YAKUSEVYCH S. Geometric modelling of effective constructions of buildings’ fasades insulation

The dissertation on competition of a scientific degree of the candidate of technical sciences on a specialty 05.01.01 - Applied geometry, engineering graphics. - Kyiv National University of Construction and Architecture, Ministry of Education and Science of Ukraine, Kyiv, 2021. The dissertation is devoted to the solution of an important scientific and technical problem of development of methods of optimization of constructive decisions of enclosing designs of buildings on the basis of modeling of temperature fields and the analysis of character of distribution of their isotherms. The paper highlights the development of a geometrically interpretive method of constructing temperature fields of energy-efficient enclosing structures of buildings and the implementation of results in the process of design and reconstruction of energy-efficient enclosing structures. Based on the analyzed by the author of the current state of research methods of geometric and numerical modeling of physical processes occurring in the operated enclosing structures of buildings, the justification of the choice of research direction and selected mathematical tools. The main aspects of the system construction of the temperature field function of enclosing structures from the standpoint of geometric modeling are investigated. Based on the integral equations of potential, an algorithm for constructing a continuous temperature field of continuous enclosing structures has been developed. The obtained results taking into account practical aspects of geometric modeling of temperature fields of enclosing constructions of buildings expanded the methodology of determination of rational thermophysical parameters of enclosing constructions on the basis of simulated temperature fields. A geometrically interpreted method and algorithm for constructing a continuous temperature field of continuous enclosing structures based on integral potential equations with constant indicators of conditional density of transmission (transmission) or absorption of thermal energy by each of the surfaces of the studied architectural and structural unit are developed. Assumptions about the constancy of the conditional indicators of thermal energy density allow to transform the system of integral equations written for the surfaces of each of the studied surfaces into a system of linear equations that can be solved with respect to the corresponding indicators. Practical aspects of geometric modeling of temperature fields of enclosing structures of buildings and their design are investigated, including the algorithm of detection and elimination of cold bridges based on the analysis of trajectories of the most rapid heat losses through a thickness of materials of investigated knots with the subsequent check of resistances. regulatory indicators. It is proposed to detect the trajectories of cold bridges using gradient search methods, which becomes possible and convenient in terms of practical implementation due to the continuity of the function of the scalar temperature field, which is described using integral equations. The simulations of temperature fields for the most characteristic units of enclosing structures were performed in the work, which allowed to perform the analysis of the nature of the distribution of their isotherms. The main possible design solutions for ensuring uniform heat leakage through external enclosing structures are considered. Recommendations for program implementation of research results are given. The corresponding block diagram and the description of software algorithms of construction of a continuous temperature field of continuous enclosing designs are offered. Keywords: geometric modeling, continuous temperature field, integral equations of potential, global interpolation.