Issue link: https://resources.rand3d.com/i/1470826
Introduction to Generative Structural Analysis (GSA) Workbench © 2020, ASCENT - Center for Technical Knowledge® 1–3 1.2 Finite Element Analysis (FEA) Finite element analysis (FEA) is a numerical mathematical method based on the following process: • Discretize (i.e., divide) the model into smaller and more simplified volumes (tetrahedra, bricks, wedges, etc.) called finite elements. The collection of finite elements approximates the shape of the model and is called finite element mesh, or just mesh. An example of a meshed model is shown in Figure 1–1. Figure 1–1 • Approximate the variation of the principal quantity of interest (such as displacement, stress, etc.) within each finite element with polynomials. These polynomials are typically called local approximation functions or shape functions. • Connect the finite elements across the inter-element boundaries, thus effectively sewing elemental polynomials together. The sewn local polynomials now approximate a variation of the quantity of interest over the entire model and, therefore, comprise the global approximation function in the form of a piece-wise polynomial. • Solve the governing equations and boundary conditions (i.e., a boundary value problem) for the global approximation function and find the best-fitting solution. In structural mechanics, the principle of minimum total potential energy is typically used to find the best-fitting solution, which results in solving a large number (sometimes hundreds of thousands) of simultaneous linear equations. • Present the results for this approximate solution. Sample provided by ASCENT for review only All copying and reuse strictly forbidden.