Patch test for cylindrical elements

This problem contains basic test cases for one or more Abaqus elements and features.

The following topics are discussed:

Elements tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/Standard

Elements tested

CCL12
CCL24
CCL24R

Problem description

Material:

Linear elastic, Young's modulus = 1.0 × 10⁶, Poisson's ratio = 0.25.

Loading

Displacement boundary conditions applied to all exterior nodes: $u_{r} = $ 10⁻³r, $u_{z} = $ 10⁻³ $(r + z)$ .

Nonuniform body force: To maintain a constant shear stress $σ_{r z} = $ 400 and preserve equilibrium, an equilibrating body force, BZNU, is defined in user subroutine DLOAD as BZNU $= - σ_{r z} / r =$ −400 $ / r$ , where r is the radius of the integration point.

Reference solution

The analytical results for each step are presented below.

Step : PERTURBATION

$σ_{r} = σ_{z} = σ_{θ} = $ 2000.
$σ_{r z} = $ 400.
$ϵ_{r} = ϵ_{z} = ϵ_{θ} = $ 10⁻³.
$γ_{r z} = $ 10⁻³.

Results and discussion

All elements yield exact solutions.

Input files

Abaqus/Standard input files

ecccgfp1.inp: CCL12 elements.
ecccgfp1.f: User subroutine DLOAD used in ecccgfp1.inp.
eccrgfp1.inp: CCL24 elements.
eccrgfp1.f: User subroutine DLOAD used in eccrgfp1.inp.
eccrgrp1.inp: CCL24R elements.
eccrgrp1.f: User subroutine DLOAD used in eccrgrp1.inp.