Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate （QAC） method. Compared with those traditional models using isoparametric coordinates, these new model...Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate （QAC） method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF （5-DOF per node） quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.展开更多
The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh disto...The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.展开更多
This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations...This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between element can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.展开更多
This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM...This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.展开更多
In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mes...In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.展开更多
The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the ...The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.展开更多
基金The project is supported by the National Natural Science Foundation of China(10502028)the Special Foundation for the Authors of the Nationwide(China)Excellent Doctoral Dissertation(200242)the Science Research Foundation of China Agricultural University(2004016).
文摘Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate （QAC） method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF （5-DOF per node） quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.
基金supported by the National Natural Science Foundation of China(11001037,11102037,11290143)the Fundamental Research Funds for the Central Universities(DUT13LK07)
文摘The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.
基金Outstanding Education Fund and Doctor Point Fund of National Education Committee and the National Science Foundation of China
文摘This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between element can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.
文摘This paper presents a curvilinear boundary quadrilateral element for the problem of thin plate of bending with curvilinear boundary. A coordinate transformation of two dimensions is performed in the calculation of FEM. The introduction of an additional stiffness matrix based on the generalized variational principles results in high accuracy and less computation time. The numerical results agree with the analytical solution very well.
基金Subsidized by the Special Funds for Major State Basic Research Projects G1999032804.
文摘In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.
基金supported by the National Natural Science Foundation of China(Grant Nos.11402015,11872090&11672019)。
文摘The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.
