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A new four-node (non-flat) general quadrilateral shell element for geometric and material non-linear analysis is presented. The element is formulated using threedimensional continuum mechanics theory and it is applic able to the analysis of thin and thick shells. The for mulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.

a b s t r a c tFluid-structure interaction (FSI) can be simulated in a monolithic way by solving the flow and structural equations simultaneously and in a partitioned way with separate solvers for the flow equations and the structural equations. A partitioned quasi-Newton technique which solves the coupled problem through nonlinear equations corresponding to the interface position is presented and its performance is compared with a monolithic Newton algorithm. Various structural configurations with an incompressible fluid are solved, and the ratio of the time for the partitioned simulation, when convergence is reached, to the time for the monolithic simulation is found to be between 1/2 and 4. However, in this comparison of the partitioned and monolithic simulations, the flow and structural equations have been solved with a direct sparse solver in full Newton-Raphson iterations, only relatively small problems have been solved and this ratio would likely change if large industrial problems were considered or if other solution strategies were used.

SUMMARYWe briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4-node shell element using a mixed interpolation of tensorial components, and present a new 8-node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.

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...

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An updated Lagrangian and a total Lagrangian formulation of a three‐dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.