Plastic Stability Theory of Thin Shells

Ai = plasticity coefficients B = axial rigidity, B = Est/(1 v ) D = bending rigidity, D = Est /12(1 v), also diameter ei = strain intensity E = modulus of elasticity E„ = secant modulus Et = tangent modulus k = buckling coefficient, k = <rtL/irD L — length of cylinder m — number of longitudinal half wave lengths M = bending moment per unit width n = number of circumferential wave lengths N = loading per unit width p = external pressure R = radius t — thickness u, v, w = displacements x, y, z = coordinates Z = cylinder curvature parameter, Z = (L/Rt) (1 -vY = (3/o-t) (1 Et/Es) (3 = wave-length parameter 7 = shear strain e = axial strain 7] = plasticity reduction factor v = Poisson's ratio ve = elastic value of Poisson's ratio, ve — 0.3 a = axial stress ai = stress intensity r = shear stress curvature differential operator V4 = (d/dx + b/dy)