Tuning of Finite Element Model Parameters to Match Nonlinear Reduced Order Models

Modeling vibratory damage with reduced-order models and the generalized finite element method

The large computational effort required for finite element analysis predictions of the dynamic response of thin aircraft panels in extreme aeroacoustic environments has led to significant research on the development of nonlinear reduced order models (ROMs). ROMs reduce the finite element model to a low-order system of nonlinear modal-like equations which can be integrated in the time domain. Although much more computationally efficient than finite element models, it may still be expensive to build and solve the ROM equations of motion for complex structures owing to the large number of nonlinear terms involved. To further reduce this computational cost, deterministic and stochastic partial linearization methodologies are introduced in this paper, in which the nonlinearity is retained only for the dominant modes of the basis. In the stochastic approach, the solution approximation error introduced by the partial linearization is recognized as an epistemic uncertainty, which is modeled by randomizing the linear stiffness terms of the non-dominant modes. The nonparametric stochastic approach is adopted for this modeling and its uncertainty level is estimated using maximum likelihood estimation. Both methods are verified on the ROM of a 96,000 degrees-of-freedom, 9-bay panel, where significant computational gains are observed for dynamic simulations. The response of the full nonlinear ROM in the verification study is within the 95% confidence bounds of the stochastic partially linearized model.

In recent years, autonomously guided parachute systems have been developed with the goal of increasing the landing accuracy of airdrop operations. These precision airdrop systems utilize an onboard global positioning system (GPS) coupled with a guidance, navigation and control (GNC) system to continuously monitor and correct the flight path of the parachute system during descent. A critical component of the GNC system is an algorithm that predicts the response of the system to various aerodynamic forces in real-time that are typically based on a low-order multi-degree of freedom (DOF) dynamics model. Reduced order modeling is the process of representing a complex dynamic system with many DOF with a model having relatively few DOF. The goal of this study is to examine the use of large scale finite element models to construct and calibrate Reduced Order Models (ROM) for parachute systems. The resulting ROM would provide parachute designers with a simple tool to examine parachute behavior under various operating conditions. The use of numerical simulations to calibrate the ROM would help to eliminate the number of physical tests needed to characterize a parachute system’s properties. In this study, a 6 degree of freedom ROM is adopted. The system dynamic properties for the ROM and the resultant forces and moments acting on the ROM are obtained from finite element simulations. The 6 DOF model originally proposed by Cockrell and Doherr and later used by Dobrokhodov is adopted for the ROM. The finite element (FE) code, TENSION, is used to perform the large scale simulations and extract the ROM dynamic properties and resultant forces. Several examples are performed that verify the ROM procedure by comparing ROM predictions to FE simulations for various parachute system trajectories. The performance of the ROM is shown to be excellent for in-plane motion under an oscillating wind field. It is shown, however, that the ROM procedure deteriorates as the FE model is refined by adding more DOF. It is demonstrated that, for highly deformable FE models with many DOF, more sophisticated ROM procedures are needed.

Inverse viscoelastic material characterization using POD reduced-order modeling in acoustic–structure interaction

Guided identification of nonlinear reduced-order models via the incorporation of von Kármán beam theory

Probabilistic finite element predictions of the human lower limb model in total knee replacement

We present a method to develop a physics-based, reduced-order model of a wind tunnel measurement system (including a sting, strain gage force balance, and test article) that can be used to predict the dynamics of the system. This reduced-order model is combined with a simple finite element beam model of a sting to estimate the dynamics of the full assembly. We make comparisons between a full finite element model and the hybrid reduced-order model to show that this hybrid reduced-order model is capable of predicting the first six natural frequencies to within 10% error. This technique could be used to identify reduced-order parameters for a large number of balances and stings, which could then be used to estimate the dynamics of different measurement assemblies.

