Implementing an Accurate Generalized Gaussian Quadrature Solution to Find the Elastic Field in a Homogeneous Anisotropic Media

Kabir, Hossein; Matikolaei, Sayed Amir Hossein Hassanpour

doi:10.24874/jsscm.2017.11.01.02

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…However, the magnitude and distribution of residual stresses are highly affected by the geometry of cross-section and roll stand design, the same longitudinal residual stress magnitude and distribution have been used for different cross-sections in the recent research studies on cold-formed members. Hence, in this study, a validated finite element model was established to simulate the roll-forming process of a channel section (SIMULIA, 2018; Kabir et al , 2018; Kabir and Matikolaei, 2017). Longitudinal and transverse residual stress components were considered as the initial condition for studying of lateral-torsional buckling of the cold-rolled channel and built-up I-section beams.…”

Section: Introductionmentioning

confidence: 99%

The effects of residual stresses and strains on lateral-torsional buckling behavior of cold-formed steel channel and built-up I-sections beams

Kabir

Parvizi

2019

IJSI

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Purpose The purpose of this paper is to focus on the influences of residual stresses which were induced during roll-forming sections on lateral-torsional buckling of thin-walled cold-formed steel channel and built-up I-sections beams. Built-up I section is made up of two back-to-back cold-formed channel beams. In this direction, at the primary stage, the roll-forming process of a channel section was simulated in ABAQUS environment and the accuracy of the result was verified with those existing experiments. Residual stresses and strains in both longitudinal and circumferential transverse directions were extracted and considered in the lateral-torsional buckling analysis under uniform end moments. The contribution of the current research is devoted to the numerical simulation of the rolling process in ABAQUS software enabling to restore the remaining stresses and strains for the buckling analysis in the identical software. The results showed that the residual stresses decrease considerably the lateral-torsional buckling strength as they have a major impact on short-span beams for channel sections and larger span for built-up I sections. The obtained moment capacity from the buckling analysis was compared to the predictions by American Iron and Steel Institute design code and it is found to be conservative. Design/methodology/approach This paper has explained a numerical study on the roll-forming process of a channel section and member moment capacities related to the lateral-torsional buckling of the rolled form channel and built-up I-sections beams under uniform bending about its major axis. It has also investigated the effects of residual stresses and strains on the behaviour of this buckling mode. Findings The residuals decrease the moment capacities of the channel beams and have major effect on shorter spans and also increase the local buckling strength of compression flange. But the residuals have major effect on larger spans for built-up I sections. It could be seen that the ratio of moment (with residuals and without residuals) for singly symmetric sections is more pronounced than doubly symmetric sections. So it is recommended to use doubly symmetric section of cold-formed section beams. Originality/value The incorporation of residual stresses and strains in the process of numerical simulation of rolled forming of cold-formed steel sections under end moments is the main contribution of the current work. The effect of residual stresses and strains on the lateral-torsional buckling is, for the first time, addressed in the paper.

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Section: Introductionmentioning

confidence: 99%

The effects of residual stresses and strains on lateral-torsional buckling behavior of cold-formed steel channel and built-up I-sections beams

Kabir

Parvizi

2019

IJSI

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“…The integration was then performed in (σ, ω) space, which assumes a rectangular shape with σ ranging from 0 to π and ω ranging from 0 to 2π. Although the obtained mathematical expressions in real space are more complicated than those obtained in reciprocal space, the real space formulation is more compatible with digital computation, thanks to the fixed integration area in CIREALS that facilitates the Gaussian quadrature method for fast integration. , The real space parameters can directly associate with crystal size and orientation, which makes CIREALS an attractive alternative to explore many structural details of a 2D monolayer and multilayers through studying diffraction patterns. CIREALS is a general method that can be applied to a variety of 2D materials such as MOFs, COFs, molybdenum disulfide, and graphene.…”

Section: Introductionmentioning

confidence: 99%

Simulating Powder X-ray Diffraction Patterns of Two-Dimensional Materials

Jiang

Cao

et al. 2018

Inorg. Chem.

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Powder X-ray diffraction (PXRD) is widely used to study atomic arrangements in ordered materials. The Bragg equation, which describes diffraction of a three-dimensional crystal, fails in two-dimensional (2D) cases. Complete integration of diffraction signals from a continuum instead of discrete directions in the Bragg equation is thus required for proper data interpretation of 2D materials. Furthermore, modeling of preferred orientation of the 2D crystals as well as geometric disorders are also of vital importance. Here, we present a complete integration method in real space (CIREALS) for PXRD simulation of monolayer or multilayer 2D crystals, especially 2D metal–organic layers and 2D covalent organic frameworks. By working in real space instead of reciprocal space, we can readily capture the 2D geometry and preferred orientation of these materials. The predicted PXRD patterns by CIREALS facilitates structure analysis of these new types of 2D material.

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“…For the Gauss-Legendre quadrature [21], the coordinate of integration points in one dimension, Ix P can be determined as the solutions of Equation ( 21) between +1 and −1 as…”

Section: Formulation Of Nodal Coordinates and Integration Quadrature ...mentioning

confidence: 99%

“…There are several methods to obtain the integration quadrature, such as the Gaussian quadrature rule [21] and Legendre-Gauss-Lobatto nodes [22] for hexahedrons. In the case of higher-order tetrahedrons, the standard collapsed coordinate system that maps the quadrature to the tetrahedron from a reference hexahedron [23] is a popular choice.…”

Section: Introductionmentioning

confidence: 99%

A General Procedure to Formulate 3D Elements for Finite Element Applications

Shahriar,

Majlesi,

Montoya

2023

Computation

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This paper presents a general procedure to formulate and implement 3D elements of arbitrary order in meshes with multiple element types. This procedure includes obtaining shape functions and integration quadrature and establishing an approach for checking the generated element’s compatibility with adjacent elements’ surfaces. This procedure was implemented in Matlab, using its symbolic and graphics toolbox, and complied as a GUI interface named ShapeGen3D to provide finite element users with a tool to tailor elements according to their analysis needs. ShapeGen3D also outputs files with the element formulation needed to enable users to implement the generated elements in other programming languages or through user elements in commercial finite element software. Currently, finite element (FE) users are limited to employing element formulation available in the literature, commercial software, or existing element libraries. Thus, the developed procedure implemented in ShapeGen3D offers FEM users the possibility to employ elements beyond those readily available. The procedure was tested by generating the formulation for a brick element, a brick transition element, and higher-order hexahedron and tetrahedron elements that can be used in a spectral finite element analysis. The formulation obtained for the 20-node element was in perfect agreement with the formulation available in the literature. In addition, the results showed that the interpolation condition was met for all the generated elements, which provides confidence in the implementation of the process. Researchers and educators can use this procedure to efficiently develop and illustrate three-dimensional elements.

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Implementing an Accurate Generalized Gaussian Quadrature Solution to Find the Elastic Field in a Homogeneous Anisotropic Media

Cited by 5 publications

References 16 publications

The effects of residual stresses and strains on lateral-torsional buckling behavior of cold-formed steel channel and built-up I-sections beams

The effects of residual stresses and strains on lateral-torsional buckling behavior of cold-formed steel channel and built-up I-sections beams

Simulating Powder X-ray Diffraction Patterns of Two-Dimensional Materials

A General Procedure to Formulate 3D Elements for Finite Element Applications

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