finite element method

A parallel preconditioning Schur complement approach for large scale industrial problems

The purpose of this paper is to introduce a new strategy to improve the convergence and efficiency of the class of domain decomposition known as Schur complement techniques related to interface variables for the simulation of mechanical, electrical and thermal problems in presence of cross points.  More precisely, we are interested not only in domain decomposition with two equal parts having the same physical properties but rather in more general splitting components.  It is known that in the first case, the optimal convergence with good pre-conditioner is obtained in t


Currently, on the world market, there are trends in the construction of a large number of monolithic and prefabricated reinforced concrete structures, and individual parts of these structures are operated with damage or defects, and the causes of these damages are quite diverse. In modern conditions, such work can be facilitated and analyzed in more detail with the help of specialized software, which can include all the necessary characteristics of material behavior and include existing defects or damage.


One of the important tasks of modern construction is the search for new constructive solutions and the introduction of new construction technologies. Cross-Laminated Timber (CLT) technology is a new material for Ukraine that has proven itself in Europe and America as effective and environmentally friendly with many advantages. Since CLT panels are not widely distributed, studied and do not contain references in the normative literature in Ukraine, the study of these structures is extremely relevant.

Алгоритмічне та програмне забезпечення системи моделювання та аналізу процесу сушіння капілярно-пористих матеріалів

Сформульовано математичну модель тепломасоперенесення та деформування капілярно-пористих матеріалів під час сушіння. У межах об’єктно-орієнтованого підходу розроб- лено алгоритмічне та програмне забезпечення для чисельної реалізації отриманої моделі.

In the article is formulated a mathematical model of heat and mass transfer and deformation of capillary-porous materials during drying. In the object-oriented approach developed algorithmic and software for numerical realization of the obtained model.

Автоматизована числова схема розв’язання крайових задач на основі h-адаптивного методу скінченних елементів

Досліджено питання розроблення та реалізації h -адаптивного обчислювального процесу на основі методу скінченних елементів, метою якого є автоматизація отримання розв’язку заданої точності. На прикладі модельної крайової задачі лінійної теорії пружності для дослідження пружного стану тіла L-подібної форми продемонстровано переваги та ефективність розробленого підходу.

Об‘єктно-орієнтована реалізація методу скінченних елементів для розрахунку в’язкопружного стану капілярно-пористих матеріалів

У межах об’єктно-орієнтованого підходу та UML розроблено програмне забезпечення для реалізації математичної моделі в’язкопружного деформування капілярно- пористих матеріалів з використанням методу скінченних елементів. Створене об‘єктно- орієнтоване програмне забезпечення складається зі задокументованих класів, які можуть повторно використовуватись для реалізації нових моделей.

Numerical modeling of surface subsidence due to compaction of soil with fine inclusions

A mathematical model of filtration consolidation of an inhomogeneous soil mass was formed taking into account the change in the size of the area during the compaction process.  The inhomogeneity is considered as the presence of fine inclusions (geobarriers) the physical and mechanical characteristics of which differ from those of the main soil.  From a mathematical viewpoint, the model is described by a one-phase Stefan problem that has a kinematic boundary condition on the upper moving boundary as its component.  The purpose of the research is to find out the effect of

The research on matrix of press-form stiffness and steadiness

The formalized algorithm of calculation of rectangular matrix of press-form is developed on durability and inflexibility with the purpose of determination of optimum geometrical sizes which would provide it optimum operating capacity. For this purpose CAD and CAE systems were used, in particular Solidwork,  Matcad. А three-dimensional model of the mold matrix was designed. Research and analysis of the stress-strain state of the matrix was carried out and its optimal parameters were determined.

A coupled compressible two-phase flow with the biological dynamics modeling the anaerobic biodegradation process of waste in a landfill

In this article, we present and study a new coupled model combining the biological and the mechanical aspects describing respectively the process of the biogas production and the compressible two-phase leachate-biogas flow during the anaerobic biodegradation of organic matters in a landfill, which is considered a reactive porous medium.  The model obtained is governed by a reaction-diffusion system for the bacterial activity coupled with a compressible two-phase flow system of a non-homogeneous porous medium.  We carry out the analysis and the numerical approximation of the model within a v

Study of the processing of small diagnostic creations on a fluid sourcing by spiral survivals

The article considers the features of the drilling process where there is a change in temperature, hole diameter, and displacement relative to the axis and the impact on the tool, when machining holes with high-speed steel drills there is wear of the transverse edge which is completely rounded to create a conical surface. There is a decrease in the negative value of the front corners on the transverse edge of the decrease in axial force, which led to a decrease in the intensity of wear of the transverse edge.