Тестування схем методу скінченних елементів з використанням B-сплайнів для пластини-смуги в межах гіпотез Кірхгофа–Лява та Тимошенка
The bending of a plate-strip subjected to a constant transverse load is considered as a test problem for the finite element method with the use of B-splines. For a thin plate-strip, the differential equations with boundary conditions and the equivalent variational formulations are presented within t...
Saved in:
| Date: | 2022 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2022
|
| Subjects: | |
| Online Access: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2022.20.61-76 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Prykladni Problemy Mekhaniky i Matematyky |
Institution
Prykladni Problemy Mekhaniky i Matematyky| Summary: | The bending of a plate-strip subjected to a constant transverse load is considered as a test problem for the finite element method with the use of B-splines. For a thin plate-strip, the differential equations with boundary conditions and the equivalent variational formulations are presented within the framework of the classical plate theory (Kirchhoff–Love hypothesis) and in consideration of transverse shear (S. P. Tymoshenko's hypothesis). In plane strain case one-dimensional B-spline basis functions are considered which have higher order of smoothness than the standard FEM approximations (based on Lagrange polynomials). In order to take into account homogeneous boundary conditions, some basis B-splines with the supports lying outside the given domain need modification, which is performed using the multiple knot technique, and due to this open B-splines are obtained. Contributions from the integrals of the basis functions and their derivatives to the finite element stiffness matrix in the case of a single-step mesh are calculated. The procedure for assembling elements to form a global system of linear algebraic equations is demonstrated. The comparison of the obtained results with analytical solutions shows their good agreement. As testing artifacts, they can be applied during the TDD (Test Driven Development) process for rapid implementation of more general-purpose software, in particular, for two-dimensional models. Cite as: M. M. Khomyak, “Testing of the finite element method schemes using B-splines for a plate-strip within the hypotheses of Kirchhoff–Love and Tymoshenko,” Prykl. Probl. Mekh. Mat., Issue 20, 61–76 (2022) (in Ukrainian), https://doi.org/10.15407/apmm2022.20.61-76 |
|---|