also outlines racial ideologies of teachers, specifically anti-bias and colorblind attitudes, and discusses how these ideologies may manifest in classroom practices surrounding race and racism. Colorblind ideology is problematized and dissected to show that colorblind practices may harm children. Young children’s interpretations of race and racism, in light of children’s cognitive developmental level, are discussed. Additionally, findings from racial prejudice intervention studies are applied to teaching. Early literacy practices surrounding race and racism are outlined with practical suggestions for teachers and teacher educators. Moreover, implications of teacher practices surrounding race and racism for children’s development, professional development, and teacher education are discussed.
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Mateus Rauen, Roberto Dalledone Machado and Marcos Arndt
The purpose of this paper is to check the efficiency of isogeometric analysis (IGA) by comparing its results with classical finite element method (FEM), generalized finite element…
Abstract
Purpose
The purpose of this paper is to check the efficiency of isogeometric analysis (IGA) by comparing its results with classical finite element method (FEM), generalized finite element method (GFEM) and other enriched versions of FEM through numerical examples of free vibration problems.
Design/methodology/approach
Since its conception, IGA was widely applied in several problems. In this paper, IGA is applied for free vibration of elastic rods, beams and trusses. The results are compared with FEM, GFEM and the enriched methods, concerning frequency spectra and convergence rates.
Findings
The results show advantages of IGA over FEM and GFEM in the frequency error spectra, mostly in the higher frequencies.
Originality/value
Isogeometric analysis shows a feasible tool in structural analysis, with emphasis for problems that requires a high amount of vibration modes.
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Wenan Wu and Hong Zheng
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable…
Abstract
Purpose
This study aims to introduce the hybrid finite element (FE) – meshfree method and multiscale variational principle into the traditional mixed FE formulation, leading to a stable mixed formulation for incompressible linear elasticity which circumvents the need to satisfy inf-sup condition.
Design/methodology/approach
Using the hybrid FE–meshfree method, the displacement and pressure are interpolated conveniently with the same order so that a continuous pressure field can be obtained with low-order elements. The multiscale variational principle is then introduced into the Galerkin form to obtain stable and convergent results.
Findings
The present method is capable of overcoming volume locking and does not exhibit unphysical oscillations near the incompressible limit. Moreover, there are no extra unknowns introduced in the present method because the fine-scale unknowns are eliminated using the static condensation technique, and there is no need to evaluate any user-defined stability parameter as the classical stabilization methods do. The shape functions constructed in the present model possess continuous derivatives at nodes, which gives a continuous and more precise stress field with no need of an additional smooth process. The shape functions in the present model also possess the Kronecker delta property, so that it is convenient to impose essential boundary conditions.
Originality/value
The proposed model can be implemented easily. Its convergence rates and accuracy in displacement, energy and pressure are even comparable to those of second-order mixed elements.
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A study of the behaviour of shear deformable plate finite elements is carried out to determine why and under what conditions these elements lock, or become overly stiff. A new…
Abstract
A study of the behaviour of shear deformable plate finite elements is carried out to determine why and under what conditions these elements lock, or become overly stiff. A new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side‐to‐thickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and are interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various plate elements. These include bilinear, biquadratic, eight‐node serendipity and heterosis elements. These analytical findings are compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behaviour of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration.
Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included…
Abstract
Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.
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J. PETERA, V. NASSEHI and J.F.T. PITTMAN
A number of finite element formulations involving discontinuous weighting functions have been tested against analytic solutions for a steady scalar convection—diffusion problem at…
Abstract
A number of finite element formulations involving discontinuous weighting functions have been tested against analytic solutions for a steady scalar convection—diffusion problem at intermediate Peclet number, with a ‘hard’ downstream boundary condition. The emphasis is on extending these methods to isoparametric bilinear and biquadratic elements. In order to do this a procedure is given for the exact calculation of shape function Laplacians. Having confirmed the success of the Brooks—Hughes streamline upwind Petrov—Galerkin (SUPG) method for isoparametric bilinear elements, formulations for biquadratic elements are examined. Galerkin least squares offers little advantage over SUPG in the test problem. The generalized Galerkin method of Donea et al. gave excellent results, but because of concern over the possibility of cross‐streamline artificial diffusion in some cases, a strictly streamline formulation incorporating the optimal parameters of Donea et al. is proposed. This gave excellent results on a sufficiently refined mesh.
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Noel Scott, Brent Moyle, Ana Cláudia Campos, Liubov Skavronskaya and Biqiang Liu
ZHI‐HUA ZHONG and JAROSLAV MACKERLE
Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite…
Abstract
Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.
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KJELL MAGNE MATHISEN and PÅL G. BERGAN
This paper discusses algorithms for large displacement analysis of interconnected flexible and rigid multibody systems. Hydrostatic and hydrodynamic loads for systems being…
Abstract
This paper discusses algorithms for large displacement analysis of interconnected flexible and rigid multibody systems. Hydrostatic and hydrodynamic loads for systems being submerged in water are also considered. The systems may consist of cables and beams and may combine very flexible parts with rigid parts. Various ways of introducing structural joints are discussed. A special implementation of the Hilber‐Hughes‐Taylor time integration scheme for constrained non‐linear systems is outlined. The formulation is general and allows for displacements and rotational motion of unlimited size. Aspects concerning efficient solution of constrained dynamic problems are discussed. These capabilities have been implemented in a general purpose non‐linear finite element program. Applications involving static and dynamic analysis of a bi‐articulated tower and a floating tripod platform kept in place by three anchor lines are discussed.