Chen Wanji

Refined quadrilateral element based on Mindlin/Reissner plate theory

A new quadrilateral thin/thick plate element RDKQM based on the Mindlin/Reissner plate theory is proposed. The exact displacement function of the Timoshenkos beam is used to derive the element displacements of the refined element RDKQM. The convergence for the very thin plate can be ensured theoretically. Numerical examples presented show that the proposed model indeed possesses higher accuracy in the analysis of thin/thick plates. It can pass the patch test required for the Kirchhoff thin plate elements, and most important of all, it is free from locking phenomenon for extremely thin plates. Copyright

Formulation of Quasi-Conforming element and Hu-Washizu principle

Abstract A new, convenient and general method called Quasi-Conforming Element Technique is introduced for Finite Element Formulations in which the strain is discretized in terms of nodal values and then the potential energy is used to obtain stiffness matrix. The Quasi-Conforming Element Technique is a multivariate finite element method so that it includes the compatible, incompatible and hybrid stress model as its special cases. The connection between this technique and Hu-Washizu principle is shown.

Refined non-conforming triangular elements for analysis of shell structures

Based on the refined non-conforming element method, simple flat triangular elements with standard nodal displacement parameters are proposed for the analysis of shell structures. For ensuring the convergence of the elements a new coupled continuity condition at the inter-element has been established in a weaker form. A common displacement for the inter-element, an explicit expression of refined constant strain matrix, and an adjustable constant are introduced into the formulation, in which the coupled continuity requirement at the inter-element is satisfied in the average sense. The non-conforming displacement function of the well-known triangular plate element BCIZ [1] and the membrane displacement of the constant strain triangular element CST [2] are employed to derive the refined flat shell elements RTS15, and the refined flat shell elements RTS18 is derived by using the element BCIZ and the Allmans triangular plane element [3] with the drilling degrees of freedom. A simple reduced higher-order membrane strain matrix is proposed to avoid membrane locking of the element RTS18. An alternative new reduced higher-order strain matrix method is developed to improve the accuracy of the elements RTS15 and RTS18. Numerical examples are given to show that the present methods have improved the accuracy of the shell analysis. Copyright

Enhanced patch test of finite element methods

Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0–1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.

The application of a refined non-conforming quadrilateral plate bending element in thin plate vibration and stability analysis

In this paper, the refined non-conforming quadrilateral thin plate element RPQ4 is used to analyze the vibration and stability problems of thin plates. For vibration analysis, a modified mass matrix is formulated to calculate the natural frequencies and in the same way, a modified geometric stiffness matrix is formed to calculate the critical load in the stability analysis of thin plates. The numerical results have demonstrated that the modified mass matrix and modified geometric stiffness matrix are efficient in improving the accuracy of natural frequency in the free vibration analysis and critical load of buckling in the analysis of stability of thin plates.

Free vibration analysis of laminated and sandwich plates using quadrilateral element based on an improved zig-zag theory

In this article, an improved zig-zag theory (ZIGT) is proposed for free vibration analysis of laminated composite plates. The proposed theory a priori satisfies the continuity conditions of transverse shear stresses at interfaces. Moreover, seven independent variables are only involved in displacement field. Compared to the early ZIGTs suffering from C1 requirement in their finite element implementation, the advantage of the proposed theory is that the first derivative of transverse displacement has been eliminated from the in-plane displacement fields. Thus, the C0 shape functions are only required during its finite element implementation. Due to its C0 continuity requirements and low computational costs, the proposed theory is adequate to implement in commercial finite element codes. Based on the proposed ZIGT, a C0 conforming quadrilateral element is developed for free vibration analysis of laminated composite and sandwich plates. Numerical results show that the proposed element is able to accurately predict the natural frequencies of laminated composite plates and sandwich plates with soft core. However, the global higher-order theories as well as the first-order theory remarkably overestimate the natural frequencies of such structures.

Refined hybrid degenerated shell element for geometrically non-linear analysis

Based on a variational principle with relaxed inter-element continuity requirements, a refined hybrid quadrilateral degenerated shell element GNRH6, which is a non-conforming model with six internal displacements, is proposed for the geometrically non-linear analysis. The orthogonal approach and non-conforming modes are incorporated into the geometrically non-linear formulation. Numerical results show that the orthogonal approach can improve computational efficiency while the non-conforming modes can eliminate the shear/membrane locking phenomenon and improve the accuracy.

Geometric nonlinear analysis by using refined triangular thin plate element and free form membrane locking

Abstract Based on a large deformation variational principle with relaxed interelement continuity requirement in the total Lagranginan description, a refined triangular thin plate element for geometric nonlinear analysis has been developed. By introducing special element displacement functions into the geometric stiffness matrix, the membrane locking phenomenon is relieved effectively. The numerical results are presented to show that the present element possesses higher accuracy and an ability to free form membrane locking.

Variational principles and refined non-conforming element methods for geometrically non-linear analysis

New variational principles with relaxed interelement continuity requirement are developed for geometrically non-linear analysis, and the refined non-conforming element methods are given. A simple modification of the constant strain can be introduced into the formulation, and the remaining procedures are the same as that of the conventional displacement method. ©1997 John Wiley & Sons, Ltd.

Geometrically non-linear generalized hybrid element and refined element method of non-conforming modes

A generalized hybrid method of non-conforming modes based on a non-linear generalized variational principles with relaxed interelement continuity requirements, is developed, and the plane quadrilateral geometrically non-linear element is presented, furthermore, non-linear refined element method is devised by orthogonal approach. It is shown that the refined element can improve the computational accuracy for non-conforming modes.