Skull stiffness of children is of great significance to protect brain tissues during traffic accidents. In this paper, the effects of skull stiffness on traumatic brain injury (TBI) are investigated by using a validated 6-year-old child head finite element (FE) model according to Chinese standard GB/T 24550-2009 Results showed that the HIC value, intracranial pressure, Von Mises stress and shear strain of brain tissue increased with the decrease of skull stiffness during the impact of FE model with engine hood. Therefore, the injury risk of the child head decreases with the increase of skull stiffness. And the skull with higher stiffness can provide a better protection for brain tissues during traffic accidents.

A method for continuous box-girder bridge structure finite element (FE) model updating based on static-load testing is proposed. The procedure includes field static-load testing, FE modeling, FE model (parameter) updating, etc. Based on this procedure, the structure FE model updating for an expressway 5-span pre-stressed concrete continuous box-girder bridge is conducted. And the bridge structure static FE model, which is consistent with the static-load testing actual measure response, is gained. The updated FE model (parameter) is foundation of structural performance evaluation for the bridge.

This work concerns the implementation of nonlinear modal reduction to flexible multi-body dynamics. Linear elastic theory will lead to instability issues with rotating beamlike structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In this work, in order to improve the convergence characteristic and also to reduce the computation time in flexible multi-body dynamics, which is extremely important for complicated large systems, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. The example used in this work is a rotating Euler-Bernoulli beam, two nonlinear reduced models were established based on modal coordinates, the first reduced model created from theoretical bending and axial mode shapes by Galerkin method; the second reduced model is derived by the standard matrix operator from a full finite element model. Transient simulation results of lower degrees of freedom from above two reduced models are compared with those obtained from full nonlinear finite element model.

A nonlinear one-dimensional finite-element model representing the axial and transverse motions of a cantilevered rotating beam is reduced to a single nonlinear normal mode using invariant manifold techniques. This system is an idealized representation for large-amplitude vibrations of a rotorcraft blade. Although this model is relatively simple, it possesses the essential nonlinear coupling effects between the axial and transverse degrees of freedom. The nature of this coupling leads to the fact that we must use many degrees of freedom, whether based on finite elements or modal expansions, in order to accurately represent the beam vibrations. In this work, the slow modal convergence problem is overcome by nonlinear modal reduction that makes use of invariant manifold based nonlinear modes. This reduction procedure generates a single-degree-of-freedom reduced-order model that systematically accounts for the dynamics of all the linear modes, or finite elements, considered in the original model. The approach is used to study the dynamic characteristics of the finite-element model over a wide range of vibration amplitudes. Using extensive simulations, it is shown that the response of the reduced-order model is nearly identical to a reference system which is based on a large-scale representation of the finite-element model, and to a reduced-order Rayleigh-Ritz model. All of the procedures presented here have been computationally automated. Hence, in this study we demonstrate that it is feasible and practical to interface nonlinear finite-element methods with nonlinear modal reduction.

Reduced order modeling of hysteretic structural response and applications to seismic risk assessment

In this paper, we examine an efficient calculation of the approximate frequency response (FR) for large-size finite element (FE) models using the Krylov subspace-based model order reduction (MOR) and its direct design sensitivity analysis with respect to design variables for sizing. Information about both the FR and its design sensitivity is necessary for typical gradient-based optimization iterations; therefore, the problem of high computational cost may occur when FRs of a large-size FE models are involved in the optimization problem. In the method suggested in this paper, reduced order models, generated from the original full-order FE models through the Arnoldi process, are used to calculate both the FR and FR sensitivity. This maximizes the speed of numerical computation of the FR and its design sensitivity. Assuming that the Krylov basis vectors remain constant with respect to the perturbation of a design variable, the FR sensitivity analysis is performed in a more efficient manner. As numerical examples, a car body with 535,992 degrees of freedom (DOF) and a 6 × 6 micro-resonator array with 368,424 DOF are adopted to demonstrate the numerical accuracy and efficiency of the suggested approach. Using the reduced-order models, we found that the FR and FR sensitivity are in a good agreement with those using the fullorder FE model. The reduction in computation time is also found to be significant because of the use of Krylov subspace-based reduced models.

Automated finite element model updating of a scale bridge model using measured static and modal test data

POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow