How to improve efficiency and robustness of the Newton method in geometrically non-linear structural problem discretized via displacement-based finite elements

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An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells (2018, background): “• With Equations 18 to 20, the following reduced-order model of dimension (m + 1) can be established for the solution of the unknown generalized displacements ξ: (ξ) +(ξ, ξ) + (ξ, ξ, ξ) = φ = Δλ e1 , (21) where Δλ is chosen to be the load parameter of the external load fext to determine the respo”