PSI - Issue 6

V.A. Meleshko / Procedia Structural Integrity 6 (2017) 115–121

118

Meleshko V.A./ StructuralIntegrity Procedia 00 (2017) 000–000

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2. Comparison of the received results with FEM in program complexes For check of the developed mathematical model programs were written to MathCad for a console rod and statically indefinable beam. Separate blocks of programs for indeterminable beam are provided to Appendix A. Within this article, comparison of results with a finite element method in ANSYS was made only for a console rod (Appendix B). In a task the following basic data were accepted:

- modulus of elasticity E =2,1 ⋅ 10 11 Pa; - tangent module of elasticity E pl =2,1 ⋅ 10 - коэффициент Пуассона ν = 0,3; - yield strength σ s = 240 MPa; - rod length l = 1 m; - width of rectangular section b = 0,2 m; - section height h = 0,1 m; - force F = 6 ⋅ 10 5 N, for the jammed console rod. 10 Pa;

As the developed mathematical model considers distribution of tension on cross-sectional area, in ANSYS as rated-reference, the solid-state model with the volume solid 186 elements (2500 elements) was used. When calculating by the generalized forces method the rod was broken into 10 sites of integration. In the nonlinear analysis 150 steps were set. Results of calculation are shown on Fig. 2.

a

b Fig. 2. Nonlinear computation of Cantilever rod in Ansys:

(a) displacements; (b) stress.

Comparison of the received results with ANSYS when you turn on the “Large deflection” shown in Tab. 1. Displacements and rotation angles were defined on the generalized formula of Mora. Taking into account the geometric nonlinearity the deviation was 11 %. Taking into account only the physical nonlinearity error was 0.25 %.

Table 1. Cantilever rod Parameter

δ , %

GFM 1662

FEA (SOLID 186)

σ , MPa ∆ , mm

1497

11 11

400

360

Nonlinear behavior in the calculation of the generalized method forces was taken into account through the projection of the curvilinear rod to the horizontal axis. It should be noted that the inclusion of large displacements in ANSYS activates different types of behavior: large rotations, large deformations and stiffening from the stress state. All of these models imply the change of stiffness during the deformation of the structure. For calculation in Ansys took about 1 hour. When calculating the generalized force method took less than 1 second. This is with the exception of the system of equations is based.