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

TLDR

The paper presents a computer‑oriented method that generates triangular meshes for plane and curved surfaces, with an extension to 3D tetrahedral elements. The method divides the domain into four‑sided zones, uses curvilinear coordinates to automatically place nodes referenced to a global Cartesian system, and assembles triangular elements from these nodes based on input data specifying zone positions, material properties, and connectivity. Examples demonstrate the method’s ability to generate a wide variety of triangular meshes on plane and curved surfaces.

Abstract

Abstract A computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi‐linear co‐ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co‐ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three‐dimensional tetrahedral elements is indicated.