An axisymmetric nodal averaged finite element

Abstract

A nodal averaging technique which was earlier used for plane strain and three-dimensional problems is extended to include the axisymmetric one. Based on the virtual work principle, an expression for nodal force is found. In turn, a nodal force variation yields a stiffness matrix that proves to be non-symmetrical. But, cumbersome non-symmetrical terms can be rejected without the loss of Newton-Raphson iterations convergence. An approximate formula of volume for a ring of triangular profile is exploited in order to simplify program codes and also to accelerate calculations. The proposed finite element is intended primarily for quasistatic problems and large irreversible strain i.e. for metal forming analysis. As a test problem, deep rolling of a steel rod is studied.

Towards the Problem of Construction an SPD Stress-Strain Curve for Low-Plastic Materials

“…As a rule, in such problems a small "representative" part is cut out the entire workpiece and some "reasonable" boundary conditions are imposed at the cut surface [11] because calculation all the workpiece beggars the possibilities of modern computers. Nevertheless, an alternative methodology is proposed in [12,13]. If deep rolling working is carried out by means of a very thin roller of large radius then the material flowing is prohibited in the tangential direction and is enabled in the axial one.…”

“…It follows that the microhardness increment is proportional to ε at super-large strain. We cannot measure the real value of ε but according to numerical simulation [13], 8 . 0 ≈ ε per one pass in the near-surface layer.…”

Gradient Strengthening Control Procedure Based on Numerical Simulation of Combined Local Loading Of Deformation Zone

“…Previously, the works pertinent to the numerical mathematical simulation of CLL deformation following the method shown in Fig. 1 were performed and based on the analysis of the results of these works [15][16][17][18][19][20], a general algorithm of designing such processes for axisymmetric products, which allows realizing the gradient strengthening characterized by the predetermined characteristics, was proposed ( Fig. 2).…”

Numerical Mathematical Simulation of Penetration of Indenters of Different Shapes During Strengthening Machine Parts via Local Loading of Deformation Zone

“…4). The numerical simulation was performed using the application software package SHTAMP 2.0 [14][15][16][17][18].…”