Non-incremental response evaluation in geometrically nonlinear structural dynamics using a space-time stiffness operator

Abstract This contribution presents a proper generalized decomposition-based nonlinear solver for an efficient solution of geometrically dynamic problems. The is built as sum dyadic products space and time modes, this so-called enrichments truncated when the required accuracy achieved. In proposed algorithm, we apply consistent linearization residual vectors around currently known over whole space-time domain. At first, set vectorized tangent stiffness matrices separated in using singular value decomposition. Then, left right are reshaped into to separate operator. latter can be incorporated alternating fixed-point algorithm compute couples modes. Numerical examples two-dimensional exact beam model demonstrate accuracy, efficiency, limits method.