The Experts below are selected from a list of 57 Experts worldwide ranked by ideXlab platform
H.t. Rathod - One of the best experts on this subject based on the ideXlab platform.
-
The Use of Parabolic Arc in Matching Curved Boundary by Point Transformations for Sextic Order Triangular Element
International Journal of Mathematical Analysis, 2010Co-Authors: K.v. Nagaraja, V. Kesavulu Naidu, H.t. RathodAbstract:This paper is concerned with curved boundary triangular element having one curved side and two straight sides. The curved element considered here is the 28-node (sextic) triangular element. On using the Isoparametric Coordinate transformation, the curved triangle in the global (x, y) Coordinate system is mapped into a standard triangle: (I¾,I·) / 0 ⤠I¾,I· ⤠1,I¾ + I· ⤠1in the local Coordinate system(I¾,I·). Under this transformation curved boundary of this triangular element is implicitly replaced by sextic arc. The equation of this arc involves parameters, which are the Coordinates of points on the curved side. This paper deduces relations for choosing the parameters in sextic arc in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangle will serve as a powerful subparametric Coordinate transformation for higher order curved triangular elements with one curved side and two straight sides.
-
The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements
Finite Elements in Analysis and Design, 2008Co-Authors: H.t. Rathod, K.v. Nagaraja, V. Kesavulu Naidu, B. VenkatesuduAbstract:This paper is concerned with curved boundary triangular elements having one curved side and two straight sides. The curved elements considered here are the 6-node (quadratic), 10-node (cubic), 15-node (quartic) and 21-node (quintic) triangular elements. On using the Isoparametric Coordinate transformation, these curved triangles in the global (x,y) Coordinate system are mapped into a standard triangle: {(@x,@h)/0=
-
Some pre-computed universal numeric arrays for linear convex quadrilateral finite elements
Finite Elements in Analysis and Design, 2001Co-Authors: H.t. Rathod, Shafiqul IslamAbstract:Abstract In this paper we investigate the finite element analysis for the solution of linear partial differential equations using linear convex quadrilateral elements. We show that a linear polygonal domain can be discretized into a set of special linear convex quadrilateral elements, which generate the same expression for the determinant of the Jacobian matrix under the Isoparametric Coordinate transformation. Analytical integration of the above element matrices is shown to depend on certain ‘universal pre-computed numeric arrays’, i.e., the arrays which are computed once, stored on a permanent file and then reused in all subsequent applications of the program. We have constructed such arrays for the five commonly used linear quadrilateral elements: Q 4, Q 8, Q 9, Q 12 and Q 16. One speciality of these pre-computed arrays is that the arrays for lower order elements are already contained in the arrays for higher order elements. The performance of the proposed method is demonstrated by means of a numerical example.
Yuqiu Long - One of the best experts on this subject based on the ideXlab platform.
-
Some Recent Advances on the Quadrilateral Area Coordinate Method
Computational Mechanics, 2007Co-Authors: Song Cen, Xiao-ming Chen, Yuqiu LongAbstract:Since the Quadrilateral Area Coordinate Method (QACM) was systematically established at the end of last century [1], some successful applications of this new tool have been achieved by various researchers [2, 3]. Compared with the usual Isoparametric Coordinate method, the QACM can make a quadrilateral finite element model less sensitive to mesh distortion, and simplifies the copmputational procedures (such as no Jacobi inverse is needed).
-
membrane elements insensitive to distortion using the quadrilateral area Coordinate method
Computers & Structures, 2004Co-Authors: Xiao-ming Chen, Yuqiu Long, Song Cen, Zhenhan YaoAbstract:Abstract Two 4-node quadrilateral membrane elements, denoted as AGQ6-I and AGQ6-II, have been developed in this paper. Instead of the traditional Isoparametric Coordinate, the quadrilateral area Coordinates were used to establish the formulations of the new elements. And several generalized conforming conditions were then introduced to determine all unknown parameters. Numerical examples showed that the presented elements exhibit excellent performances in both regular and distorted mesh divisions. They could even yield exact solutions for pure bending problems under distorted meshes and provide lock-free solutions for the MacNeal’s test problem of trapezoidal locking. Besides, the weak patch test was conducted to guarantee the convergence of both new elements. It has also been demonstrated that the area Coordinate method is an efficient tool for developing simple, effective and reliable serendipity plane membrane elements.
