FINITE ELEMENT SOFTWARE FOR SOLVING THREEDIMENSIONAL PROBLEMS BY USE OF CLOUD TECHNOLOGIES

The basic relations of the Finite Element Method are presented in the paper in a general three-dimensional formulation. They are used to build a software tool designed for computational analysis of the stress-strain state using cloud resources in the case of large amounts of data. The mathematical problem statement is given. The main dependencies used to build finite element relations for an element in the form of a four-node tetrahedron are described. Linear shape functions are used. The system of linear algebraic equations is solved by the conjugate gradient method. The structure of additional programs designed for pre- and post-processing of data is discussed. Examples of the work of these programs are given, demonstrating the possibilities of analyzing finite element models, their individual fragments and the distribution of the stress-strain state components over the volume of the structural element being analyzed. The results of verification studies are discussed, which showed satisfactory reliability of the data obtained when solving elastic problems. The proposed approach for the use of cloud resources using Terraform and Kubernetes technologies, which allows performing numerical modeling using the developed software tool, is described. The characteristics of computational processes using a program for a separate personal computer and computing in the cloud are compared. It is emphasized that according to the data of the comparisons performed, it follows that the use of the Microsoft Azure infrastructure in combination with the automated tools Terraform and Kubernetes significantly accelerates the execution of the analyzed tasks. The advantage of the proposed approach in implementing the capabilities of dynamic management of system resources in accordance with the current computational load is noted.