CC BY
10
Section 9. Technical sciences
Razmuhamedov D. Dj., Teacher of entrant's school, SEI"ILSE CIRTAUTAS"
Polatov A. M.,
Professor of the Algorithms and Software Technologies Department of the National University of Uzbekistan Doctor of Physical and Mathematical Sciences E-mail: shohista11@mail.ru
DEVELOPMENT OF THE TECHNIQUE OF OPTIMIZATION OF COMPOSITIONS OF HEAVY CONCRETE USING THE METHODS OF FINAL ELEMENTS
Abstract. This article is devoted to the study of issues related to the scientific substantiation of the techniques and methods of optimization, the creation of a computer-aided design system for heavy concrete compositions using numerical simulation. In a comparative aspect, numerical algorithms have been developed for solving problems of physically nonlinear deformation of structures made of structural materials, which make it possible to efficiently use the capabilities of computer technology.
Keywords: composite materials, methods of mathematical statistics, mathematical modeling, structural simulation modeling.
Relevance. The modern level of development The currently used methods of mathematical sta-
of construction technologies necessitates the pre- tistics as the main tool of theoretical research, based
sentation of the physic-mechanical properties of on the results of experiments, often do not allow
composite materials in the form of mathematical establishing the physical nature and patterns of the
dependencies on their internal structure and exter- relationship of structure with properties. Analytical
nal factors acting in given conditions of operation of methods for describing the dependence of the prop-
structures. The mathematical description allows to erties of cement compositions on their structure in
identify the factors that ensure the formation of an the form of deterministic dependencies are practi-
effective structure of materials, as well as to evaluate cally inapplicable to systems that have a multilevel
the durability and reliability of building structures probabilistic nature [1-2].
without long and expensive field experiments. The A description of such complex-structured sys-
greatest complexity in mathematical modeling is rep- tems associated with the representation of the dis-
resented by cement composite materials: the struc- tribution in volume, mutual orientation and conju-
ture of mortars and concretes, which determine their gation of individual components of the structure, as
properties, is multi-layered and polyfunctional and well as their collaboration at various levels, is pos-
requires a characteristic approach. sible through the use of numerical methods, which
constitutes the technology of structural-imitational modeling of cement compositions [2-3].
The advantage of structural simulation modeling is the reproduction of explicitly taken into account, using mathematical physics and elasticity theory equations, parameters determined during preliminary structural studies that contribute to a more realistic reflection of the structure of the material and the possibility of obtaining system responses to various external and internal effects. This method allows, first of all, to directly linking the structure and properties of the composite material, which is one of the fundamental tasks of building materials science.
The description of the joint work of phases of heterogeneous properties in the stochastic structure of compositions at different structural levels is possible, as noted, using numerical methods [3]. The most developed and approved numerical method for solving differential equations describing the behavior of continuous media is the finite element method (FEM). Efficient implementation of FEM algorithms for describing the interaction of individual structural elements of cement systems has become due to the powerful development of computer technology.
Objective: to study in detail the issues related to the scientific substantiation of the techniques and methods of optimization, the creation of a computer-aided design system for heavy concrete compositions using numerical modeling.
Materials and methods: as a material for experimental studies was used a composite material used for the manufacture of heavy concrete brands offered in order to develop and improve methods for optimizing the composition ofheavy concrete using the finite element method.
In the present paper, the methods of mathematical physics, set theory, computational mathematics, algorithmization, modular and structured programming technologies, as well as computational experiments are applied.
The results of the study.
Development of an algorithm for calculating the composition of concrete. One of the main methods of researching the objects of this work is modeling, in which real objects are replaced by analogues obtained from the original by idealization, abstraction. When modeling the composition of heavy concretes, the priority requirement is the fact that in the proposed model the object should be formed so that it is possible to obtain new information about the original.
To assess the effectiveness of the development of the algorithm for calculating the composition of concrete, we carried out laboratory studies related to obtaining experimental data based on the definition of various types of properties inherent in materials. In these studies, physical and mechanical properties were studied. Laboratory studies were carried out in relation to cement concretes of various compositions. The results obtained served as the basis for creating a source data layout that serves to refine and test the numerical simulation system.
Mechanical methods. The mechanical properties of building materials are characterized, first of all, by compressive strength and modulus of elasticity.
