MOMENTARY FINITE ELEMENT FOR SOLVING 3D DYNAMIC ELASTICITY AND PLASTICITY PROBLEMS
D. T. Chekmarev, Abu Dawwas Yasser
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.3. С. 80-90.
A description of a new 8-node finite element for solving 3D dynamic elasticity and plasticity problems is given. This 8-node finite element in the form of a hexahedron has the following features: 1) stresses and their moments (three bending and one torsional moments) are constant within the element; 2) it has one integration point; 3) the element has four parameters, by setting them one can control the numerical solution convergence. The finite element construction method is based on a combination of the two ideas: the rare mesh FEM scheme with a finite element in the form of a simplex inscribed in an $n$-dimensional cube is used and a mesh problem of high dimensionality is projected onto a lower dimension mesh. The implementation of the numerical solution technique to solve 3D nonstationary elasticity and plasticity problems based on a given finite element is described. The paper presents solutions for a number of test elasticity and plasticity problems and compares them with those based on the other numerical schemes. Keywords: the finite element method, the hourglass instability, a 3D problem, a nonstationary elasticity problem
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English
