О решении многоточечных краевых задач расчета конструкций в трехмерной постановке на основе совместного применения метода конечных элементов и дискретно-континуального метода конечных элементов. Часть 1: Постановка и общие принципы аппроксимации задач

The distinctive paper is devoted to formulation and basic principles of approximation of multipoint boundary problem of static analysis of three-dimensional structure with the use of combined application of finite element method and discrete-continual finite element method. Basic notation system, design model, general formulation of the problem (based on three-dimensional theory of elasticity), basic principles of domain approximation, rule of numbering of subdomains, rule of numbering of finite elements, rule of numbering of discrete-continual finite elements are considered. Construction of discrete (finite element) and discrete-continual approximation models for subdomains is under consideration as well.В настоящей статье рассматриваются постановка и общие принципы аппроксимации многоточечной краевой задачи статического расчета трехмерной конструкции на основе совместного применения метода конечных элементов и дискретно-континуального метода конечных элементов. В частности, описаны основные обозначения и соглашения, представлены расчетная модель и общая постановка задачи (на основе трехмерной теории упругости), общие принципы аппроксимации области, принятые правила нумерации подобластей, правила нумерации конечных элементов и дискретно-континуальных конечных элементов; описано построение дискретной (конечноэлементной) и дискретно-континуальной аппроксимирующих моделей на подобластях

Solution of boundary problems of structural mechanics with the combined application use of Discrete-Continual Finite Element Method and Finite Element Method

In most structural problems the object is usually to find the distribution of stress in elastic body produced by an external loading system. The theory of elasticity is a methodology that creates a linear relation between the imposing force (stress) and resulting deformation (strain), for the majority of materials, which behave fully or partially elastically. This paper is devoted to combined semianalytical and numerical static analysis of three-dimensional structures. The stress-strain or constitutive behavior is given for isotropic materials. Solution of multipoint (particularly, two-point) boundary problem of three-dimensional elasticity theory based on combined application of finite element method (FEM) and discrete-continual finite element method (DCFEM) is under consideration. The given domain, occupied by structure, is embordered by extended one within method of extended domain. The application field of DCFEM comprises fragments of structure (subdomains) with regular (constant or piecewise constant) physical and geometrical parameters in some dimension ("basic" dimension). DCFEM presupposes finite element mesh approximation for non-basic dimensions of extended domain while in the basic dimension problem remains continual (corresponding correct analytical solution is constructed). FEM is used for approximation of all other subdomains. Discrete (within FEM) and discrete-continual (within DCFEM) approximation models for subdomains and coupled multilevel approximation model for extended domain are constructed. © Published under licence by IOP Publishing Ltd

О решении многоточечных краевых задач расчета конструкций в трехмерной постановке на основе совместного применения метода конечных элементов и дискретно-континуального метода конечных элементов. Часть 1: Постановка и общие принципы аппроксимации задач

The distinctive paper is devoted to formulation and basic principles of approximation of multipoint boundary problem of static analysis of three-dimensional structure with the use of combined application of finite element method and discrete-continual finite element method. Basic notation system, design model, general formulation of the problem (based on three-dimensional theory of elasticity), basic principles of domain approximation, rule of numbering of subdomains, rule of numbering of finite elements, rule of numbering of discrete-continual finite elements are considered. Construction of discrete (finite element) and discrete-continual approximation models for subdomains is under consideration as well.В настоящей статье рассматриваются постановка и общие принципы аппроксимации многоточечной краевой задачи статического расчета трехмерной конструкции на основе совместного применения метода конечных элементов и дискретно-континуального метода конечных элементов. В частности, описаны основные обозначения и соглашения, представлены расчетная модель и общая постановка задачи (на основе трехмерной теории упругости), общие принципы аппроксимации области, принятые правила нумерации подобластей, правила нумерации конечных элементов и дискретно-континуальных конечных элементов; описано построение дискретной (конечноэлементной) и дискретно-континуальной аппроксимирующих моделей на подобластях

Numerical simulation of loads and impacts, stress-strain state, strength and stability of unique structures, buildings and facilities. Experience of StaDyO research & engineering centre

The paper contains analytical overview of the most important unique/critical objects and the computational analysis problems of the mechanical safety, carried out by the team of Research & Development Centre StaDyO (StaDyO R&D Centre) researchers for the last two years (2016-2018). Corresponding complex coupled problems of continuum mechanics were solved with the use of contemporary methods and models of numerical modeling (nonlinear models, coupled problems, substructures, submodeling, etc.), implemented in verified software complexes. Some of these results are briefly considered and analyzed. Conclusions about the main directions of further research and development are presented as well. © Published under licence by IOP Publishing Ltd