Multicomplex Newmark-Beta Time Integration Method for Sensitivity Analysis in Structural Dynamics

Garza, Jose; Millwater, Harry

doi:10.2514/1.j053282

Cited by 27 publications

(9 citation statements)

References 14 publications

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“…Examples in other disciplines include: aerodynamics [Anderson et al, 2001;Newman et. al., 2003], structural dynamics [Wang, and Apte, 2006;Garza and Millwater, 2015], and nonlinear structural analysis [Kim, Ryu, Cho, 2011], among others.…”

Section: Introductionmentioning

confidence: 99%

A virtual crack extension method to compute energy release rates using a complex variable finite element method

Millwater

Wagner

Baines

et al. 2016

Engineering Fracture Mechanics

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The complex-valued finite element method, ZFEM, is proposed as a new virtual crack extension method to compute the energy release rate. The energy release rate is computed as a numerical derivative of the strain energy with respect to a crack extension using the complex Taylor series expansion method (CTSE). This is accomplished using a finite element method with complex nodal coordinates and extending the crack by a very small quantity along the imaginary directions of the complex nodal coordinates. The resulting finite element formulation becomes complex valued with the imaginary component of the strain energy containing the energy release rate. This method retains the conceptual simplicity of numerical differentiation but eliminates numerical issues regarding perturbation of the crack size. Both two-and three-dimensional examples are provided. Numerical examples indicate that the energy release rate computed using ZFEM is of the same accuracy as the domain-based J integral formulation. The method is very general and can be applied to self-similar or non-self-similar crack extensions.

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Section: Introductionmentioning

confidence: 99%

A virtual crack extension method to compute energy release rates using a complex variable finite element method

Millwater

Wagner

Baines

et al. 2016

Engineering Fracture Mechanics

Self Cite

View full text Add to dashboard Cite

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“…Fins are present in almost all heat transfer applications such as engines, computers and electronics, and cooling systems. It is worth highlighting that ZFEM has been verified in a number of application areas such as elastic analysis [60], fatigue [68,69], fracture mechanics [61,[70][71][72][73], plasticity [74], residual stresses [75], creep [76], variance estimates [77], reliability-based design optimization [78], steady-state thermo-elasticity [79], structural dynamics [80], and periodic material design [81]. However, this is the first demonstration of ZFEM in transient heat transfer problems.…”

Section: Introductionmentioning

confidence: 83%

Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method

et al. 2022

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Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are required to predict the thermal response. Numerical tools are even more relevant when the number of parameters influencing the model is large, and it is necessary to isolate the most influential variables. In this regard, sensitivity analysis can be conducted to increase the process understanding and identify those variables. Here, we combine the complex-variable differentiation theory with the finite element formulation for transient heat transfer, allowing one to compute efficient and accurate first-order sensitivities. Although this approach takes advantage of complex algebra to calculate sensitivities, the method is implemented with real-variable solvers, facilitating the application within commercial software. We present this new methodology in a numerical example using the commercial software Abaqus. The calculation of sensitivities for the temperature and heat flux with respect to temperature-dependent material properties, boundary conditions, geometric parameters, and time are demonstrated. To highlight, the new sensitivity method showed step-size independence, mesh perturbation independence, and reduced computational time contrasting traditional sensitivity analysis methods such as finite differentiation.

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“…The improved Newmark- β method (Fleissner et al., 2007; Garza and Millwater, 2015) is applied for the solution of kinetic differential equation and has second order accuracy as γ = 1/2 and β = 1/4 (Zheng and Hasebe, 2000), which is an unconditional stability method.…”

Section: Dynamic Modelingmentioning

confidence: 99%

Dynamic modeling and simulation of inter-shaft bearings with localized defects excited by time-varying displacement

Jun

Fei

et al. 2019

Journal of Vibration and Control

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To accurately describe the dynamic features of inter-shaft bearings with localized defect under operation, the dynamic model of inter-shaft bearing with localized defects was established with respect to time-varying displacement excitation. Based on fault simulations on a birotor experimental rig, the developed dynamic model of inter-shaft bearing is validated to have high accuracy (over 99%) when localized defects happen on inner and outer race with co- and counter-rotation, which indicates that the model can be adopted to simulate the faults of inter-shaft bearing instead of experiment. Through investigation of the square-root (SR) amplitudes of bearing vibration with different defect sizes, radial loads, and rotational directions, we find that the SR amplitudes of bearing vibration increase with increasing defect size and radial load for both co- and counter-rotation. The amplitudes of counter-rotation are larger than those of co-rotation for inner race and outer race, and the amplitude of inner race defect are larger than that of outer race defect for the same defect size or same radial load. This work reveals the SR variation of bearing vibration with localized surface defects under different defect sizes and radial loads, and accurately describes the dynamic characteristics of inter-shaft bearing with localized defects. The efforts of this study open a door to adopt a dynamic model in the future to evaluate and monitor the health condition of inter-shaft bearings in an aeroengine or other rotating machinery.

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Multicomplex Newmark-Beta Time Integration Method for Sensitivity Analysis in Structural Dynamics

Cited by 27 publications

References 14 publications

A virtual crack extension method to compute energy release rates using a complex variable finite element method

A virtual crack extension method to compute energy release rates using a complex variable finite element method

Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method

Dynamic modeling and simulation of inter-shaft bearings with localized defects excited by time-varying displacement

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