A GPU-Resident MITC4 Shell Solver for a Nakajima Hemispherical-Dome Forming Benchmark: Verification, Abaqus Validation, and LS-DYNA Throughput Benchmarking

Fully integrated MITC4 (mixed interpolation of tensorial components) shells remain costly for large-deformation sheet-metal forming benchmarks at production mesh sizes. This paper presents a GPU-resident explicit MITC4 shell solver, implemented as a single CUDA pipeline in which co-rotational kinematics, assumed natural strain transverse shear, through-thickness J2 elasto-plasticity, and rigid-surface penalty contact remain in device memory. The study is positioned as computational verification and benchmarking for the Nakajima hemispherical-dome forming benchmark. Canonical shell tests verify the element kernel through membrane and bending patches and a force-driven cantilever, with the cantilever deflection agreeing with the MacNeal–Harder reference within about 2%. On the 10K-element Nakajima benchmark, the present solver agrees with Abaqus/Explicit with a mean von Mises error of 2.95% over 94% of specimen elements and a maximum shell thickness error of 2.08%. In the clamped/binder transition band, section-mean von Mises agrees to +1.0%, whereas section-maximum stress is under-predicted by 10.9%. A 50K-element Abaqus check remains bounded at 80 mm stroke, with section-mean von Mises differences of +0.6% globally and +0.4% in the transition band. For throughput, a separate 500K-element deck over 1.0 × 10−3 s and 15,808 steps give per-step speed-ups of 43.7×, 17.7×, and 13.5× versus 1-, 8-, and 32-core LS-DYNA MPP.