- The study proposes a new way of combining two mathematical techniques, NURBS and RBF, within the RPIM framework. NURBS are used to model the geometry of the problem domain exactly, while RPIM is used for field variables interpolation. This new approach is called N-RPIM.
- N-RPIM is a hybrid method that combines the advantages of NURBS and RPIM. NURBS are used to represent the geometry of the problem domain exactly, which is important for accurate modeling. RPIM is then used to interpolate field variables such as stress and displacement, which are necessary for solution calculations.
- To demonstrate the effectiveness of N-RPIM, the method is applied to a specific problem, the web of a cellular beam under plane stress condition. This problem is commonly used in structural engineering and allows for a direct comparison of N-RPIM with other methods.
- The study found that N-RPIM works efficiently and is able to provide results that are comparable to the Finite Element Method (FEM), which is a well-established numerical method commonly used in engineering. This is a promising result, as N-RPIM is a relatively new method.
- N-RPIM was found to converge faster than FEM, which suggests that it has the potential to become a powerful tool for solving engineering problems. The faster convergence time also suggests that N-RPIM could be more efficient than FEM for larger and more complex problems. This highlights the potential for future development and application of N-RPIM.
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