Shafiqul Islam - One of the best experts on this subject based on the ideXlab platform.
-
Some pre-computed universal numeric arrays for linear convex quadrilateral finite elements
Finite Elements in Analysis and Design, 2001Co-Authors: H.t. Rathod, Shafiqul IslamAbstract:Abstract In this paper we investigate the finite element analysis for the solution of linear partial differential equations using linear convex quadrilateral elements. We show that a linear polygonal domain can be discretized into a set of special linear convex quadrilateral elements, which generate the same expression for the determinant of the Jacobian matrix under the Isoparametric Coordinate transformation. Analytical integration of the above element matrices is shown to depend on certain ‘universal pre-computed numeric arrays’, i.e., the arrays which are computed once, stored on a permanent file and then reused in all subsequent applications of the program. We have constructed such arrays for the five commonly used linear quadrilateral elements: Q 4, Q 8, Q 9, Q 12 and Q 16. One speciality of these pre-computed arrays is that the arrays for lower order elements are already contained in the arrays for higher order elements. The performance of the proposed method is demonstrated by means of a numerical example.
-
Some pre-computed universal numeric arrays for linear convex quadrilateral finite elements
'Elsevier BV', 2001Co-Authors: Rathod H.t., Shafiqul IslamAbstract:In this paper we investigate the finite element analysis for the solution of linear partial differential equations using linear convex quadrilateral elements. We show that a linear polygonal domain can be discretized into a set of special linear convex quadrilateral elements, which generate the same expression for the determinant of the Jacobian matrix under the Isoparametric Coordinate transformation. Analytical integration of the above element matrices is shown to depend on certain 'universal pre-computed numeric arrays', i.e., the arrays which are computed once, stored on a permanent file and then reused in all subsequent applications of the program. We have constructed such arrays for the five commonly used linear quadrilateral elements: Q4, Q8, Q9, Q12 and Q16. One speciality of these pre-computed arrays is that the arrays for lower order elements are already contained in the arrays for higher order elements. The performance of the proposed method is demonstrated by means of a numerical example. © 2001 Elsevier Science B.V. All rights reserved
Song Cen - One of the best experts on this subject based on the ideXlab platform.
-
Application of the quadrilateral area Coordinates: A 4-node quadrilateral membrane element beyond MacNeal’s theorem
2015Co-Authors: Pei-lei Zhou, Song CenAbstract:In this paper, the second form of quadrilateral area Coordinate method (QACM-II) was employed to develop a novel 4-node quadrilateral membrane element insensitive to mesh distortion. First, two stress functions in terms of the QACM-II ( S , T ) are given to represent exact solutions of pure bending state in x and y directions. Their linear combination can reflect exact solutions for pure bending in all directions because the QACM-II is a local natural Coordinate system. Thus, the basic analytical solutions of stresses, strains and displacements corresponding to the pure bending state for the isotropic and anisotropic plane problems can be obtained. Then, the unsymmetric element technique was adopted to formulate an unsymmetric 4-node, 8-DOF (2DOFs per node) quadrilateral membrane element. This approach is derived from the virtual work principle, and uses different test and trial functions. The test function employs the Isoparametric Coordinate interpolation to satisfy inter-element compatibility, while the trial function adopts a novel composite Coordinate interpolation of the Cartesian Coordinates and QACM-II to satisfy the completeness requirements in physical space. Due to the linear relationship between quadrilateral area and Cartesian Coordinates, the order of trial displacement fields will not degrade when the meshes are distorted. Since the test displacement fields satisfy the compatibility requirements and the trial displacement fields contain analytical solutions of pure bending in all directions, the new element can produce exact solutions in both constant stress/strain patch test and pure bending problem in any directions, which means the well-known contradiction declared by MacNeal’s theorem: any 4-node, 8-DOF plane membrane element will either lock in in-plane bending or fail to pass a C 0 patch test when the element’s shape is an isosceles trapezoid, has been perfectly broken through. The authors would like to acknowledge the financial supports of the National Natural Science Foundation of China (Project No. 11272181), the Specialized Research Fund for the Doctoral Program of Higher Educationof China (Project No. 20120002110080), and Tsinghua University Initiative Scientific Research Program (Project No. 2014z09099).
