Largedeflection

Large deflection, in structural mechanics, describes a regime in which deflections of a structural member are large enough that linear, small-deflection assumptions are invalid. When deflections are not small compared with the member length, the current deformed geometry alters stiffness, load paths, and boundary conditions, making the problem geometrically nonlinear.

In large-deflection analysis, the classical small-deflection beam or plate equations are replaced by nonlinear equations that couple axial, bending, and sometimes shear effects. The geometry is described in terms of deformed shapes, slopes, or arc length, and the governing relations often involve nonlinear differential equations or variational formulations. Because deflection affects the system response, loading and boundary conditions must be treated in their current, deformed configuration.

Solution approaches are primarily numerical. Nonlinear finite element analysis with geometric nonlinearity (often denoted as nonlinear geometry) is standard, and methods such as Newton-Raphson iterations and arc-length continuation are used to trace equilibrium paths. The problems can exhibit multiple equilibria, instability, and path dependence, requiring careful numerical treatment and sometimes sophisticated continuation techniques to obtain post-buckling paths.

Applications and phenomena commonly involve large deflections, including arches and frames under significant loading, slender columns subject to lateral loads, cables and membranes, and post-buckling behavior where the structure undergoes large, path-dependent shape changes. Large-deflection theory provides more accurate predictions for stability, strength, and overall behavior in these regimes than linear, small-deflection models.

See also: geometric nonlinearity, nonlinear finite element method, large-deflection theory.