thinwalled

Thin-walled, in engineering and physiology, describes a structure whose wall thickness is small relative to its other dimensions. Under this assumption, walls are modeled as membranes with nearly uniform in-plane stresses and little bending, enabling simple closed-form formulas. The term is used for metal, polymer, and composite walls as well as for certain biological vessels such as arteries when the wall behaves as a thin membrane.

In thin-walled cylinders under internal pressure p, radius r and thickness t with t much less than r, the hoop stress is approximately sigma_h = p r / t and the axial stress is sigma_a = p r / (2 t). For thin-walled spheres the hoop stress is sigma = p r / (2 t). These relations result from balancing forces on a representative strip and assume elastic, uniform material response. If t is not small relative to r, thick-wall (Lame) equations must be used.

Applications include pipes, pressure vessels, and structural tubes in industries such as oil and gas, aerospace, and automotive. The concept also appears in biomechanics when modeling vessels like arteries or capillaries that can be treated as thin membranes under pressure.

Limitations and design considerations: the thin-wall model ignores bending, buckling, and local stress concentrations, and its accuracy diminishes as t/r grows. Codes often specify a threshold (commonly t/r around 0.1 or less) beyond which thick-wall analysis is required. Material properties, allowable stresses, and safety factors determine whether the thin-walled approach is appropriate.