The content of the components of concrete and the preparation of the compositions was carried out manually. Before preparing the samples, the aggregates were washed and dried to constant weight. Fillers only dried. Weighing binder, fillers, additives and fillers were carried out on a scale with an accuracy of up to 0.5 g. Samples were made in metal molds, which were lubricated with technical oil before the mixture was laid. After lying, the samples were hardened under normal conditions for 1 day, and then in a steaming chamber according to the mode of 1.5 + 6.0 + 1.5 h.
Optimization of the composition of concrete is carried out taking into account their application, conditions of construction and operation, the type and purpose of the structural elements: floor slabs and coatings, columns, beams, beams-walls, trusses
and others; external and internal, bearing and protecting walls, panels, and internal partitions.
Depending on the purpose, the structural elements have requirements that determine the properties of deformability and strength, heat - sound insulation and water and vapor impermeability, bio-stability, frost resistance, etc. Among these properties, the most significant, determining the reliability and durability of concrete, are mechanical properties (strength and deformability). When modifying materials (thermal conductivity, sound permeability, etc.). As a rule, at this stage, the selection of binders, fillers, additives and granular aggregates is carried out. When selecting the composition, based on the physic-technical properties, the basic structure of the modified material is formed on the basis of the corresponding experimental work and the choice of their optimal content. In the future, work is carried out to determine the mechanical parameters of the material and adjust its composition.
The method developed in this paper is intended to predict the mechanical parameters of optimized materials and adjust their composition by adjusting the volume content of the used components of the structure to ensure the required strength and deformability. The technique was developed in relation to the use of the finite element method (plane stress state).
When using the technique, one should pay attention to the identity of the nature of the stress-deformable state in the numerical simulation and experimental work carried out to determine the mechanical parameters (strength and deformation modulus, coefficient of lateral expansion of materials under compression). To develop a mathematical description of the process of the development of cracks in concrete, we have created an initial material model.
The analysis and generalization of the existing volume of experimental data presented in the works of researchers in the field of concrete scientists makes it possible to formulate the above model [4-7]. It is important to note that the mod-
el is based on a number of simplifying hypotheses and boils down to the following, successively performed operations:
1. considers a solid body in the form of a matrix with inclusions (aggregate grains) of various sizes, with defects of the first (pore) and second (crack) kind at different levels of the material structure;
2. defects of the first kind have a different shape, but the same characteristic size and are considered at the same micro level;
3. defects of the second kind can have various outlines and sizes; they are subject to review at the micro and macro level;
4. the matrix material between defects and inclusions is uniform;
5. the matrix material between defects and inclusions is isotropic;
6. the size of defects and inclusions is small in comparison with the size of the body;
7. deformations are small;
8. the triaxial stress state can be replaced by a biaxial - flat stress state;
9. in case of a short-term action of the load, it is considered possible to neglect the phenomenon of creep and to assume that the material is basically its mass (except for the zone immediately adjacent to cracks) works elastically; at the same time, the effect of possible physical nonlinearity of the material is taken into account;
10. with long-term load action, it is considered acceptable to transfer from solutions of an elastic instantaneous problem by using an operator;
It also takes into account the influence of the physical nonlinearity of the material for both elastic and long-term deformations.
Concrete macrostructure. The structure of concrete, visible to the eye or with a slight increase. In the macrostructure of concrete there are structural elements: coarse aggregate, sand, cement stone, air pores. Sometimes the macrostructure of concrete is conventionally made of two components: coarse aggregate and cement-sand mortar.
The matrix is a component of a two-component system of concrete, representing the mortar part. Physical parameters of the matrix:
- Elastic modulus E ;
M
Poisson's ratio u ;
M
Considering the above information, we have developed software algorithms that include the formation of a finite element model (flat stress state). In the course of calculations, it was conditionally determined in the work that the properties of materials can be estimated from the results of testing samples as properties of a continuum. This allowed the use of appropriate theoretical models. The developed ARPEK system is based on the fragmentation of modeling objects, the principles of its formation, and is based on the finite element method. Fragmentation of the object, performed in the finite element method, allowed the modeling to assign individual properties to individual fragments and, thus, realize specific structural elements such as matrices, inclusions (for example, crushed stone, sand, pore fractions, etc.). The change in the volumetric content of structural components and the replacement of the input of structural elements made it possible to significantly speed up the process of predicting properties. According to the simulation results, we obtained effective parameters equivalent to those experienced.
