Three-node Triangular Element Research Articles

Vibrations of orthotropic triangular plates

The effect of fibre orientation and boundary conditions on vibration behaviour of thin orthotropic triangular plates is studied using a three-noded triangular plate finite element. Isosceles triangular plates having three different included angles are analysed.

EVALUATION AND ENHANCEMENTS OF SOME CONTROL VOLUME FINITE-ELEMENT METHODS—PART 2. INCOMPRESSIBLE FLUID FLOW PROBLEMS

This is the second of two companion papers dealing with the evaluation and enhancements of some control volume finite-element methods (CVFEMs) for fluid flow and heat transfer. One unequal-order CVFEM and two versions of an equal-order CVFEM, for the prediction of two-dimensional incompressible fluid flow are examined in this paper. In the unequal-order CVFEM, six-node macroelements and three-node subelements are used to discretize the calculation domain, and the velocity components are interpolated by flow-oriented upwind-type functions. In the equal-order CVFEM, the calculation domain is discretized by three-node triangular elements, the dependent variables are colocated, and the velocity components are interpolated by flow-oriented upwind-type functions which explicitly account for the influence of the pressure gradient on the velocity distribution in each element. The SIMPLEC procedure is used to solve the discretized equations in all three CVFEMs. The proposed equal-order CVFEM is more accurate than ...

Finite-element analyses of water flooding in irregularly shaped reservoirs

A finite-element solution is developed for flow of two immiscible and incompressible fluids through compressible porous media, representing subsurface oil reservoirs. The spatial domain is discretized using three-noded triangular and four-noded rectangular elements. The element matrices are derived by the Galerkin method. The resulting non-linear system of equations is solved by a new technique introduced in the present study. This technique eliminates instabilities or oscillations even for relatively large time increments used to advance the solution in time. The method is demonstrated by simulating two-phase flow through a regular square domain, a domain with impervious pockets, a domain with varying material properties, and a lense-shaped domain. The analytical results are confirmed qualitatively by comparing the immiscible front profiles with those observed experimentally in similar systems.

A refined four-noded membrane element with rotational degrees of freedom

The paper begins by noting the development and recent success of membrane elements which include in-plane nodal rotations as degrees of freedom. Particular attention is given to Allman's solution ( Comput. Struct. 19, 1–8, 1984) for the three-noded triangular element and the extension of his method by Cook to four-noded quadrilaterals ( Comput. Struct. 22, 1065–1067, 1986). An analysis of the number and type of internal degrees of freedom is used to point out certain deficiencies of Cook's four-noded quadrilateral, including ambiguity in the status of one of the element's two spurious modes, the incomplete representation of linear strain states, and the existence of locking for nearly incompressible materials. Three modifications are then proposed whose combined effect is to correct the deficiencies while preserving satisfaction of the C 0 patch test. The modifications include least square smoothing of the strains computed from displacement shape functions so as to retain only linear terms, the addition of two auxiliary strain terms whose adjoint effect is to enforce internal stress equilibrium, and spurious mode control. Test results are described which show improved accuracy for the modified element rivaling, and in some cases exceeding, that of the eight-noded isoparametric with reduced order integration. The tests also show that in some cases accuracy tends to degenerate above certain threshhold values of spurious mode control.

Construction of new efficient three-node triangular thin plate bending elements

The status of three-node, triangular, thin plate bending elements is summarized, from which the Hansen-Bergan (HBS) and composite triangle (CT) elements emerge as the most competitive, but still exhibit some difficulties in efficient formulation. By combining discrete Kirchoff theory and least squares techniques it is possible to construct high performance displacement type elements, and two such elements are presented here. These elements offer performance comparable or better than HBS and CT elements, and are efficiently formed explicitly by simply pre- and post-multiplying two (9 × 9) matrices. Both linearly varying thickness and uniform thickness plates are considered. The performance is demonstrated for the standard problems widely used to assess such elements.

Shape: (A membrane shape-finding program for tension structures)

This paper describes a complete three-dimensional finite element package suitable for the design and analysis of membrane and pneumatic structures. It utilises both the linear two-node element as well as the three-node triangular flat membrane element formulated using the natural mode technique. Various non-linear iteration schemes are implemented to cater for possible different convergence rates in specific application of the program. The package includes a triangular mesh generation pre-processor and a post-processor plotting routine for viewing of the final structure form.

Remarks on 4cst-elements for incompressible materials

Abstract Three-node triangular elements obtained from the intersecting diagonals of quadrilaterals are thoroughly investigated for the penalty method formulation of incompressible problems such as Stokes flow, Navier-Stokes flow, and small-deformation rubber elasticity. Equivalence of the present formulation to the one using 4-node quadrilateral isoparametric elements with selective reduced integration, is presented. Convergence, instability phenomenon, smoothing of the pressure distribution are studied together with decompositions into triangular elements.

A simple and effective element for analysis of general shell structures

A simple flat three-node triangular shell element for linear and nonlinear analysis is presented. The element stiffness matrix with 6 degrees-of-freedom per node is obtained by superimposing its bending and membrane stiffness matrices. An updated Lagrangian formulation is used for large displacement analysis. The application of the element to the analysis of various linear and nonlinear problems is demonstrated.

A NEW FINITE-ELEMENT FORMULATION FOR CONVECTION-DIFFUSION PROBLEMS

A general numerical method for convection-diffusion problems is presented. The method is formulated for two-dimensional problems, but its key Ideas can be extended to three-dimensional problems. The calculation domain is first divided into three-node triangular elements, and then polygonal control volumes are constructed by joining the centroids of the elements to the midpoints of the corresponding sides. In each element, the dependent variable is interpolated exponentially in the direction of the element-average velocity vector and linearly in the direction normal to it. These interpolation functions respond to an element Peclet number and become linear when it approaches zero. The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes. The proposed method has the conservative property, can handle problems in the whole range of Peclet numbers, and avoids the false-diffusion difficulties that commonly afflict o...

Turbines

Vibration characteristics of pre-twisted composite blades are analysed using a three-noded triangular cylindrical shell element. The specific example of glass fibre reinforced plastic material is analysed with its material damping. The effect of different parameters such as pre-twist, fibre orientation, skew angle, taper ratio and aspect ratio on natural frequency and system loss factor is investigated. It is found that the maximum fundamental frequency and maximum fundamental loss factor occur at different twist angles and at different fibre orientations. The influence of taper ratio and aspect ratio on 0° and 90° fibre orientations is reported. The effect of skew angle on natural frequency and on system loss factors is seen to be low.