Main / Issues / Vol. 25, N 2 (2019) / Articles

Features of the Implementation of the Finite Element Method in the Spatial Formulation when Creating Authoring Programs

V. F. MushchanovDonbas National Academy of Civil Engineering and ArchitectureA. N. OrzhekhovskyDonbas National Academy of Civil Engineering and ArchitectureA. I. DemidovDonbas National Academy of Civil Engineering and ArchitectureS. A. FomenkoDonbas National Academy of Civil Engineering and ArchitectureF. F. StifeevDonbas National Academy of Civil Engineering and Architecture
Abstract: The article discusses some features of the implementation of the finite element method in the spatial formulation when creating authoring applications for calculating the internal efforts of building structures. The technique of automating the formation of local and global stiffness matrices, the calculation of stiffness matrices of rod elements under various boundary conditions is considered. The method is based on the method of condensation of the stiffness matrix. The most optimal ways of forming the cosine guide matrices and the external load vector are given. The method of calculating the main block of the matrix of cosine guides is based on the use of Euler angles. We consider the method of forming local vectors of the external load, as well as the algorithm for forming the vector of the external load of the system as a whole from local components. A test example of calculating the spatial frame according to the proposed method implemented in the programming language MATLAB is given. The obtained results were compared with the calculation of a similar design in the LIRA-SAPR software package. The difference was less than one percent.

Keywords: building structures, finite element method, cosine guide matrix, stiffness matrix, software.

Pages: 65-75.

PDF

For citation: Mushchanov, V. F.; Orzhekhovsky, A. N.; Demidov, A. I. [et al.]. Features of the Implementation of the Finite Element Method in the Spatial Formulation when Creating Authoring Programs. – Text : electronic. – In: Metal Constructions. – 2019. – Vol. 25, N 2. – Р. 65-75. – URL: https://donnasa.ru/publish_house/journals/mk/2019-2/03_mushchanov_orzhekhovsky_demidov_fomenko_stifeev.pdf (date of access: 21.11.2024). – ISSN 1993-3517.

Issue Cover
Vol. 25, N 2 (2019)
Journal: Metal Constructions
Publish house: Donbas National Academy of Civil Engineering and Architecture