Oleg A. Negrozov

Local High-Accuracy Plate Analysis Using Wavelet-Based Multilevel Discrete-Continual Finite Element Method

The distinctive paper is devoted to application of wavelet-based discrete-continual finite element method (WDCFEM), to analysis of plates with piecewise constant physical and geometrical parameters in so-called “basic” direction. Initial continual and discrete-continual formulations of the problem are presented. Due to special algorithms of averaging using wavelet basis within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem for system of ordinary differential equations is given.

Application of discrete-continual finite element method for global and local analysis of multilevel systems

This paper is devoted to discrete-continual finite element method (DCFEM) of analysis of structures with regular (constant or piecewise constant) physical and geometrical parameters in some coordinate direction (so-called “basic” direction). Effective qualitative multilevel analysis of local and global stress-strain state of such structures is normally required in various technical problems. It is commonly known that defects and failures are mostly local in nature. However total load-bearing capacity of the structure, associated with the condition of limit equilibrium, is determined by its global behavior. Therefore multilevel approach within DCFEM is peculiarly relevant and apparently preferable in all aspects for qualitative and quantitative analysis of calculation data. Wavelet analysis (wavelet-based DCFEM) provides effective and popular tool for such researches.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 1: Continual and Discrete-Continual Formulations of the Problems

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Two-dimensional and three-dimensional problems of analysis of structures with piecewise constant physical and geometrical parameters along so-called “basic” direction are under consideration. High-accuracy solution of the corresponding problems at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known local domains. Wavelet analysis is a powerful and effective tool for corresponding researches. Initial continual and discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are presented.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 2: Reduced Formulations of the Problems in Haar Basis

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are transformed to corresponding localized formulations by using the discrete Haar wavelet basis and finally, with the use of averaging and reduction algorithms, the localized and reduced governing equations are obtained. Special algorithms of localization with respect to each degree of freedom are presented.

Combined application of finite element method and discrete-continual finite element method

This paper is devoted to the so-called semianalytical structural analysis based on combined application of finite element method (FEM) and discrete-continual finite element method (DCFEM). Boundary problems of three-dimensional theory of elasticity are under consideration. In accordance with the method of extended domain, the given domain is embordered by extended one. The field of application of DCFEM comprises structures with regular (constant or piecewise constant) physical and geometrical parameters in some dimension (“basic” dimension). DCFEM implies finite element mesh approximation for non-basic dimension of extended domain while in the basic dimension problem remains continual. Corresponding discrete and discrete-continual approximation models for subdomains and coupled multilevel approximation model for extended domain are under consideration. The paper presents brief review of software and verification samples.

ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF TWO-DIMENSIONAL STRUCTURAL ANALYSIS WITH THE USE OF COMBINED APPLICATION OF FINITE ELEMENT METHOD AND DISCRETE-CONTINUAL FINITE ELEMENT METHOD PART 2: SPECIAL ASPECTS OF FINITE ELEMENT APPROXIMATIO

As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM), and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM). In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging)) are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic) variants are available)) are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.

Semianalytical solution of multipoint boundary problems of structural analysis with the use of combined application of finite element method and discrete-continual finite element method

Development, research and verification of correct mathematical models and methods of structural mechanics are the most important aspects of ensuring safety of buildings and complexes. The distinctive paper is devoted to semianalytical solution of multipoint boundary problems of structural analysis with the use of combined application of finite element method and discrete-continual finite element method. Structures containing parts (subdomains) with regular (in particular, constant or piecewise constant) physical and geometrical parameters in some dimension are under consideration. Operational formulations of two-dimensional and three-dimensional problems of structural mechanics with the use of so-called method of extended domain, corresponding numerical implementations (including construction of discrete (finite element) and discrete-continual approximation models for subdomains) and numerical examples are presented.

О ПРОГРАММНО-АЛГОРИТМИЧЕСКОЙ РЕАЛИЗАЦИИ И АПРОБАЦИИ ПОДХОДА К РАСЧЕТУ СТРОИТЕЛЬНЫХ КОНСТРУКЦИЙ НА ОСНОВЕ СОВМЕСТНОГО ПРИМЕНЕНИЯ МЕТОДА КОНЕЧНЫХ ЭЛЕМЕНТОВ И ДИСКРЕТНО-КОНТИНУАЛЬНОГО МЕТОДА КОНЕЧНЫХ ЭЛЕМЕНТОВ

В настоящей статье рассматриваются некоторые особенности программной реализации дляапробации (решения простейших тестовых задач) подхода к статическому расчету строительных кон-струкций, основанному на совместном применении метода конечных элементов (МКЭ) и дискретно-континуального метода конечных элементов (ДКМКЭ), выполняются сопоставления результатов расчетас результатами, найденными с использованием верифицированного программного комплекса промыш-ленного типа ANSYS Mechanical