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. The metal stress-strain state simulation needs high precision computations. The use of any simplifying assumptions, such as the plane section hypothesis, the deformable material relative compressibility, uniform temperature distribution over the cross and longitudinal sections of the strip, etc. reduces the computation accuracy of strain and stress at the nodes. Standard programs often use such assumptions. It is acceptable for solving the routine problems. For the manufacture of critical elements such assumptions can lead to undesirable serious consequences. Modeling of the metal forming processes by using the finite element method gives a more accurate solution of the problem. However, the solutions require to solve a linear equations system of high dimensionality. The coefficient matrix is sparse, namely it consists of mainly zero elements, randomly scattered. This leads to considerable computation time for solution methods. In general, the number of arithmetic operations is proportional to the cube of the system's order. In this paper, we propose to increase the computational efficiency analysis through the use of the high-sparse matrix properties. In this case computer time will be proportional to the system order to the 1.2 power. The proposed solution SLAE comprises sparse matrix methods, which include techniques for optimal ordering of matrix rows and columns by using the criterion of the rows in order to increase the first non-zero elements number. This paper shows the application of the computation method for the process of the Belleville spring upset. Belleville springs can be classified as critical elements. One of its possible applications is the rail joint. Unlike conventional parts the elastic elements are characterized by the presence of large deformation under loads. The main factor that determines the service properties of the elastic element is the amount of strain energy that it can be accumulated. Accumulation and dispersing of the Belleville springs strain energy is directly depends to the relation of the meridian cross-section size and the spring working area. The establishment of this dependence is necessary for its rational design.

APPLICATION THE SPARSE MATRIX METHOD TO CALCULATE THE METAL ELASTIC STRESS-STRAIN STATE, USING THE FINITE ELEMENT METHOD