Fast Nonlinear Buckling Solver

Benchmarking Awatif Against Abaqus

Mohamed Adil, Awatif Musaab Mahjoub, Awatif Kaison Cheung, Awatif

Nonlinear post-buckling response of the clamped-clamped IPE 300 column after prescribed axial shortening and lateral end displacement.
Figure 1. Nonlinear post-buckling response of the clamped-clamped IPE 300 column after prescribed axial shortening and lateral end displacement (interactive 3D animation available online).

1Introduction

Nonlinear buckling analysis is important for slender and lightweight structures, where large displacements and second-order effects can strongly influence the response. However, nonlinear simulations can be slow, difficult to converge, and expensive to run in practical engineering workflows.

Awatif introduces a new class of nonlinear solvers that is an order of magnitude faster than conventional FEM-based methods.

This white paper benchmarks Awatif's nonlinear solver against Abaqus on three buckling-sensitive problems. The comparison focuses on displacement accuracy, solver iterations, solve time, and convergence behavior.

The goal is to evaluate whether Awatif can produce comparable nonlinear results while reducing computational effort on the tested benchmark cases.

2Benchmark Cases

All three benchmark cases are modeled using frame elements.

Benchmark case definitions Three benchmark cases: a cantilever column under combined tip load, a 3D portal frame with top-joint load, and a clamped-clamped IPE 300 column with prescribed end displacement. (a) Cantilever column under combined tip load F y = -3500 kN F x = +10 kN 3.0 m 250 x 250 mm +Y +X +Z (out of plane) Material: concrete, E = 32,836,000 kN/m2 ν = 0.2 Section: A = 0.0625 m2 , I x = I z = 3.255x10-4 m4 Members: 1 member, 20 segments/member Analysis: static geometric nonlinearity; force-controlled (b) 3D portal frame with top-joint load F y = -12,000 kN F z = +100 kN 3.0 m 4.0 m +y +x +z (out of plane) Material: E = 32,836,000 kN/m2 , ν = 0.2 Section: square 250 x 250 mm Members: 3 members, 10 segments/member Analysis: static geometric nonlinearity; force-controlled. (c) Clamped-clamped IPE 300 column with prescribed end displacement Weak-axis imperfection (z-buckling) IPE 300 Δy = +1.0 m Δx = -0.15 m 3.0 m +y +x +z (out of plane) Material: steel, E = 210 GPa ν = 0.3 Section: IPE 300, A = 0.005381 m2 Members: 1 member, 20 segments/member (21 nodes) Analysis: displacement-controlled Imperfection: small weak-axis rest-curvature to trigger z-buckling.
Figure 2. Benchmark case definitions.

3Accuracy

Accuracy is evaluated by comparing key displacement results from Abaqus and Awatif. For the cantilever column and portal frame, the compared value is the global X displacement at the loaded point. For the clamped-clamped IPE 300 column, the compared value is the maximum global Z displacement near mid-span after buckling.

Case Compared displacement Abaqus Awatif Difference
1. Cantilever column Global X at loaded point 1.950 m 1.929 m 1.00%
2. Portal frame Global X at loaded point 0.379 m 0.382 m 0.50%
3. Clamped-clamped IPE 300 column Maximum global Z near mid-span 0.394 mm 0.393 mm 0.00%
Mid-span out-of-plane displacement history for the IPE 300 column comparing Awatif and Abaqus.
Figure 3. Mid-span out-of-plane displacement history for the clamped-clamped IPE 300 column.

The mid-span out-of-plane displacement history for the IPE 300 column shows close agreement between Awatif and Abaqus throughout the load path. Both solvers capture the growth of the weak-axis buckling displacement, the peak response, and the unloading-like reduction during the lateral displacement phase.

4Performance

Performance is evaluated using two solver quantities: the number of iterations required to reach convergence and the final residual error.

The iteration count indicates the computational effort required by each solver. The final error indicates whether the solution reached the required convergence tolerance.

This comparison avoids hardware-dependent timing results and focuses on solver behavior.

Case Abaqus iterations Awatif iterations Iteration speedup Abaqus final error Awatif final error
Cantilever column 257,194 5 51,438.8× 1.04 × 10-5 4.54 × 10-6
Portal frame 294,741 7 42,105.9× 1.48 × 10-4 1.25 × 10-6
IPE 300 column 5,669 60 94.5× 1.92 × 10-4 6.75 × 10-4

5Conclusion

Across the three nonlinear buckling benchmarks, Awatif closely reproduced the Abaqus displacement response, with the reported displacement differences remaining at or below 1.00%. The force-controlled cantilever and portal-frame cases showed the largest efficiency gains, reducing the required solver iterations by more than four orders of magnitude. The displacement-controlled IPE 300 column converged more easily, so its relative gain was smaller; nevertheless, 5,669 to 60 iterations is a 94.5× improvement with the same buckling trend. This marks the beginning of a new paradigm: next, the framework will be extended to shell elements and other nonlinearities, including material nonlinearity.