Algorithmization in Magneto-elasticity of Thin Plates and Shells of the Complex Configurations

The work is devoted to algorithmization with regard to solution of tasks classes in magneto-elasticity of thin plates and shells of complex form in plan, thus, adhering to the general theory of algorithmization offered by the academician V.K.Kabulov, formation, composition and structure of the basic (data, laws, principles, models, algorithms, applied programs) and auxiliary algorithmic (statement and operational) banks are described in brief.


Introduction
Now, one of modern methodologies of automation of scientific researches is the algorithmization methodology offered by the academician V.K.Kabulov [1][2][3]. The point of algorithmization methodology consists of formalization and working out of automating system in which process of research of various objects is divided into seven consecutive stages, representing a cybernetic chain with feedback: experience -laws -problems -mathematical modelsalgorithms -software -computing experiment.
As it is marked in works [1][2][3], at practical realization algorithmization stages are made out in the form of six basic and two auxiliary algorithmic banks (AB). The basic banks are bank of data (B1), laws (B2), features (B3), models (B4), algorithms (B5) and applied programs (B6), and auxiliary ones -bank of statement (B0) and operational bank (B7). And each bank consists of two parts: information and operational. The numerical or symbolical data in fixed languages which are brought in advance (the constant information) are stored in information part. Operational part of АB contains software packages processing information collections of this bank.
Recently, the algorithmization theory is applied in various areas of science and technology, such as: mechanical engineering, medical, biological and technical cybernetics, social and economic sphere and others.

Algorithmization in Magneto-elasticity of Thin Plates and Shells
Algorithmization with regard to the solution of problem classes in magneto-elasticity of thin bodies (plates and shells) of complex form in plan is resulted in the given work. We will briefly describe formation, composition and structure of the basic and auxiliary АB in magneto-elasticity of thin plates and shells on the basis of the general theory of algorithmization. Thus, are referred to certain obtained results in the given direction of researches [3][4][5][6][7].
Firstly, bank of data is described. Values from laws and also the factors characterizing movement of system, particularly from the elasticity and electrodynamics theory are stored in bank of data: Parameters (constants): 1) Е -modules of elasticity of Yung.
4) δ ij -Kronecker symbol, etc. Operators: The bank of laws in algorithmization represents basic axioms of the theory, i.e. formed on the basis of laws (variation principles, laws of conservation, relations of the theory of elasticity and electrodynamics laws) from which mathematical models magneto-elasticity thin plates and shells are deduced in consequence.
Here are fundamental laws concerning magneto-elasticity: The bank of statement provides problem statement of magneto-elasticity thin bodies (shells and plates) and consists of atomic words -making terminological basis of theory, based on which, statement and problem solving are carried out. It consists of the name of problem, boundary conditions and factors. The set of atomic words provides choice of the equations from bank of laws, conditions imposed on parameters from bank of features and on their basis, the conclusion of mathematical models and choice of algorithms of solving is carried out.
As example of such atomic words in magneto-elasticity can serve 1) problems: plate, shell, bend, state, vibration, stability, flat, spherical, cylindrical, linear, nonlinear, statics, dynamics and etc.

Algorithmization in Magneto-elasticity of Thin Plates and Shells of the Complex Configurations
In methodology of algorithmization, the conclusion of mathematical models is carried out by means of the computer. And classes of problems, in particular, magneto-elasticity are formed by means of principles space (certain restrictions). Set of problems principles is entered in the bank of principles. As principles of create of models of magneto-elasticity thin plates and shells are restrictions on movings, i.e. hypotheses of the theory of elasticity and magneto-elasticity can serve: Let's notice that the conclusion of mathematical models is carried out in operational bank.

Mathematical Model of Magneto-Elasticity of Thin Plate
At construction of mathematical models of magneto-elasticity of thin plates and shells are used systems of mathematical algebra, particularly, mathematical system Maple which has large opportunities for carrying out of analytical calculations can be used. We will give some equations of plates movement deduced on the basis of the above-mentioned principles in Maple system [6,7]: Here is 12 Computer Science and Information Technology 3 (3): 66-69, 2015   69 The corresponding initial and boundary conditions depending on the way of fastening of edges of plate (shell) are added to these equations.
Next, the mathematical models deduced from general laws on magneto-elasticity according to the bank of principles are analyzed by means of procedures of bank of models, i.e. methods of mathematical and functional analyses [1][2].
Then, the computing scheme is chosen from the bank of algorithms, resolving equations are constructed, numerical data from bank of data and program for calculation from bank of applied programs are selected. In particular, at solving problems of magneto-elasticity of thin plates and shells of complex form in the plan, joint application of variation methods of Bubnov-Galerkin and structural method of R-functions are used [8]. Thus, resolving equations have view of the system of ordinary differential equations -in case of dynamics, the system of linear algebraic equations -in case of statics or problem of own values and vectors -in case of consideration of stability problem of thin plates and shells in electromagnetic field.
The bank of applied programs consists of library of subprograms and library of modules. Programs consist of software of computer (ready predetermined procedures and functions), as well as software for solution of resolving equations, in particular, solution -systems of ordinary differential equations, systems of linear algebraic equations, problems of own values and vectors and others can be part of this [9]. Programs on results registration, i.e. their visualization by means of representation in form of tables, schedules, etc.

Conclusions
In conclusion, we will notice that the algorithmic system is created for realization of all blocks of algorithmization in magneto-elasticity of thin plates and shells of the complex form in the plan for computers. Some calculating results of electro-magnetic fields' affection of thin conducting plates by complex form are given in paper [10].