Thin structures, such as thin films and coatings, have been widely designed and utilized in many industries recently. However, the widespread experimental research in thin structural problems underlies a general lack of modeling efforts which can accurately and efficiently predict their performance. In this paper, the boundary element method (BEM) based on elasticity theory is developed for two-dimensional (2D) thin structures with the thickness to length ratio in the micro (10-6) or nano (10-9) scales. The BEM-based approach proposed in this paper is constructed using a combination of the regularized indirect boundary integral equations (BIEs) and a general nonlinear transformation which can eliminate the nearly singular properties of the integral kernels. For the test problems studied, very promising results are obtained when the thickness to length ratio is in the orders between 10-6 and 10-9, which is sufficient for modeling most thin structures in the micro- or nano-scales.
Zhang, Yao-Ming; Gu, Yan; and Chen, Jeng-Tzong
"BOUNDARY ELEMENT ANALYSIS OF THIN STRUCTURAL PROBLEMS IN 2D ELASTOSTATICS,"
Journal of Marine Science and Technology: Vol. 19:
4, Article 10.
Available at: https://jmstt.ntou.edu.tw/journal/vol19/iss4/10