An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co‐ordinates

A versatile two-dimensional mesh generator with automatic bandwidth reduction

By using the finite element and direct stiffness method, piecewise linear load deflection relationship, and step-by-step computational algorithm, a general procedure for the solution of problems of elastoplasticity is developed. The change of material properties at each step is expressed in the general differential form of Prandtl-Reuss equations of the theory of plastic deformations, with special treatment of the plane strain case. The effect of initial stresses is also considered when the rotations at each step are not negligible, although the strains are assumed small compared to unity. Application of the principle of virtual work to define the equilibrium of an element subject to initial and additional stresses yields a geometrical stiffness matrix which satisfies macroscopic equilibrium requirements. Computational difficulties arising from the repeated solution of large numbers of linear simultaneous equations are overcome by using an iteration method with an over-relaxation factor. The accuracy of the propagated solution is improved by the application of half-step procedure, which is a special case of the Runge-Kutta method.

Solution of nonlinear problems of elastoplasticity by finite elementmethod.

This paper presents a generalized method which generates linear, triangular, quadrilateral and pentahedral elements for the finite element method. Depending on geometrical and material variations, the region to be discretized is manually divided into blocks such as lines, triangles, quadrilaterals, pentahedrons and hexahedrons in several appropriate co-ordinate systems. However, no connectivity information of the adjacent blocks is required by the user as input. The continuity of the generated nodal co-ordinates and element configurations at the block interface are automatically maintained to describe the geometry of structures, no matter how these five types of blocks are connected. Furthermore, a mesh grading algorithm which generates reliable mesh grade distributions in the interior of the triangular and quadrilateral blocks is established corresponding to the arbitrarily defined subdivision numbers for each edge line of blocks. This algorithm is extended to the mesh grading in the interior of the hexahedral and pentahedral blocks. Element numbers are also renumbered in this scheme, in addition to node numbers, in order to increase the computational efficiency of the global matrix assembly. Additional facilities, i.e. loading data generation, boundary condition data generation and so on, are also discussed. An illustrative and a practical example are given to demonstrate the capabilities of this scheme.

A generalized automatic mesh generation scheme for finite element method

An interactive computer graphic system has been developed for generating and editing three-dimensional finite element meshes. The various difficulties inherent to the generation of solid three-dimensional geometries through an effective use of computer graphic techniques are examined to explain the advantages of this system. The method is a combination of discrete transfinite mapping and cubic spline blending algorithms, used, respectively, to create plane cross-sectional meshes, and to generate the three-dimensional geometry by interpolaring between the cross-sections. The communication between analyst and machine is based on a digitizing tablet and a refresh vector scope. The dynamic viewing capabilities and depth cueing of the vector display greatly enhance the perception of the mesh three-dimensionality. Multi-view dynamic display is also employed to facilitate node or element selection. The flexibility and usefulness of the system are illustrated with the help of three examples of practical interest.

Fevzican A. Akyuz

Papers

Natural coordinate systems an automatic input data generation scheme for a finite-element method

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