README.md

MeshTool is a MATLAB class library designed for advanced mesh manipulation and analysis. It enables users to dynamically modify meshes, such as splitting elements and interpolating node coordinates, making it a valuable tool for computational geometry and finite element analysis.

Features

• Dynamic Mesh Modification: Supports operations like element splitting, allowing for localised mesh refinement.
• Flexible Coordinate Systems: Supports multiple coordinate systems (Cartesian, Polar, Spherical).
• Visualisation: Includes built-in methods for mesh visualisation, with options to display nodes and element numbering.

Usage

To use the tool, follow these steps:

1. Create a Mesh Instance: Instantiate the Mesh object. This will be the primary object for your mesh manipulations.

obj = Mesh();

2. Define Mesh Properties: Set the number of element nodes (nen) and dimensions (ndm) for the mesh. In this example, a 2D mesh composed of quadrilateral elements is being created.

obj.nen = 4;
obj.ndm = 2;

3. Specify Node Coordinates: Define the coordinates of each node in the mesh.

obj.x(1,:)  = [0, 0];
obj.x(2,:)  = [1, 0];
obj.x(3,:)  = [2, 0];
obj.x(4,:)  = [2, 1];
obj.x(5,:)  = [1, 1];
obj.x(6,:)  = [0, 1];
obj.x(7,:)  = [0, 2];
obj.x(8,:)  = [1, 2];

4. Define Elements by Nodes: Construct elements by specifying the indices of the nodes that form each element.

obj.ix(1,:)  = [ 1,  2,  5,  6];
obj.ix(2,:)  = [ 2,  3,  4,  5];
obj.ix(3,:)  = [ 6,  5,  8,  7];

5. Update Node and Element Counts: Update the total number of nodes and elements.

obj.numnp = length(obj.x);
obj.numel = length(obj.ix);

6. Refine the Mesh: Use the split method to refine specific elements by dividing them into smaller elements.

obj.split(1, 2, 4); % Split between nodes 1 and 2 into 4 segments
obj.split(2, 3, 4); % Split between nodes 2 and 3 into 4 segments
obj.split(1, 6, 4); % Split between nodes 1 and 6 into 4 segments
obj.split(6, 7, 4); % Split between nodes 6 and 7 into 4 segments

7. Smooth the Mesh: Optionally, smooth the mesh to improve the quality of the mesh after splitting. This is achieved by averaging node positions over a specified number of iterations.

obj.smoothInternal(50);

8. Visualise the Mesh: Display the refined mesh using the plotMesh method. To view node numbers, use obj.plotMesh('nodes');, to see element numbers, use obj.plotMesh('elements');, or to display both, use obj.plotMesh('nodes', 'elements');.

The runnable code for this example is provided in example1.m.

Examples

The following table showcases various meshes that can be generated using MeshTool.

Example 3	Example 4

Contributing

Contributions are welcome! Please feel free to submit pull requests with bug fixes, improvements, or new features.