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Introduction to Generative Structural Analysis (GSA) Workbench © 2020, ASCENT - Center for Technical Knowledge® 1–5 Figure 1–3 Next, the deflection Y within each finite element is approximated by a polynomial. In this example, you use linear polynomial , which means that deflection within each element is approximated by essentially a straight line. Sewing local polynomials at the nodes ensures continuity of the global approximation function and, therefore, of the FEA solution for the deflection over the entire beam. Next, the local linear polynomials are sewn together at the nodes, creating a global approximation function in the form of a piece-wise linear polynomial, which is a polyline. Finally, the global approximation function is best-fit to satisfy both the bending differential equations and beam boundary conditions (loads and constraints). The resulting function (the dashed line shown in Figure 1–3) now represents the FEA solution for the true deflection (the solid line shown in Figure 1–3) in the beam. It is important to note that your FEA result contains a certain amount of error, which is the deviation between the true deflection (the solid line shown in Figure 1–3) and the FEA solution (the dashed line shown in Figure 1–3), and which is called the discretization error. Any FEA solution is just an approximation, which means it always contains a discretization error. Therefore, in the FEA process, it is critical to know how to estimate, how to control, and how to reduce this unavoidable approximation error to acceptable levels. Sample provided by ASCENT for review only All copying and reuse strictly forbidden.