A Moving Kriging-Based Meshfree Approach for Vibration Analysis of Functionally Graded TPMS Nanoplate: Published online: 24/09/2025

Lieu Nguyen Thi Bich

doi:10.54644/jte.2025.1909

Authors

Lieu Nguyen Thi Bich Ho Chi Minh City University of Technology and Education, Vietnam https://orcid.org/0009-0000-4536-0526

Corressponding author's email:

lieuntb@hcmute.edu.vn

DOI:

https://doi.org/10.54644/jte.2025.1909

Keywords:

Functionally Graded Nanoplate, Moving Kriging-Based Meshfree, Triply periodic minimal surface (TPMS), Eringen’s elasticity theory, Higher-order shear deformation theory (HSDT)

Abstract

Triply Periodic Minimal Surfaces (TPMS) constitute a novel class of architected materials characterized by three-dimensionally periodic geometries derived from minimal surface mathematics. These materials exhibit a unique combination of low density and high mechanical efficiency, making them highly suitable for applications that demand optimized strength-to-weight performance. Due to their continuous, smoothly curved surfaces and topological complexity, TPMS structures have emerged as promising candidates for use in fields such as biomedical engineering, lightweight structural design, and energy absorption systems. TPMS architectures can be realized through two primary strategies: either by thickening the minimal surface to form sheet-based structures or by solidifying the enclosed volume to generate skeletal or solid-based configurations. This study explores the size effect on the free vibration responses of functionally graded (FG) nanoplates with triply periodic minimal surface (TPMS) design. By employing the higher-order shear deformation theory (HSDT) with five unkown variables, in combination with the moving Kriging meshfree method and incorporating nonlocal Eringen’s elasticity theory, we examine two kinds of porous nanostructures: Primitive and Gyroid patterns. For each pattern, four distinct volume dispersal scenarios are considered. The mechanical properties, including elastic modulus, shear modulus, and Poisson's ratio-are obtained through a curve-fitting approach using a two-phase piecewise model. The numerical findings are rigorously compared with reference data from existing literature, ensuring the accuracy of the results.

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Author Biography

Lieu Nguyen Thi Bich, Ho Chi Minh City University of Technology and Education, Vietnam

Lieu Nguyen Thi Bich was born in Vietnam. She has a Ph.D. degree in Engineering Mechanics in 2019. Now, she is a lecturer at the Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, Vietnam. Her research interests are the computational mechanics, numerical methods for advanced materials.

Her email: lieuntb@hcmute.edu.vn. ORCID: https://orcid.org/0009-0000-4536-0526

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