TY - GEN

T1 - Semi hyper-reduction for nonlinear surface loads on finite element structures by the use of stress modes

AU - Koller, Lukas

AU - Witteveen, Wolfgang

AU - Pichler, Florian

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Model order reduction

KW - Multibody simulation

KW - Reynolds equation

KW - Semi Hyper-Reduction

KW - State-dependent nonlinear load

UR - http://www.scopus.com/inward/record.url?scp=85091584376&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-47626-7_2

DO - 10.1007/978-3-030-47626-7_2

M3 - Conference contribution

AN - SCOPUS:85091584376

SN - 9783030476250

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 9

EP - 13

BT - Nonlinear Structures and Systems, Volume 1 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020

A2 - Kerschen, Gaetan

A2 - Brake, Matthew R.W.

A2 - Renson, Ludovic

PB - Springer

T2 - 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020

Y2 - 10 February 2020 through 13 February 2020

ER -