THE WRINKLING OF THIN, FLAT, RECTANGULAR WEBS

A web is termed wrinkled when one of the in-plane principal stresses i n tensile and the other is sufficiently compressive. A criterion is de rived that predicts wrinkling of isotropic, compressible rectangular w ebs under uniform in-plane principal stresses. The compressive stress at impending wrinkling depends on the flexural stiffness, and it equal s zero in the case of a membrane. A criterion of wrinkling is also der ived using isotropic, incompressible membrane theory. This criterion p redicts an infinite number of wrinkle waves in a wrinkled region. With small flexural stiffness, the number of wrinkle waves becomes finite at wrinkling and it is predictable along with the shape and the size o f the wrinkled region. The number of the wrinkle waves increases as th e aspect ratio of the rectangular web increases, as the in-plane princ ipal tension increases, and as the flexural stiffness decreases. Analy ses of wrinkling of a rectangular web under simple shear and under uni form longitudinal stretching illustrate the above predictions.