2.1.4 Two-point bending of a pipe due to self weight: CAXA and SAXA elements

Product: ABAQUS/Standard

Problem description

The material is linear elastic with a Young's modulus of 207 GPa, a Poisson's ratio of 0.3, and a weight density of 0.15 MN/m³. on the plane; at point . A gravity force is considered to be acting in the positive x-direction.

CAXA mesh

In the analyses that test the CAXA elements, only the symmetric half of the structure is considered. The models using full-integration and reduced-integration second-order elements employ one element through the thickness and seven elements along the pipe, with two equal-sized elements along and five equal-sized elements along . The models using the lower-order fully integrated elements employ twice as many elements in both the radial and axial directions. The models using the lower-order reduced-integration elements employ four times as many elements in both the radial and axial directions.

SAXA mesh

In the analyses that test the SAXA elements, only the symmetric half of the structure is considered. Second-order element models use seven elements along the pipe, with two equal-sized elements along and five equal-sized elements along . First-order element models use 14 elements along the pipe, with four equal-sized elements along and 10 equal-sized elements along .

Reference solution

This problem provides a test on the body force type BX for the axisymmetric solid elements with nonlinear, asymmetric deformation. The reference solution is obtained from the analysis of an equivalent three-dimensional model using the 20-node brick element C3D20. The three-dimensional mesh employs one element in the radial direction, six elements in the circumferential direction, and seven elements along the pipe. The input file for the reference solution is eref3ksg.inp.