Michal Sokolowski

2025-01

Ultimate load collapse analysis including both material and geometric nonlinearity — ANSYS large deformation with elastic-plastic material for aluminum fittings, continued loading to actual collapse (loss of load-carrying capacity).

Challenge: The analysis was very sensitive to load step size near collapse — too large a step would overshoot the collapse load, too small would take days. Implemented adaptive step sizing with automatic bisection when convergence failed, combined with a load-displacement curve monitor to detect approaching collapse.

Learned: Collapse analysis requires monitoring the load-displacement curve to distinguish convergence difficulty near collapse from solver divergence. An 'approaching collapse' detector based on stiffness reduction triggers step size reduction before convergence failure occurs.

2024-10

Combined compression + shear buckling interaction diagram for wing skin panel — generated interaction curve using ANSYS eigenvalue analysis at multiple N_x/N_xy ratios. Compared with classical interaction equation (Rs + Rc^2 = 1).

Challenge: Classical interaction equation (Rsc + Rs^2 = 1 for compression + shear) is approximate and can be non-conservative for anisotropic composite panels. FEM-generated interaction curve showed 15% deviation from classical formula at high shear ratios for the QI laminate.

Learned: Classical buckling interaction equations are derived for isotropic plates. For composite plates with anisotropic bending stiffness, FEM-generated interaction curves are more accurate. Always generate a few FEM points to verify before relying on classical formulas for composites.

2024-05

Crippling analysis of Z-section and J-section stiffeners using Needham's method — divided each cross-section into flat sub-elements, computed crippling stress for each sub-element, combined with area weighting for total section crippling stress.

Challenge: Needham's Fcc/Fcy vs b/t curve is parameterized by edge condition (one edge free vs both edges supported). For the web-to-flange junction of the J-section, both edges are supported — but one support is much more flexible than the other. Used an effective edge fixity coefficient between 0 and 1.

Learned: Needham's method edge condition classification is binary (free edge vs supported edge) but real structures have intermediate boundary conditions. An effective edge fixity coefficient calibrated against FEM for the specific junction geometry gives more accurate crippling predictions.

2023-12

Postbuckling analysis of stiffened composite panel — geometric and material nonlinearity, continued loading past initial skin buckling to panel collapse (stiffener crippling and failure).

Challenge: Abaqus standard implicit solver had difficulty with the snap-through at initial skin buckling — required switching to dynamic implicit (quasi-static) with automatic stabilization to pass the limit point. Static Riks method was tried first but failed due to multiple snap-throughs.

Learned: Quasi-static dynamic analysis (with mass scaling or explicit time stepping) is often more robust than Riks for postbuckling problems with multiple snap-throughs. Riks works well for single limit point problems but fails for structures with sequential local failures.

2023-07

Geometric imperfection sensitivity study for cylindrical shell buckling — seeded first eigenmode as imperfection shape at amplitudes of 0.1%, 0.5%, 1.0%, 5% of shell thickness. Generated imperfection sensitivity curve.

Challenge: Shell buckling is extremely sensitive to imperfection amplitude and shape. The linear bifurcation load overestimated the actual collapse load by 3.2x for perfect geometry and 2.1x with 1% imperfection — classic Koiter imperfection sensitivity behavior.

Learned: Shell buckling test knockdown factors (KDFs) in design codes account for imperfection sensitivity empirically. Using linear buckling load directly in structural assessment (without KDF) is severely non-conservative. Always apply the appropriate KDF from NASA SP-8007 or ECSS for shells.

2023-02

Linear bifurcation buckling analysis in ANSYS Mechanical — Euler column, plate, and shell buckling for engine cowling stiffener. Compared ANSYS eigenvalue with Roark closed-form formula for verification.

Challenge: Shell buckling eigenvalue analysis with membrane-bending coupling (non-zero B matrix) gave negative eigenvalues — indicating pre-buckling non-linearities were not captured in the linearized model. Required applying pre-stress from nonlinear static analysis before extracting eigenvalues.

Learned: Linear bifurcation buckling is only valid when the pre-buckling response is linear. For thin shells with significant membrane-bending coupling, a nonlinear pre-buckling solution followed by linear eigenvalue extraction (SOL 106/105 combination) is necessary.