Reduced order modeling of large contact interfaces to calculate the non-linear response of frictionally damped structures

Battiato, Giuseppe; Firrone, Christian Maria

doi:10.1016/j.prostr.2020.02.074

Cited by 3 publications

(3 citation statements)

References 21 publications

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“…Linear‐elastic contact problems represent variational problems under unilateral constraints 20,21 and are often nonlinear due to the unknown moving contact interface, see, for example, References 20 and 22‐24 for introduction to contact mechanics. Those problems are commonly solved by the penalty method 25 or the augmented Lagrange method 26 after the discretization.…”

Section: Introductionmentioning

confidence: 99%

A physics‐based model reduction approach for node‐to‐segment contact problems in linear elasticity

Manvelyan

Simeon

Wever³

2022

Numerical Meth Engineering

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The article presents a novel model order reduction method for mechanical problems in linear elasticity with nonlinear contact conditions. Recently, we have proposed an efficient reduction scheme for the node‐to‐node formulation [Manvelyan et al., Comput Mech 68, 1283–1295 (2021)] that leads to linear complementarity problems (LCPs). Here, we enhance the underlying contact problem to a node‐to‐segment formulation, which leads to quadratic inequalities as constraints. The adjoint system corresponds to a nonlinear complementarity problem that describes the Lagrange multiplier. The latter is solved by a Newton‐type iteration based on a LCP solver in each time step. Since the maximal set of potential contact nodes is predefined, an additional substructuring by Craig–Bampton can be performed. This contact treatment turns out to be necessary and allows exclusion of the Lagrange multipliers and the nodal displacements at contact from reduction. The numerical solutions of the reduced contact problem achieve high accuracy and the dynamic contact carries over the behavior of the full order model. Moreover, if the contact area is small compared to the overall structure, the reduction scheme performs very efficiently. The performance of the resulting reduction method is assessed on two 2D computational examples from linear elasticity.

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Section: Introductionmentioning

confidence: 99%

A physics‐based model reduction approach for node‐to‐segment contact problems in linear elasticity

Manvelyan

Simeon

Wever³

2022

Numerical Meth Engineering

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“…Plenty of scientific papers have been published on this topic in the recent past years, and several numerical methods have been developed in order to efficiently predict the FR of structures in the presence of friction contacts. Most of these have been purposely developed for industrial applications, mainly in the turbomachinery field [11,12], but also concerning mechanical assemblies where bolted flanges and lap joints are used [7,13,14]. The key idea behind the NFR prediction is the estimation of the contact forces by means of appropriate contact models [15][16][17][18], and the solution of a reduced set of nonlinear equation of motion (EQM) in the frequency domain by using the harmonic balance method (HBM) [15] or the multi-harmonic balance method (MHBM) [19,20].…”

Section: Introductionmentioning

confidence: 99%

Self-adaptive macroslip array for friction force prediction in contact interfaces with non-conforming meshes

Battiato

2021

Nonlinear Dyn

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The steady-state nonlinear forced response (NFR) of finite element (FE) models with friction joints is usually computed in the frequency domain through the combination of node-to-node contact elements and the Harmonic Balance Method (HBM). In the current state of the art, rare are the cases where the friction forces are estimated for contact interfaces with non-conforming mesh grids. This need is nowadays taking place due to the improving capability of commercial FE software to manage any kind of boundary condition (i.e., either coupling or contact), without requiring coincident pairs of nodes at the joint interfaces. Such an advantage becomes a drawback when the analysts are requested to investigate the NFR of the assembly by using build-in codes, where the contact forces prediction usually requires node-to-node contact elements whose parameters (i.e., the contact stiffnesses and friction coefficients) can be easily identified by means of experiments. This paper addresses the mentioned limitation, and proposes a novel self-adaptive macroslip array (SAMA) model for the estimation of the nonlinear friction forces on FE contact interfaces with non-conforming meshes. The SAMA model consists on a set of node-to-node contact elements ordered in parallel, whose contact parameters and normal preloads are identified through a step-by-step self-adaptive weighting algorithm that depends on the topology of the meshes in contact. The goodness of the proposed model is assessed on the calculation of the NFR of a bladed disk with shroud contacts, under the hypotheses of cyclic symmetry and HBM. The nonlinear dynamic behavior of the bladed disk is evaluated in two different cases. First, in the case of lack of node-to-node congruence at the contact interface for the structure being in its undeformed configuration, and second, in the case of a relevant static misalignment of the contact interfaces due to the application of large static loads.

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“…In this paper we focus on reduction approaches for dynamic contact problems in linear elasticity. Such problems are naturally nonlinear due to the unknown moving contact interface, see, e.g., [20,31,46,21] for introduction to contact mechanics and [32] for first results on reduction approaches in this matter. In [4], a dynamic problem with a linear contact condition is discussed and both the displacements and the Lagrange multipliers are reduced using methods such as the singular value decomposition or the non-negative matrix compression.…”

Section: Introductionmentioning

confidence: 99%

A Physics-Based Model Reduction Approach for Node-to-Segment Contact Problems in Linear Elasticity

Manvelyan,

Simeon,

Wever

2021

Preprint

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The paper presents a new reduction method designed for dynamic contact problems. Recently, we have proposed an efficient reduction scheme for the node-to-node formulation, that leads to Linear Complementarity Problems (LCP). Here, we enhance the underlying contact problem to a node-to-segment formulation. Due to the application of the dual approach, a Nonlinear Complementarity Problem (NCP) is obtained, where the node-tosegment condition is described by a quadratic inequality and is approximated by a sequence of LCPs in each time step. These steps are performed in a reduced approximation space, while the contact treatment itself can be achieved by the Craig-Bampton method, which preserves the Lagrange multipliers and the nodal displacements at the contact zone. We think, that if the contact area is small compared to the overall structure, the reduction scheme performs very efficiently, since the contact shape is entirely recovered. The performance of the resulting reduction method is assessed on two 2D computational examples.

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Reduced order modeling of large contact interfaces to calculate the non-linear response of frictionally damped structures

Cited by 3 publications

References 21 publications

A physics‐based model reduction approach for node‐to‐segment contact problems in linear elasticity

A physics‐based model reduction approach for node‐to‐segment contact problems in linear elasticity

Self-adaptive macroslip array for friction force prediction in contact interfaces with non-conforming meshes

A Physics-Based Model Reduction Approach for Node-to-Segment Contact Problems in Linear Elasticity

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