Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration

As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff’s thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM.

OPTIMAL NODE LOCATION IN TRIANGULAR PLATE BENDING ELEMENTS

Many triangular elements have been formulated for bending plate analysis so far. In this type of element, researchers generally considered the same distance between the side nodes. The present study will show that these types of node locations are not the best. To clarify the effect of side node locations, three new triangular elements will be formulated for the analysis of thin bending plates. These are nonconforming elements and have 10, 15, and 21 degrees of freedom, respectively. Merits and disadvantages of these proposed elements will be revealed by solving different structures. Optimal side nodes' location will be positioned by changing the place of element nodes. Numerical tests will confirm that element accuracy in the best possible situation is much better than the state in which side nodes have the same distance. Moreover, this study will reveal that the presented optimal locations of nodes have no significant dependence on the load cases, boundary conditions, distortion of element shape, and variation of the meshes.

Application of P1-Nonconforming Element for Shell Structure of Incompressible Materiel

This research focused on solving volumetric locking problem of shell structure of incompressible material. Degenerated solid-shell elements are widely applied on curved structure. But, volumetric locking will take place when the structure is made of incompressible material, such as rubber. Due to Poisson’s locking free property of P1-nonconforming element, it is employed to solve volumetric locking problem of shell structure. Furthermore, the study on shell structure is extended to topology optimization design. To verify the volumetric locking free of P1-nonconforming element on shell structure of incompressible material, some structures are studied by different elements. Comparing with the utilization of high order elements to solve volumetric locking problems, P1-nonconforming elements can save calculation time and reduce the numerical cost.