It would like to be noted that the model of modeling can be considered as a system of structure-forming objects with its own inherent properties at a given qualitative stage of deformation or destruction. The properties of such an object are determined by its geometric shape, position, and functions that characterize the laws of its deformation or destruction. In the formulation of practical experiments, the principle of describing such an object is defined by us as the principle of encapsulation. The establishment of a function in a numerical simulation was performed using continuum theories. The fragmentation of an object by finite elements was defined as a special kind of medium in which a change in
mechanical properties takes place, when moving from one fragment to another. The selected methodological approach allowed the use of the principle of polymorphism in the development of numerical modeling systems.
It should be emphasized that for the practical application of the principle of polymorphism, first of all, we determined the type of the base object (fragment) by selecting the type of the final element and the interpolation function. In turn, using the principle of polymorphism, in the work the basic elements of the first order, having their own functions, are defined. For example, the basic functions of fragments of inclusions, their shells, matrices, pores. On the other hand, the use of the principle of inheritance allowed us to determine the properties of objects of the entire structure.
In the research, special attention is paid to the adjustment of the developed program and making amendments, as well as the corresponding changes. The process of building a finite element model is automated and implemented in the software module APCEM. The user is connected with the software package by launching the program and implementing a sequence of modules from the library of discretization modules that are elementary in the configuration of subregions. The library also includes modules for "stitching" and "separating" subregions, modules for visualizing and minimizing the difference in node numbers in the finite element model. Interactive communication of the user with the software package allows the sampling process to be implemented in accordance with the algorithm for constructing a finite-element partitioning ofthe source domain with a complex configuration occupied by the object under study. The results of the calculations are recorded on the MD.Further, based on the volume ratio of the fiber and the matrix in the composite material, as well as their mechanical characteristics, effective mechanical parameters are calculated, which together with the data on the finite element model serve as input data for the LIREK software module, where mathematical
modeling of linear deformation of composite materials is performed. Here, the coefficients of the stiffness matrix of finite elements and the vector of external influences are calculated. The process of forming the resolving system of linear algebraic equations taking into account the boundary conditions and its solution is carried out. The obtained solutions of the elastic problem are recorded on the MD and are the initial information for the nonlinear calculation of composite materials, the calculation of which is performed in
the NERPEC software module. Nonlinear calculation implements an iterative process for solving an elasto-plastic problem based on the theory of small elasto-plastic deformations for a transversal homogeneous medium. The obtained values of the nodal displacements are recorded on the MD, and serve as input data for the TASVIR software module, in which the parameters of the stress-strain state are calculated, the finite element model of the object under consideration and the calculation results are visualized.
Figure 1. The main modules of the ARPEK system and their interconnection
The developed ARPEK software package is built according to a modular principle, where each module implements a certain stage of calculation. Various service and auxiliary functions are implemented by a separate service module. Some modules are executed as links of a sequential chain of problem solution, others are connected according to the "master-slave" scheme, that is, some modules use other modules. A list of the main modules developed for the implementation of the above algorithm is given in (fig. 1), where the directions of the arrows indicate the logical interdependence of the modules.
The relationship between the modules is carried out through the files that make up the system data set:
1. *.dsk - files for storing intermediate data obtained at the stage of body sampling;
2. *.kmg - files for storing the coefficients of the global system of equations.
3. *.kvn- files to store load vector coefficients.
4. *.kff - files for storing form function coefficients.
5. *.kti - files for storing the coefficients of Gaussian integration points in the local coordinate system.
6. *.kzp - files for storing values of nodal displacements.
7. *.khs - files for storing the values of the stressstrain state.
The operation of the complex is controlled through the "ARPEK" program, which in the form of a menu provides an opportunity to select the main operating modes of the system (Fig. 2).
Giving a description of the modes of operation of the developed system, in particular:
I. Mode "DISCRET". The mode is intended for sampling the specified area. This mode is implemented by the procedures from the DISKRET module, which includes the following submodules:
1. "SEKTOR" - the formation of a discrete model of the surface of the cavity;
2. "NUMER" - the numbering of the nodal points of a discrete model of the body.
Figure 2. Menu of operating modes of the ARPEK system
II. Mode "CPU". This mode is used to form the coefficients of the system of solving equations of the finite element method, based on a discrete body model. It is implemented by the procedures of the SRU module, which uses the following sets of submodules:
1. "MATR_J" - the formation of the coefficients of the stiffness matrix of the final element and the unit vector of loads;
2. "GRAN_USL" - transformation of the system of equations with regard to specified displacements;
3. "UCHET_PR" - consideration of the directions of specified displacements along the coordinate
axes;
4. "YAKOBIAN" - definition of the components of the Jacobi matrix;
5. "DIFEREN" - calculation of derivatives of a function of a form from given displacements;
6. "PODSTAN" - determination of the interpolation polynomial value.
