Journal ArticleDOI
An alternate stable midpoint quadrature to improve the element stiffness matrix of quadrilaterals for application of functionally graded materials (FGM)
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TLDR
In this paper, a weighted integration route with robust stable one-point integration is recommended, which is an alternative to Gauss quadrature to obtain stiffness matrix of quadrilaterals.About:
This article is published in Computers & Structures.The article was published on 2017-01-01. It has received 18 citations till now. The article focuses on the topics: Gauss–Kronrod quadrature formula & Stiffness matrix.read more
Citations
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Journal ArticleDOI
Enhanced nodal gradient finite elements with new numerical integration schemes for 2D and 3D geometrically nonlinear analysis
TL;DR: The performance of the CIP-enhanced elements is found to be equivalent to that of quadratic Lagrangian finite element counterparts, while having the same discretization with that by the linear finite elements.
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Incompatible Graded Finite Elements for Analysis of Nonhomogeneous Materials
Asmita Rokaya,Jeong-Ho Kim +1 more
TL;DR: Comparison between six-node incompatible (QM6) and four-node compatible (Q4) graded elements is presented and incompatible graded element is shown to give better performance in terms of accuracy and computation time over other element formulations for functionally graded materials (FGMs).
Journal ArticleDOI
An Efficient and Rapid Numerical Quadrature to generate element matrices for quadrilateral and hexahedral elements in Functionally Graded Materials (FGMs)
TL;DR: A robust, efficient and stabilized midpoint quadrature to generate element stiffness matrices for quadrilateral and hexahedral elements in finite element method (FEM) based on Passive Richardson extrapolation which has the inherent ability to stabilize and improve the accuracy of the extrapolated results.
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Fast numerical algorithms with universal matrices for finding element matrices of quadrilateral and hexahedral elements
TL;DR: In this article, a new closed-form formulation with universal matrices strongly recommends that Weighted Richardson Extrapolation (WRE) with robust and hourglass controlled one-point quadrature can absolutely replace the conventional Gauss Quadrature in terms of efficiency, accuracy, and speed to find element stiffness matrices of quadrilateral and hexahedral elements.
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A simple and robust quadrilateral non-conforming element with a special 5-point quadrature
TL;DR: The new 4-node, 8-DOF non-conforming quadrilateral element with four internal modes, denoted as iQ8, achieves the best performance in the aspects of anti-distortion, being free of trapezoidal locking, and exactness in pure bending.
References
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Journal ArticleDOI
Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials
Jeong-Ho Kim,Glaucio H. Paulino +1 more
TL;DR: In this article, a generalized isoparametric formulation of graded finite elements is presented for boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions.
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NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter
N. Valizadeh,Sundararajan Natarajan,Octavio Andrés González-Estrada,Timon Rabczuk,Tinh Quoc Bui,Stéphane Bordas +5 more
TL;DR: In this article, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates.
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On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory
Tinh Quoc Bui,Thom Van Do,Lan Hoang That Ton,Duc Hong Doan,Satoyuki Tanaka,Dat Tien Pham,Thien-An Nguyen-Van,Tiantang Yu,Sohichi Hirose +8 more
TL;DR: In this paper, a displacement-based finite element formulation associated with a novel third-order shear deformation plate theory was developed, taking the desirable properties and advantages of the TSDT theory as its kinematics of displacements are derived from elasticity theory rather than the hypothesis of displacement.
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A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates
TL;DR: In this paper, a novel approach based on isogeometric analysis (IGA) and a simple first-order shear deformation plate theory (S-FSDT) is presented for geometrically nonlinear analysis of homogeneous and non-homogeneous functionally graded plates.
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Finite elements for functionally graded Reissner–Mindlin plates
Lucia Della Croce,Paolo Venini +1 more
TL;DR: In this paper, the behavior of rectangular plates made of functionally graded materials (FGMs) is determined using the variational approach. But the main focus of the paper is the proposal of a locking-free hierarchic family of finite elements that is numerically tested on plates of different material grading.