Abstract
Introduction
.
The dynamic analysis of the behavior of buildings and structures featuring complex foundations on multilayered soils, as well as the analysis of multilayered coverings containing local inclusions and inhomogeneities, are subjects of great interest to the scientific community. These topics necessitate the further development of dynamic analysis methods and the creation of efficient algorithms for calculating wave fields in such media. This study aims to analyze the stress-strain state of a complex structure resting on a multilayer soil foundation using FEM-BEM coupling, and to comparatively assess the efficiency of various parallel computing technologies to optimize the calculation of these characteristics.
Materials and Methods.
The technique of transition from the description of steady-state oscillations of an isotropic linear elastic medium in the form of the Lamé equation to the fundamental solutions of the boundary element method (BEM) by means of integral Fourier transforms is considered. The form of the fundamental solution matrices is based on the superposition of solutions to three auxiliary problems. The problem under consideration is reduced to the combined solution of a discretized BEM SLAE and the FEM equation of motion. The numerical analysis of a structure with a partially embedded foundation on a multilayer soil base is examined using a developed software solution and the Ansys Mechanical software suite.
Results
.
Amplitude-frequency characteristics were obtained for a specific point within a multilayer 3D foundation subjected to dynamic surface loading. Several problem formulations were considered — accounting for the presence or absence of a structure, as well as varying stiffness configurations of the foundation layers. Additionally, data were obtained regarding the displacement of points at the layer interfaces within the section beneath the structure. The computation time of the stress vector for the BEM fundamental solutions was measured. The impact of Coarray, MPI, and OpenMP parallelization techniques, implemented in Fortran, on the software module wall-clock and CPU execution time was analyzed.
Discussion.
The results obtained confirm theoretical concepts regarding the interaction between the structure, including its foundation, and the surrounding soil mass. Given that solving the problem in question is a resource-intensive and time-consuming process, the use of parallel computing technologies to optimize calculations represents a natural step in the software evolution. An analysis of real-time and processor-time costs for the program, utilizing up to eight parallel threads, made it possible to assess the potential for further scaling this task.
Conclusion.
The results lead to the conclusion that the matrix-based technique for constructing fundamental solutions for multilayer media with surface and embedded objects is an effective tool. It allows the dispersion properties of the multilayer medium and the radiation conditions at infinity arising from object-foundation interaction to be accurately captured, while also naturally enabling parallelization of the computational processes when the BEM and FEM are coupled. The use of Coarray, MPI, and OpenMP technologies for parallel computing significantly reduces the software module execution time without incurring a substantial increase in resource consumption.