3DNLG-2: End shortening of a pear-shaped cylinder

Scope

Measure the first full-cylinder end-load collapse peak under uniform axial shortening of a pear-shaped cylinder.

Geometry

Quarter model: half cross-section consisting of tangent straight segments and unit-radius 135-degree and 45-degree arcs; half axial length 0.4 m, thickness 0.01 m. The outer half-profile spans y=0 to 2.70710678 m.

Material

Elastic E=10 MPa, nu=0.3; SI length and force convention.

Boundary conditions and loading

Reflection symmetry on x=0 and z=0; constrain transverse translations at z=0.4 m and prescribe uniform negative axial displacement there up to 0.0016 m.

Assumptions

Quasistatic large-rotation elasticity. No plasticity or added mesh perturbation.

AM-DT formulation

AM-DT S4 model with analytic tangent geometry rather than rounded input coordinates. Uniform end displacement is enforced directly, equivalently to the source's tied end DOFs. This driver uses displacement-controlled production equilibrium; it must fail rather than jump a branch or manufacture a result if this control cannot follow the full path. It does not claim a shell arc-length implementation.

Measurement location and recovery

Sum axial internal reactions on the shortened quarter-model end, then multiply by two to report the full-cylinder end load. Only half the circumference is modeled; axial half-length symmetry does not add another end-load multiplier. Treat the 2619 N reference as a full-cylinder end load by the explicitly approved comparison convention, not as a conclusively verified Abaqus postprocessing definition. Require the maximum on the completed path to be bracketed by lower loads on both sides, and sample the unchanged y displacement at the source's node 1. Refine the mesh and shortening increments together.

AM-DT solver results

The full-cylinder end-load convention changed after the last solver run. Current-specification numerical results await a rerun; the historical quarter-model reactions have not been relabeled as new solver evidence.

Reference observables

collapseLoad_N = 2619 N

transverseAtCollapse_m = -0.03116 m