Abstract
The work is devoted to obtaining the stiffness matrix of a high-precision, flat finite element with 6 degrees of freedom in the node, for solving plane elasticity problems by the finite element method.
 The scientific literature describes higher order elements. However, the theoretical results of these studies are quite far from their practical application. This paper gives a very detailed derivation of the stiffness matrix of a high-precision finite element. Similarly, a stiffness matrix of a tetrahedral finite element with 12-degree-of-freedom node can be obtained. To test the obtained stiffness matrix, a program based on the FEM was written, with the help of which the cantilever beam is calculated. The error in calculating displacements is only 0.22%.
 Conclusion: the stiffness matrix presented in the paper can be used with great success in numerical methods for calculating the stress-strain state.
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