Equivalent Nodal Force Versus Thermal Load in Nonlinear Welding Distortion Analysis of Stiffened Panels

Abstract

Accurate prediction of welding-induced deformation is essential for dimensional control in large-scale ship block construction. In production design, transverse shrinkage directly governs the cutting allowance and shrinkage margin among various deformation modes. The inherent strain framework is widely used due to its computational efficiency, but the interaction between the implementation of equivalent loads and geometric nonlinearity has not been systematically investigated. This study evaluates two conventional loading representations: the equivalent nodal force method and the equivalent thermal load method, under both linear and geometrically nonlinear analysis formulations. In linear elastic analysis, both representations are equivalent and successfully provide identical, stable in-plane shrinkage predictions because both methods utilize input loads formulated from the same target inherent deformation. However, in shipbuilding practice, a geometrically nonlinear formulation is frequently required to capture large-displacement behaviors or structural instabilities in thin-walled assemblies. When geometric nonlinearity is introduced into these shrinkage predictions, a critical discrepancy emerges depending on the load implementation: the equivalent nodal force method violates the physical basis of shrinkage prediction by introducing unwanted out-of-plane deformation artifacts. This is a numerical artifact arising from the interaction of localized artificial compressive stresses with the stress-dependent geometric stiffness matrix. In contrast, the equivalent thermal load method is robust and always preserves the target in-plane shrinkage without any undesired out-of-plane geometry. Therefore, even though both methods are robust in the linear regime, the equivalent thermal load method is recommended when a geometrically nonlinear formulation is involved to ensure numerical consistency and reliability in production design.