-
Some Recent Advances on the Quadrilateral Area Coordinate Method
Computational Mechanics, 2007Co-Authors: Song Cen, Xiao-ming Chen, Yuqiu LongAbstract:Since the Quadrilateral Area Coordinate Method (QACM) was systematically established at the end of last century [1], some successful applications of this new tool have been achieved by various researchers [2, 3]. Compared with the usual Isoparametric Coordinate method, the QACM can make a quadrilateral finite element model less sensitive to mesh distortion, and simplifies the copmputational procedures (such as no Jacobi inverse is needed).
-
membrane elements insensitive to distortion using the quadrilateral area Coordinate method
Computers & Structures, 2004Co-Authors: Xiao-ming Chen, Yuqiu Long, Song Cen, Zhenhan YaoAbstract:Abstract Two 4-node quadrilateral membrane elements, denoted as AGQ6-I and AGQ6-II, have been developed in this paper. Instead of the traditional Isoparametric Coordinate, the quadrilateral area Coordinates were used to establish the formulations of the new elements. And several generalized conforming conditions were then introduced to determine all unknown parameters. Numerical examples showed that the presented elements exhibit excellent performances in both regular and distorted mesh divisions. They could even yield exact solutions for pure bending problems under distorted meshes and provide lock-free solutions for the MacNeal’s test problem of trapezoidal locking. Besides, the weak patch test was conducted to guarantee the convergence of both new elements. It has also been demonstrated that the area Coordinate method is an efficient tool for developing simple, effective and reliable serendipity plane membrane elements.
Xiao-ming Chen - One of the best experts on this subject based on the ideXlab platform.
-
Some Recent Advances on the Quadrilateral Area Coordinate Method
Computational Mechanics, 2007Co-Authors: Song Cen, Xiao-ming Chen, Yuqiu LongAbstract:Since the Quadrilateral Area Coordinate Method (QACM) was systematically established at the end of last century [1], some successful applications of this new tool have been achieved by various researchers [2, 3]. Compared with the usual Isoparametric Coordinate method, the QACM can make a quadrilateral finite element model less sensitive to mesh distortion, and simplifies the copmputational procedures (such as no Jacobi inverse is needed).
-
membrane elements insensitive to distortion using the quadrilateral area Coordinate method
Computers & Structures, 2004Co-Authors: Xiao-ming Chen, Yuqiu Long, Song Cen, Zhenhan YaoAbstract:Abstract Two 4-node quadrilateral membrane elements, denoted as AGQ6-I and AGQ6-II, have been developed in this paper. Instead of the traditional Isoparametric Coordinate, the quadrilateral area Coordinates were used to establish the formulations of the new elements. And several generalized conforming conditions were then introduced to determine all unknown parameters. Numerical examples showed that the presented elements exhibit excellent performances in both regular and distorted mesh divisions. They could even yield exact solutions for pure bending problems under distorted meshes and provide lock-free solutions for the MacNeal’s test problem of trapezoidal locking. Besides, the weak patch test was conducted to guarantee the convergence of both new elements. It has also been demonstrated that the area Coordinate method is an efficient tool for developing simple, effective and reliable serendipity plane membrane elements.
