Article
Engineering, Mechanical
Kamaljyoti Nath, Anjan Dutta, Budhaditya Hazra
Summary: This study introduces an Iterative Polynomial Chaos method to solve structural mechanics problems, reducing the curse of dimensionality by iteratively solving problems with smaller sizes of PC expansions. By combining Polynomial Dimensional Decomposition, the method achieves higher computational efficiency and converged solutions.
PROBABILISTIC ENGINEERING MECHANICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Dilaksan Thillaithevan, Paul Bruce, Matthew Santer
Summary: We demonstrate a methodology for robust optimization using multivariable parameterized lattice microstructures. By introducing material uncertainties at the microscale, we are able to simulate manufacturing variations and design structures tolerant to those variations. We impose different types of material uncertainties to generate more robust structures.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Engineering, Mechanical
Zhibao Zheng, Hongzhe Dai, Yuyin Wang, Wei Wang
Summary: This paper introduces a new numerical scheme for simulating stochastic processes based on their specified marginal distribution functions and covariance functions. By generating stochastic samples to meet target marginal distribution functions and using an iterative algorithm to match the simulated covariance function to the target, the proposed method can accurately represent stochastic samples in series forms. The approach is applicable to non-stationary non-Gaussian stochastic processes and is demonstrated through three examples to be accurate and efficient.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Thermodynamics
Sufia Khatoon, Jyoti Phirani, Supreet Singh Bahga
Summary: We propose a fast Bayesian inference framework for solving inverse heat conduction problems. The framework combines polynomial chaos expansions and dimensionality reduction based on Karhunen-Loeve expansion to generate efficient surrogate models. We demonstrate the potential of this approach using three model problems for heat flux estimation.
APPLIED THERMAL ENGINEERING
(2023)
Article
Engineering, Aerospace
Loic Brevault, Mathieu Balesdent
Summary: The early design phase of launch vehicles often involves low fidelity models with high levels of modeling uncertainties. These uncertainties need to be propagated throughout the design process to ensure robustness, which can be computationally costly due to trajectory optimization and uncertainty quantification.
Article
Engineering, Industrial
Ruijing Zhang, Hongzhe Dai
Summary: This paper presents a method based on polynomial chaos and fractional moments for constructing non-Gaussian random models from limited observations. The method is able to quantify the randomness and uncertainty of the observed non-Gaussian field simultaneously, and facilitates the implementation of polynomial chaos-based stochastic analysis in practical engineering applications.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Article
Engineering, Mechanical
Ying Zhang, Wei Qu, He Zhang, Tao Qian
Summary: This paper proposes the adaptive Fourier decomposition (AFD) type methods to solve the two-match problem, which is to simultaneously meet a given marginal distribution condition and be compatible with a given covariance function. The AFD-Type methods offer flexibility and efficiency, and can be applied to various stochastic processes.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Computer Science, Interdisciplinary Applications
Mohamad Sadeq Karimi, Mehrdad Raisee, Mohamed Farhat, Patrick Hendrick, Ahmad Nourbakhsh
Summary: The study investigates the effects of operational and geometrical uncertainties on Tip Leakage Vortex (TLV) characteristics, showing profound impacts on cavitating tip leakage vortex flow, lift, and drag coefficients, and describing the discrepancies between numerical and experimental results. Operational uncertainties mainly influence TLV characteristics like circulation and velocity field, while geometrical randomness affects the vortex core position and viscous core radius, specifically gap distance.
COMPUTERS & FLUIDS
(2021)
Article
Engineering, Electrical & Electronic
Yiwei Qiu, Jin Lin, Xiaoshuang Chen, Feng Liu, Yonghua Song
Summary: This paper proposes an efficient and nonintrusive method for quantifying uncertainty in dynamic power systems subject to stochastic excitations. The method accurately and efficiently quantifies the probability distribution and high-order moments of system dynamic response and performance index using Ito process and adaptive sparse probabilistic collocation method. Based on commercial simulation software, this method is easy to use for power utility companies.
IEEE TRANSACTIONS ON POWER SYSTEMS
(2021)
Article
Engineering, Industrial
Mishal Thapa, Samy Missoum
Summary: This paper presents a framework for uncertainty quantification (UQ) and global sensitivity analysis (GSA) of composite wind turbine blades using polynomial chaos expansion (PCE) with l(1)-minimization. The framework is capable of handling a large number of random parameters and can assess the relative importance of these parameters using Sobol Indices. It also allows for arbitrary distributions of random inputs and spatial variations of material and geometric properties. The presented framework is applied to three composite wind turbine blade problems, and results are compared to Monte Carlo simulations.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Article
Engineering, Multidisciplinary
Yi Gao, Yang Jiao, Yongming Liu
Summary: This paper introduces a novel methodology for probabilistic material reliability analysis considering fine-scale microstructure stochasticity, addressing challenges of handling uncertainties and dimensionality for probabilistic solvers. By utilizing analytical and hierarchical uncertainty quantification methods and forming a probabilistic solver with adjoint first-order reliability method, the proposed approach demonstrates high efficiency in solving high-dimensional material reliability problems.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Acoustics
Karl-Alexander Hoppe, Kevin Josef Li, Bettina Chocholaty, Johannes D. Schmid, Simon Schmid, Kian Sepahvand, Steffen Marburg
Summary: This study expands the methods for non-destructively identifying material properties of a structure using modal data. It improves the results significantly by using eigenvectors instead of eigenvalues and accelerates the inversion process with a generalized polynomial chaos surrogate. A methodology for reusing surrogate models across inversion tasks is also developed.
