As you develop your script, the assembly process becomes the most critical phase. You will need to loop through each element to calculate the local stiffness matrix. In MATLAB, this is often done using numerical integration techniques like Gaussian quadrature. Once the local matrix is computed, you use the connectivity information to "scatter" these values into the global stiffness matrix. Efficient indexing is key here; using sparse matrix functions in MATLAB can significantly speed up the solution process for large-scale models.
Finite element analysis remains a cornerstone of modern engineering design and structural simulation. While commercial software packages offer powerful interfaces, writing your own MATLAB codes for finite element analysis provides a deeper understanding of the underlying mathematics. Using M-files allows you to automate repetitive tasks, customize element formulations, and visualize results with precision.
Boundary conditions and loading scenarios are the final pieces of the puzzle. You must apply constraints to prevent rigid body motion and define the external forces acting on the system. After partitioning the global equations to account for fixed displacements, you can use MATLAB’s backslash operator to solve the resulting linear system. This direct solver is highly optimized for performance, making it ideal for the matrix operations central to FEA.
The core of any FEA program in MATLAB is the organization of global stiffness matrices and force vectors. A typical M-file structure begins with defining the geometry and material properties. You must establish a nodal coordinate matrix and an element connectivity matrix. These arrays act as the roadmap for your simulation, telling the code how each discrete piece connects to the whole.
Post-processing is where MATLAB truly shines. Once you have solved for the nodal displacements, you can write additional M-files to compute strains and stresses across the mesh. Using the built-in plotting functions like patch or trisurf, you can generate colorful contour plots that reveal high-stress regions or deformed shapes. This visual feedback is essential for verifying your model and making informed engineering decisions based on your finite element results.
