การวิเคราะห์การดัดของพื้นหนาที่ผลิตจากวัสดุ FGMs บนฐานรากยืดหยุ่น ด้วยวิธีบาวดารีเอลิเมนต์

Tinnapop Boontos; Boonme Chinnaboon; Somchai  Chucheepsakul; Monchai  Panyatong

Authors

Tinnapop Boontos Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
Boonme Chinnaboon Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
Somchai Chucheepsakul Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand
Monchai Panyatong Faculty of Engineering, Rajamangala University of Technology Lanna, Chiang Rai, Thailand

Keywords:

Elastic Foundation, Thick Functionally-Graded Plate, Boundary Element Method, Analog Equation Method

Abstract

Background and Objectives:Functionally Graded Materials (FGMs) are garnering significant attention in engineering due to their versatile applications in structural components, especially in plate structures. Their properties, which vary continuously with thickness, enable the tailoring of mechanical properties and resistance to meet specific operational needs. Analyzing the bending behavior of thick FGM plates on elastic foundations is nevertheless a complicated task, requiring consideration of the interactions between the plates and the foundations as well as the implications of variation in material properties with thickness. Although Finite Element Method (FEM) and other analytical approaches have been extensively developed to analyze the bending of thick FGM plates on elastic foundations, such methods continue to encounter limitations in managing complex boundary conditions and structural shapes. Consequently, in this research, the Boundary Element Method (BEM) was developed as an alternative for analyzing thick FGM plates on elastic foundations.

Methodology: The governing equations and boundary conditions were derived using the principle of virtual work, based on the first-order shear deformation plate theory. The properties of FGMs were modeled using a power law distribution model. The presented method was developed using the concept of the Analog Equation Method, where the differential equations of the original problem were substituted with three Poisson’s equations under fictitious forces, maintaining the original boundary conditions. These fictitious forces were generated using techniques based on the Boundary Element Method and approximated using radial basis functions. The reliability of the proposed method was assessed by comparing the results of the present research with outcomes from other established approaches.

Main Results: The numerical results obtained from the proposed method are highly accurate and precise when compared to those of other relevant research, demonstrating convergence of the solution as the number of boundary elements and internal nodes increases. Furthermore, it effectively analyzed thick FGMs plates on elastic foundations under complex conditions, such as an elastic support and elastic restraint, or plates with various shapes. Such complex problem has not been investigated in previous research studies.

Conclusions: The present research developed the Boundary Element Method (BEM) in conjunction with the Principle of Analog Equation to analyze the bending of complex thick plates made from Functionally Graded Materials (FGMs) resting on elastic foundations, considering both the boundary conditions and the plate shapes. The results demonstrate the accuracy and efficiency of the proposed methods, capable of accurately simulating the interactions and effects of material properties and various parameters on the bending response of the plates.

Practical Application: This study proposes an effective method for analyzing the bending of thick plates made from Functionally Graded Materials (FGMs) on elastic foundations, capable of analyzing plates with complex shapes and boundary conditions that are common in real-world applications. This allows for the safe and efficient design of such structures.

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