A Hermitian C Differential Reproducing Kernel Interpolation Meshless Method for the 3D Microstructure-Dependent Static Flexural Analysis of Simply Supported and Functionally Graded Microplates
Chih-Ping Wu*, Ruei-Syuan Chang
Department of Civil Engineering, National Cheng Kung University, Tainan, 70101, Taiwan
* Corresponding Author: Chih-Ping Wu. Email: 
(This article belongs to the Special Issue: Theoretical and Computational Modeling of Advanced Materials and Structures-II)
Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2024.052307
Received 29 March 2024; Accepted 21 June 2024; Published online 23 July 2024
Abstract
This work develops a Hermitian
C differential reproducing kernel interpolation meshless (DRKIM) method within the consistent couple stress theory (CCST) framework to study the three-dimensional (3D) microstructure-dependent static flexural behavior of a functionally graded (FG) microplate subjected to mechanical loads and placed under full simple supports. In the formulation, we select the transverse stress and displacement components and their first- and second-order derivatives as primary variables. Then, we set up the differential reproducing conditions (DRCs) to obtain the shape functions of the Hermitian
C differential reproducing kernel (DRK) interpolant’s derivatives without using direct differentiation. The interpolant’s shape function is combined with a primitive function that possesses Kronecker delta properties and an enrichment function that constituents DRCs. As a result, the primary variables and their first- and second-order derivatives satisfy the nodal interpolation properties. Subsequently, incorporating our Hermitian
C DRK interpolant into the strong form of the 3D CCST, we develop a DRKIM method to analyze the FG microplate’s 3D microstructure-dependent static flexural behavior. The Hermitian
C DRKIM method is confirmed to be accurate and fast in its convergence rate by comparing the solutions it produces with the relevant 3D solutions available in the literature. Finally, the impact of essential factors on the transverse stresses, in-plane stresses, displacements, and couple stresses that are induced in the loaded microplate is examined. These factors include the length-to-thickness ratio, the material length-scale parameter, and the inhomogeneity index, which appear to be significant.
Keywords
Consistent/modified couple stress theory; differential reproducing kernel methods; microplates; point collocation methods; static flexural; 3D microstructure-dependent analysis
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