A study of three‐node triangular plate bending elements

Abstract

An assessment of flat triangular plate bending elements with displacement degrees-of-freedom at the three comer nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees-of-freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three-node plate bending elements are the DKT and HSM elements. 1.A particular shell theory is used and discreti~,ed.'*~ 2. Three-dimensional continuum equations are used and discretized (isoparametric elements) (References 6 and 7, etc.). 3. Plate bending and membrane element stiffnesses are superimposed and assembled in a global co-ordinate system (References 8 and 9, etc.).The three approaches have advantages and disadvantages, and it is still difficult to state which of the three approaches is most effective based on criteria combining accuracy, computational cost and simplicity in use (in the data input phase as well as in the interpretation of results). Approach 3 received a great deal of attention for the linear analysis of shell structures in the mid-l960s," but the activities related to approaches 1 and 2 have dominated the past 10 years. It is only recently that a new impetus has been given to the analysis of shells using approach 3. 0029-598 1 /80/ 12 15-177 1 $01 .OO Considering this approach, triangular flat elements having displacements and rotations at the corner nodes as degrees-of-freedom-the engineering dof-are particularly appealing for many practical reasons; for example, arbitrary shell geometries, general supports and cut-outs, and beam stiffeners can be modelled. These elements have a total of 18 dof (3 translations and 3 rotations at each node) or 15 dof (3 translations and 2 rotations) depending on whether the rotation about the normal is included as a dof. The element formulation is based on a superposition of membrane and bending actions. Among the most recent papers on this subject, References 12 and 13 deal with the linear analysis, whereas References 9,14,8 and 15 deal with the geometrically nonlinear analysis of shells with large displacements and rotations. In References 1 2 , 9 and 14 the hybrid stress formulations are used, whereas in References 13, 8 and 15, displacement-type formulations are employed.A very important consideration in the development of these shell elements is the representation of the bending behaviour. Although several theoretical and numerical studies on plate bending finite elements have appeared in the past 15 years, a detailed recent study and comparison of triangular plate bending elements with only 3 dof at the corner nodes (displacement w and rotations & and By...

Fluid–structure interaction of three-dimensional magnetic artificial cilia

“…Solid mechanics model The cilia are modelled using shell elements based on the superposition of the bending and membrane stiffness in the local coordinate axes of the shell element. The membrane stiffness is based on constant strain triangles with drilling degrees of freedom (Allman 1984), and the bending stiffness is based on the discrete Kirchhoff triangular elements proposed by Batoz, Bathe & Ho (1980). We start with the principle of virtual work containing the relevant energies, linearize it, and finally adopt an updated Lagrangian framework to arrive at the final set of equations.…”

“…The forms of H x , H y and C are given by Batoz et al (1980). The variation of the membrane strains can be written using the DKTs for the nonlinear part and CSTs with drilling degrees of freedom for the linear part.…”

Revisiting Some Developments of Boundary Elements for Thick Plates in Brazil

“…However, the accuracy of the linear and quadratic element can be further improved by optimizing the offset of the end nodes, since these are discontinuous elements. (Batoz et al [1980]) LR FE (Pugh et al [1978]) QUAD4* FE (Hinton e Huang [1986]) QUAD9* FE (Hinton e Huang [1986] Tables 1 and 2 present results of normalized central displacement, obtained earlier by the authors using RBM and Kutt's quadrature. They remain excellent reference results.…”

Time reduction in implicit single point incremental sheet forming simulation by refinement - derefinement

“…The RD approach controls the generation or the degeneration of elements from the RD mesh to reference mesh. Two element types are used: discrete Kirchhoff triangle DKT and discrete shear triangle DST [6,7]. Both elements have 6 degrees of freedom per node.…”