Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

Algorithm 1

Computation of TVD for a given reduction base 𝝋₁ to 𝝋_𝑣+𝑠.

Input: 𝝋₁,…,𝝋_𝑖,…,𝝋_𝑣+𝑠,𝐊

Output: 𝚽_𝑇=𝝋_1,1,…,𝝋_1,𝑣+𝑠,…,𝝋_𝑖,1,…,𝝋_{𝑖,𝑣+𝑠},…,𝝋_𝑣+𝑠,1,…,𝝋_{𝑣+𝑠,𝑣+𝑠}

(1) 𝐅=[]

(2) for 𝑗=1∶(𝑣+𝑠)

(3)   determine 𝜕𝐊/𝜕𝑞_𝑗

(4)   for 𝑖=1∶(𝑣+𝑠)

(5)       𝐟_𝑖,𝑗=𝜕𝐊𝜕𝑞_𝑗𝝋_𝑖

(6)       𝐅=𝐅𝐟_𝑖,𝑗

(7)   end

(8) end

(9) use FE software to compute 𝚽_𝑇 based on 𝐊𝚽_𝑇=𝐅