Semi hyper-reduction for nonlinear surface loads on finite element structures by the use of stress modes

The determination of nonlinear state-dependent surface loads, acting on finite element (FE) structures, represents a computationally challenging and costly task in dynamic simulations. While for time integration an enormous reduction of the FE models number of degrees of freedom (DOFs) can be achieved by subspace projection, the computation of nonlinear surface loads usually depends on the non-reduced physical DOFs. In order to overcome this issue, so-called Hyper-Reduction (HR) methods have been introduced. These methods try to compute the surface loads in a reduced subspace as well. In this publication, an intermediate approach is proposed, which is called “Semi Hyper-Reduction” (SHR). The equations for computing the surface loads are built up in the full space and then projected into a lower dimensional subspace via proper force trial vectors. The required force trial vectors, called “stress modes”, thereby can be determined a priori without any nonlinear computations using the full DOF model. As a numerical example, a 3D crank drive is used, where the piston and the cylinder are separated by a hydrodynamic lubrication film, which is considered by Reynolds equation.