III. Mode "PR_MATR". The algorithm of the modified square root method for solving systems of algebraic equations is implemented (decomposition of the original matrix into the product of two triangular matrices, and the sequential implementation of the direct and reverse moves of this method). At this stage, the coefficients of the matrix of the system of resolving equations are converted to a triangular form.
IV. Mode "RESH_SRU". Performing the reverse of the square root method.
V. Mode "VICH_NDS." The calculation of the stress-strain state.
VI. Mode "PLASTIC". Execution of the iterative process of the method of elastic solutions A. A. Ily-ushin. This mode is implemented by the procedures from the "PLAST" module, which includes the following sub-modules:
Figure 3. The overall architecture of the complex ARPEK
1. "MATR_P" - the formation of the coefficients of the stiffness matrix of the final element in the zone of plastic deformations;
2. "GRARAN_USP" - transformation of the system of equations with regard to specified displacements that are in the zone of plastic deformations;
3. "INTEN_DEF" - calculation of the intensity of deformations;
4. "INTEN_NAPR" - calculation of stress intensity.
VII. Mode "RESULT". Reading information from a data set for the formation of tables, graphs and plots.
VII. Exit mode. The mode ofexit from the system.
The results of the solution are recorded in the same output VAT file. As shown in fig. 3, then (optionally) a visualization module for graphical interpretation of calculation results can be launched.
The results in the table are presented in the form of numbers in the exponential format and are in the
output file of the complex. The line numbering in this file is identical to the numbering of nodes in the finite element mesh.
Justifying the trends and prospects for the development of building technologies related to the development of techniques for optimizing the compositions of heavy concrete using finite element methods, it is advisable to draw the following conclusions:
1. An optimization technique has been developed that represents a plan for conducting research on the modification ofvarious types of concrete taking into account all the necessary conditions, such as developing an initial experimental plan, applying computer simulations, analyzing the obtained results and dependencies, establishing the optimal concrete composition.
2. The compressive strength and the modulus of deformation are considered as optimized parameters taken as the basis for the modification of concrete.
3. For the purposes of the optimization methodology, the software package ARPEK was developed. The system of numerical simulation is based on the finite element method. The purpose of the system is to accelerate the work on the optimization method.
4. The main algorithms for the formation of the system are described. They include the formation of a finite element model and its fragmentation, the formation of the material composition of the objects of modeling, the stages of the path of destruction and deformation. The software database of the ARPEK system is considered, which reveals the structure of the system and its individual components (source text, modules).
5. The optimization method is designed to predict the mechanical properties of optimized concrete compositions for various types ofbuilding structures, as well as to adjust and control the volume content of the used components of the concrete structure to ensure the required strength and deformability.
References:
1. Kalashnikov V. I. The basic principles of the creation of high-strength and very high-strength concrete // Popular concrete science. 2008.- No. 3.- P. 102-107.
2. Berg O. Ya. The physical basis of the strength of concrete and reinforced concrete // O. Ya. Bazhenov.-M.: Gosstroyizdat, 1962.- 96 p.
3. Kondrashenko V. I. Optimization of the composition and technological parameters of the production of bar-type products by means of computer materials science: Author's abstract. dis.kand.tehn.nauk.- M., 2005.- 48 p.
4. Garboczi E. J. The Past, Present, and E. J. Garboczi, D. P. Bentz G. J. Frohnsdorff // Materials Science of Concrete Workshop; Proceedings: Center for Advanced -Cement-Based Materials (ACBM), Lake Shelbyville, IL. 2000.- P. 1-10.
5. Polatov A. M., Ikramov A. M. The structure of the RFP for the study of the stress state of bodies of complex configuration // Sat. abstracts ofthe report. "Modern problems of algorithms". Tashkent. 1991.- 116 p.
6. Polatov A. M., Kurmanbaev B., Kadyrova N. R. Automation of the elastic calculation of three-dimensional bodies with cavities and inclusions. // Abstracts of the report. scientific conf. "Mechanics and its applications." - Tashkent. 1993.- 114 p.
7. Polatov A. M., Fedorov A. Yu. An algorithm for minimizing the width of a tape of a system of equations // Materials of the All-Russian scientific-practical conference with international participation "Modern information technologies in science, education and practice." - Orenburg. 2007.- P. 103-105.
