Вплив степені дискретизації технічного об’єкту на результати прогнозу за МГЕ

Abstract

A significant difference between soils and homogeneous elastic bodies is that under action External loads residual deformations are always concomitant elastic, even at low loads. The sum of residual and elastic deformation is the total deformation of the soil base. The simultaneous presence in the soil of zones operating in both elastic and plastic zones requires the involvement of the theory of elasticity and plasticity to model its behavior [1-4]. It is known that the solution of the mixed problem of the theory of elasticity and the theory of soil plasticity brings the results of sedimentation calculations much closer to reality. The current trend towards automated calculation methods has dramatically changed the priorities towards the need to develop more reliable mathematical models of nonlinearly deformed soil massifs composed of layers with different properties. Urban planning and modern industry require the construction of responsible structures on increasingly complex engineering and geological conditions for which the rational type of foundations are piles. Widespread use of pile foundations requires the development of reliable methods for their calculation in order to obtain reliable design solutions. Therefore, the current stage of development of soil mechanics is characterized by an active transition to new computational models that more fully reflect the nonlinearity of deformation and rheological properties of soils and these issues remain an urgent problem today. The paper uses the numerical method of boundary elements, which emerged as a result of further theoretical development of a wide class of numerical methods, united under the common name of finite element theory. It is based on the existence of a fundamental solution of the boundary value problem, which corresponds to the source function given in the form of the Dirac delta function. The availability of a fundamental solution is very important from a practical point of view for the numerical implementation of the IHE task. A fundamental solution is a partial solution of the Laplace equation for a semi-infinite domain for a potential value of one given at some point. This type of solution is widely used in boundary value problems and is a Green's function or influence function. In the presence of a fundamental solution, finite elements are used to approximate the boundary of the domain, and the apparatus of classical integral equations is applied to the inner part of the domain/