Elements tested
- S3
- S3R
- S4
- S4R
- S4R5
- S8R
- S8R5
- S9R5
- STRI3
- STRI65
ProductsAbaqus/Standard Elements tested
Problem descriptionElastic and elastic-plastic cases of a beam under pure bending are tested. Nonlinear multipoint constraints and section ovalization are also tested. Model:A quarter model is used because of symmetry. Material:Young's modulus = 1.93 × 105, Poisson's ratio = 0.26, plastic (isotropic hardening).
Boundary conditions:Symmetry on plane z = 0 ( ; symmetry on plane x = 0 ( ; symmetry on rotated plane: i) Shell nodes must remain in rotated plane (Nonlinear MPC). ii) The z-rotation of shell nodes in the rotated plane must be the same as the main node (Linear MPC). iii) The component of rotation about the local -axis must be zero (Nonlinear MPC). The main node is constrained to move on the x-axis only. Loading:Z-rotation applied to pipe end ( = 0.004). Reference solutionThis is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 3DNLG-8 from NAFEMS Publication R0024 “A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3D Beams and Shells (SUMMARY).” The published results of this problem were obtained with Abaqus. Thus, a comparison of Abaqus and NAFEMS results is not an independent verification of Abaqus. The NAFEMS study includes results from other sources for comparison that may provide a basis for verification of this problem. Results and discussionIn the following table, the end moments for the elastic and elastic-plastic cases are reported at three rotation values of the main node. All the meshes have the same nodal spacing.
Response predicted by AbaqusEssentially identical moment-rotation curves (at the main node) are obtained for all test cases. The response predicted using S8R5 elements is shown below. Input filesElasticity:
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