2. Reference solution#
2.1. Calculation method used for the reference solution#
The results considered to be reference were obtained by SAMCEF using 60 increments for each loading step. The characteristics of the various resolution methods are as follows:
A |
Using the elastic matrix. |
B |
Using the tangent matrix; this is only reevaluated at the first iteration of each increment (REAC_INCR = 1 and REAC_ITER = 0). It’s the modified Newton method. |
C |
Using the tangent matrix; this is reevaluated at each iteration of each increment (REAC_INCR = 1 and REAC_ITER = 1). It’s the classical Newton method. |
2.2. Benchmark results#
Results achieved with 60 increments for each loading step |
||||||
Element 1 |
Element 2 |
Element 3 |
||||
Force |
\({\sigma }^{\mathrm{xx}}\) |
\({\sigma }^{\mathrm{yy}}\) |
\({\sigma }^{\mathrm{xx}}\) |
\({\sigma }^{\mathrm{yy}}\) |
\({\sigma }^{\mathrm{xx}}\) |
\({\sigma }^{\mathrm{yy}}\) |
3.00 |
1.500000D+00 |
6.938894D—18 |
9.000000D—01 |
—1.040834D—17 |
6.000000D—01 |
—6.938894D—18 |
6.00 |
3.000000D+00 |
4.861944D—13 |
1.800000D+00 |
—2.081668D—17 |
1.200000D+00 |
—3.469447D—18 |
9.00 |
3.147155D+00 |
3.199571D—01 |
3.511707D+00 |
—1.900098D—01 |
2.341138D+00 |
—1.279828D—01 |
12.95 |
3.252919D+00 |
5.950074D—01 |
5.814267D+00 |
—3.523377D—01 |
3.878832D+00 |
—2.380030D—01 |
15.00 |
3.213822D+00 |
4.873069D—01 |
6.017834D+00 |
3.174572D—02 |
5.768340D+00 |
—5.231355D—01 |
16.93 |
3.2092970D+00 |
4.753345D—01 |
6.149462D+00 |
3.048490D—01 |
7.571241D+00 |
—7.863557D—01 |
2.3. Uncertainty about the solution#
Uncertainty less than \(\text{1 \%}\).
2.4. Bibliographical references#
Fundamental tests for two and three dimensional, small strain, elastoplastic finite element analysis, 1987, NAFEMS