98 Riccardo Rossi,Vitaliani Renato,and Eugenio Onate Table 1.Pseudo-Static solution procedure for pseudo-static strategy:calculate the constant matrices D=BM set M =0 after initializing the damping matrix.(if M is not set to 0,"real" dynamic simulation can be performed) choose Newmark constants:a classical choice is 1 1 6=2；a=4 evaluate the constants a41 i a1=6 1 1 a0= -at i 02=adt s=六-1：a=日-1；s=兰（很-2） predict the solution at time t+At using for example x8+a1=XL+文△t x+△t= :=0 iterate until convergence -calculate the system's contributions Key=[Ktan]+do[M]+1 [D] Ray")=(R)-[M][D] solve the system for the correction dx update the results as x=xitar+dx Ax=x牛4-x t+At=a1△x-a4xt-a5戈t 戈4+At=a0△x-a2:-a3戈： go to next time step compressive stress tends to appear on a part of a structure,it is immediately removed by local instability phenomena,that manifest with the formation of little"waves"of direction perpendicular to the direction of stresses.Predic- tion of the size of those "waves"commonly called "wrinkles"is not generally possible as their disposition is somehow random and connected to initial im- perfections.However their average size is strictly connected to the bending stiffness meaning in particular that for the problems of interest the wrinkle98 Riccardo Rossi, Vitaliani Renato, and Eugenio Onate Table 1. Pseudo–Static solution procedure • for pseudo–static strategy: calculate the constant matrices D = βM set M = 0 after initializing the damping matrix. (if M is not set to 0, “real” dynamic simulation can be performed) • choose Newmark constants: a classical choice is δ = 1 2 ; α = 1 4 • evaluate the constants a0 = 1 α∆t2 ; a1 = δ α∆t ; a2 = 1 α∆t a3 = 1 2α − 1 ; a4 = δ α − 1 ; a5 = ∆t 2  δ α − 2  • predict the solution at time t + ∆t using for example x0 t+∆t = xt + x˙ t∆t x˙ t+∆t = x˙ t x¨t+∆t = 0 • iterate until convergence – calculate the system’s contributions  Kdyn tan  = [Ktan] + a0 [M] + a1 [D] 1 Rdyn 2 = {R} − [M] 1 x¨i t+∆t 2 − [D] 1 x˙ i t+∆t 2 – solve the system for the correction dx – update the results as xi+1 t+∆t = xi t+∆t + dx ∆x = xi+1 t+∆t − xt x˙ t+∆t = a1∆x − a4x˙ t − a5x¨t x¨t+∆t = a0∆x − a2x˙ t − a3x¨t • go to next time step compressive stress tends to appear on a part of a structure, it is immediately removed by local instability phenomena, that manifest with the formation of little ”waves” of direction perpendicular to the direction of stresses. Predic￾tion of the size of those ”waves” commonly called ”wrinkles” is not generally possible as their disposition is somehow random and connected to initial im￾perfections. However their average size is strictly connected to the bending stiffness meaning in particular that for the problems of interest the wrinkle