Open Access

ARTICLE

PDE Standardization Analysis and Solution of Typical Mechanics Problems

Ningjie Wang¹, Yihao Wang¹, Yongle Pei², Luxian Li^1,*

1 State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Key Laboratory of Environment and Control for Flight Vehicle, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049, China
2 Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi’an, 710119, China

* Corresponding Author: Luxian Li. Email:

Computer Modeling in Engineering & Sciences 2024, 141(1), 171-186. https://doi.org/10.32604/cmes.2024.053520

Received 02 May 2024; Accepted 15 July 2024; Issue published 20 August 2024

Abstract

A numerical approach is an effective means of solving boundary value problems (BVPs). This study focuses on physical problems with general partial differential equations (PDEs). It investigates the solution approach through the standard forms of the PDE module in COMSOL. Two typical mechanics problems are exemplified: The deflection of a thin plate, which can be addressed with the dedicated finite element module, and the stress of a pure bending beam that cannot be tackled. The procedure for the two problems regarding the three standard forms required by the PDE module is detailed. The results were in good agreement with the literature, indicating that the PDE module provides a promising means to solve complex PDEs, especially for those a dedicated finite element module has yet to be developed.

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Keywords

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