PSI - Issue 6

V.A. Meleshko et al. / Procedia Structural Integrity 6 (2017) 140–145 Meleshko V. А ., Rutman Y.L. / Structural Integrity Procedia 00 (2017) 000–000

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-elasticity module E =2.1  10 11 Pa; -tangent elasticity module E =2.1  10 10 Pa; -Poisson’s ratio  = 0.3; -yield point  T = 240 MPa; -rod length l = 1 m; -rectangular cross-section a = 0.2 m; -cross-section height h = 0.1 m; -force F = 1.5  10 5 N, for the restrained cantilever beam; force F = 1.5  10 6 N, for single statically indeterminable beam at both supports.

a

b

Fig. 4. (a) cantilever rod; (b) static indeterminable beam.

As the developed mathematical scheme takes into account stresses distribution over the section area, then a solid model with solid elements was used as a simulation-reference model in ANSYS solid 186 (20,000 elements). When calculating by the generalized flexibility method, the rods were divided into 10 integration sections. 150 steps were set in the nonlinear analysis. Calculation results are given in Fig. 5.

a

b Fig. 5. Elastoplastic calculation of statically indefinable beam in Ansys:

(a) cantilever rod; (b) static indeterminable beam.

The comparison of the obtained results with ANSYS PC has shown well coincidence of both stresses, and cross section displacements (Tab. 1, 2). The calculation of the solid model by means of finite elements took about one hour of computer time. And the framed structure calculation took 1.5 min. However, in this case, change of stresses over the cross-section area is not taken into account, which can lead to incorrect results in transferring from the elastic to the plastic zone of the diagram  -  . When calculating by the generalized flexibility method, it took less than 1 second. This is due to that the number of equations in the system is equal to the number of static indeterminacy, i.e less than those specified in the finite element method. When increasing the number of integration sections, the solution tends to be accurate with no significant time consumption. Thus, the application of the generalized flexibility method for the elastoplastic analysis can significantly increase a calculation rate and accuracy.

Table 1. Cantilever rod