A computationally efficient numerical integration scheme in the meshless method framework for graded material models

S.H. Srinivasan, Thamarai Selvan Vasu, P.V. Jeyakarthikeyan and Sai Naga Kishore Vutla

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 1-16

Abstract: A computationally efficient numerical integration scheme, the Element Midpoint Method is integrated into the Radial Point Interpolation Method framework to investigate the computational efficiency of handling Functionally Graded Materials (FGM) structures across various problem types. The results are validated by comparing them with the standard Gauss Quadrature of orders 3 × 3 (GQ3) and 6 × 6 (GQ6) reported in the literature. Furthermore, the computational time required to achieve similar accuracy is noted and compared with the Gauss Quadrature of orders GQ3 and GQ6. The results are demonstrated for three types of problems: beam bending, free vibration, and plate under in-plane loading. Material gradation profiles, such as linear, exponential, and power-law, are selected from the literature to illustrate the results. The study reveals that the Element Midpoint method can serve as an alternative to Gauss Quadrature, while being computationally efficient and effective.

Keywords: Radial Point Interpolation Method; Richardson Extrapolation; Integration technique; Functionally Graded Materials; Element Midpoint Method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:1-16

DOI: 10.1016/j.matcom.2026.03.039

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