Papers by Keyword: Approximation

Abstract: In this scientific work, mathematical modeling of tetrahedron elements in the finite element method is presented, which includes the determination of geometric shape, shape functions, and material properties. Unknown fields such as displacement vectors, strain, and stress tensors are considered. The methodology of applying the principle of virtual work and equilibrium equations is described, allowing the derivation of a system of differential equations to describe the behavior of the tetrahedral element. Integration over the volume and consideration of boundary conditions help reduce the equations to a system of linear algebraic equations for numerical solution using the finite element method. It was found that modeling tetrahedral elements with a specific given radius (for example, R=0.3 mm) involves stages such as geometry determination, element generation, shape function formation, stiffness matrix computation, and solving a system of linear equations. The radius R of tetrahedral elements is taken into account at all stages, ensuring accuracy and reliability in tetrahedra modeling. The research also focuses on the fact that the occurrence of minor errors in iterative processes may result from several factors, including iteration step, the number of iterations, stopping criteria, linear or nonlinear material behavior, solution method selection, the presence of geometric inhomogeneities, and element size.

Abstract: The technique and results of experimental studies of creep deformations of compressed elements made of foam concrete at constant compressive stresses in the 0.15-0.75 range of R_b are presented. The nature of the relationship between stresses and the corresponding deformations, the degree of reversibility of creep deformations during unloading of samples and the tendency of concrete to aging have been established. From the standpoint of the hereditary theory of aging, analytical expressions have been selected to approximate the curves of specific creep deformations depending on the average density of foam concrete and the magnitude of compression stresses. The largest deviations of the specific creep deformations of foam concrete between theoretical and experimental values are 11.4%, and the standard deviations for the entire observation period are 2.0%

Abstract: The article deals with the development of approach for providing of structural strength of complicated thin-walled machine-building structures, which operate in the conditions of geometric and physical nonlinearities using design solution validation. The developed approach is based on the use of mathematical model for stress-strain state taking into account geometric and physical nonlinearities and methods of approximation for constructing functions describing the evaluated characteristics of the object under study. The various factors behind the search for design solutions (including characteristics of strength, rigidity, technological and economic factors), are being added into this function. The developed algorithm for rational parameters search, which takes into account the peculiarities of the response surface shape observed in solving applied problems, is applied to them. In this case, the solution is sought over the whole range of parameter changes. Thus, in the search process, global trends of changes in design decisions are taken into account, and not local ones, as in other approaches. This allows obtain a rational solution that is stable to changes in parameters, which are possible in course of design work and production conditions. Investigations are illustrated on the freight rail-car, tractor cabin frame, carrier personnel hull.

Abstract: Composite material is considered as a complex system with corresponding system attributes. The systematization of studies on the structure formation of composites is carried out to ensure the fundamentalization of building materials based on the use of analytical methods. The experience of using the linearization of kinetic processes in polydisperse systems is given. The most important cases are considered. Examples of parametric identification of a table-specified and nonlinear kinetic processes are given. The results were used in the development of special purpose composite materials.

Abstract: The prospects and novelty of using the expression of Lame's superellipse for approximating the curvature of shells in superplastic forming (SPF) and for predicting the geometry of a product are shown. Different versions of the SPF facilitate the realization of different radii of curvature of the shell contours, which differ significantly from the radius of the spherical segment. The regularities of the change in the radius of conjugation of the bottom and the wall of the spherical shell for various SPF variants are established.

Abstract: The rheological properties of polymer composite materials for special purposes in molecular, structural and complex plasticization are investigated. The possibility of approximating the rheological properties of epoxy composites to protect against radiation by a multiplicative polynomial-exponential function is shown (approximation of the functions of two arguments in the form of a product of two one-dimensional functions). Analytical dependences of the viscosity of epoxy binder on temperature and percentage of additive are given. The results of optimization (optimal concentration of plasticizer) are indicated.

Abstract: The free-form surface closed to a sphere of brittle material has been used widely, but it is difficult for machining and the efficiency of processing is insufficient. In order to get a product, several processes are needed, such as rough machining, semi-finishing and finishing. Axisymmetric curved surface can take place of the free-form surface in roughing or semi-finishing for wiping off the mass allowance efficiently. Therefore, a spherical approximation algorithm of free-form surface closed to sphere is presented in which free-form surface optical lens will be replaced by a spherical surface in semi-finishing and get the approximate sphere of the free-form surface. It can be certified in the test that this method is simple and reliable. The efficiency and precision in machining is excellent and the distribution of allowance for finishing is uniform in the whole surface, which has great practical significance in machining of optical free-form surface of brittle materials.

Abstract: The paper proves the application of a compensation testing method for geodynamic monitoring when using multi-pole electrical systems. The transfer functions of a geoelectric section are presented as a system of equations, whose coefficients are determined at the initial setup of the measuring system. The block diagram of the compensation method application for geodynamic monitoring based on a multi-pole electrical system is given. Approximation in terms of continuous piecewise-linear functions will be used to distinguish the geodynamic offset vector of the geoelectric section. A system of equations for defining the geodynamic offset vector through the approximation vector by continuous piecewise-linear functions on a recorded geoelectric signal error is considered.

Abstract: The paper presents compare methods of approximation results of studies using regression analysis and neural networks. As a research facility used theoretical values of surface roughness based on theoretical values of surface roughness calculated as kinematics-geometric projection of the cutting edge on finish surface. Pointed to the limitations of the presented methods of research results approximation.

Abstract: In the paper we propose an approximation model of the measured point cloud for machined cylindrical surfaces. The developed model is different from the traditional view because it relies on the contact of mating surfaces. The model allows to determine the parameters of cylindrical surfaces such as the coordinates of the center and the radius. To evaluate the geometrical parameters of the model the objective function is formulated, which characterizes the nature of the interface and a number of limitations. The approximation problem is solved by use of nonlinear optimization methods. The model takes into account the surfaces contact, which influences in deformation of its irregularities. The irregularities it is form deviations and surface roughness. The application of the model on the example of the shaft coupling with the inner ring of the bearing. There is given an estimate of geometric parameters for interfacing compared to method of least squares, which is widely used for coordinate measurements. As a result of research it was obtained that the proposed method can predict more accurately the parameters, which describe the location of the cylindrical surfaces made during assembly.