The possibility of constructing adequate and economical mathematical models of especially dangerous and technically complex objects when solving problems of monitoring their dynamic stress-strain state using the finite element method is discussed. The desired result is achieved on the basis of the application of the developed volumetric finite elements with a mixed degree of interpolation, both geometry and displacements for all edges. At the same time, it is possible to combine both subparametric and isoparametric approaches by varying the degree of interpolating polynomials from one to three within each element. The results of evaluating the effectiveness of the proposed approach are presented on the example of solving a model problem on free oscillations of a pipeline. The proposed family of volumetric finite elements is implemented in the COMPASS finite element package, as well as in the specialized software package MStruct, designed for continuous monitoring of industrial equipment, as well as buildings and structures in real time. An example of the practical application of the developed software for monitoring the dynamic stress-strain state of equipment at a hazardous production facility is presented.
Трутаев С.Ю. О построении адекватных и экономичных математических моделей в задачах постоянного мониторинга особо опасных и технически сложных объектов. Математическое моделирование и численные методы, 2021, № 1, с. 31–48.