JOURNAL OF SOUND AND VIBRATION
(2024)
Article
Mechanics
Xuan-Bach Bui, Trung-Kien Nguyen, Phong T. T. Nguyen
Summary: In this paper, a stochastic vibration and buckling analysis method for functionally graded sandwich thin-walled beams with I-section based on the first-order shear deformation theory is proposed for the first time. The material properties of the beams are assumed to vary continuously in thickness, and the constituent material properties follow lognormal distributions. The stochastic variabilities are propagated to the stochastic responses of the beams using a beam solver with hybrid series-type approximation functions. A polynomial chaos expansion (PCE) based surrogate model is developed for efficient evaluations of the stochastic responses, and its accuracy is assessed by comparing with crude Monte Carlo simulation. Sensitivity analysis is conducted to compare the importance of material properties uncertainty to stochastic responses. The results reported in this paper can serve as interesting benchmarks for the scientific and engineering community in the future.
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
(2023)
Article
Computer Science, Interdisciplinary Applications
Kurupasseril Tomy Jos Gladwin, Kalarickaparambil Joseph Vinoy
Summary: This paper investigates the spatial variations in material properties caused by fabrication tolerance in electromagnetic systems. The variations are modeled using Karhunen-Loeve expansion and quantified using a spectral stochastic finite element method based on intrusive polynomial chaos expansion. A numerical example demonstrates the accuracy and computational efficiency of the proposed approach for stochastic response analysis. The impact of correlation length of the covariance function used in the spectral expansion is also analyzed.
INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING
(2022)
Article
Engineering, Mechanical
Ming-Na Tong, Yan-Gang Zhao, Zhao Zhao
Summary: A novel method combining Karhunen-Lo & egrave;ve expansion with L-moments-based Hermite polynomial model is proposed for simulating strongly non-Gaussian and non stationary processes. The method effectively transforms non-Gaussian processes into Gaussian processes and addresses incompatibilities that may occur in strongly non-Gaussian processes.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Engineering, Multidisciplinary
Pramod Y. Kumbhar, A. Francis, N. Swaminathan, R. K. Annabattula, S. Natarajan
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
(2020)
Article
Engineering, Multidisciplinary
Tittu Varghese Mathew, Lars Beex, Stephane P. A. Bordas, Sundararajan Natarajan
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
(2020)
Article
Mathematics, Interdisciplinary Applications
Qingyuan Hu, Yang Xia, Sundararajan Natarajan, Andreas Zilian, Ping Hu, Stephane P. A. Bordas
COMPUTATIONAL MECHANICS
(2020)
Article
Engineering, Multidisciplinary
Tittu Varghese Mathew, Jayamanideep Rebbagondla, Sundararajan Natarajan
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
Junqi Zhang, Sundararajan Natarajan, Ean Tat Ooi, Chongmin Song
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
Shaima M. Dsouza, Tittu M. Varghese, Ean Tat Ooi, Sundararajan Natarajan, Stephane P. A. Bordas
Summary: This paper introduces a non-intrusive scaled boundary finite element method for handling multiple input uncertainties, including material and geometric uncertainties such as the shape and size of inclusions. A polynomial chaos expansion is utilized to represent the input and output uncertainties, and the efficiency and accuracy of the proposed framework are demonstrated through comparison with the conventional Monte Carlo method. A sensitivity analysis based on Sobol' indices is employed to identify the critical input parameter that has a higher influence on the output response.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Computer Science, Interdisciplinary Applications
Changkye Lee, Indra Vir Singh, Sundararajan Natarajan
Summary: In this paper, the cell-based smoothed finite-element method (CS-FEM) is proposed for solving boundary value problems of gradient elasticity in two and three dimensions. The method eliminates the need for explicit form of the shape functions and iso-parametric mapping. The results show that the proposed framework is accurate and robust.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mechanics
Yicong Li, Tiantang Yu, Sundararajan Natarajan, Tinh Quoc Bui
Summary: This work aims to study dynamic crack propagation in brittle materials under time-dependent loading conditions using the adaptive isogeometric phase-field approach. The proposed approach combines the advantages of the phase-field method and isogeometric analysis, and is enhanced by utilizing locally refined non-uniform rational B-spline basis. The results demonstrate that the proposed approach can achieve accurate results with reduced degrees-of-freedom.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Engineering, Multidisciplinary
Tiancheng Zhang, Hirshikesh, Tiantang Yu, Chen Xing, Sundararajan Natarajan
Summary: This work presents an adaptive phase-field method incorporated into a finite element framework combined with variable-node elements to investigate cohesive dynamic fracture. The proposed framework utilizes a hybrid form of the history field to drive the crack evolution and employs a staggered iteration scheme to compute the displacement and phase-field variables. The error indicator, utilizing the phase-field and history strain variables, is used to control the adaptive refinement process. The variable-node element technique facilitates adaptive mesh refinement and acts as a transition element between coarse and refined elements. The proposed method shows significant improvement in computational efficiency without sacrificing numerical accuracy.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Mechanical
M. D. Iqbal, C. Birk, E. T. Ooi, S. Natarajan, H. Gravenkamp
Summary: This paper extends the scaled boundary finite element method (SBFEM) to model fracture in functionally graded materials (FGMs) and examines the effects of fully coupled transient thermoelasticity. It utilizes the previously developed SBFEM supplementary shape functions to model thermal stresses and approximates the spatial variation of thermal and mechanical properties of FGMs by polynomial functions. The dynamic stress intensity factors (SIFs) are evaluated semi-analytically from their definitions without the need for additional post-processing. This approach is validated through numerical examples and comparison with reference solutions.
THEORETICAL AND APPLIED FRACTURE MECHANICS
(2023)
Article
Materials Science, Multidisciplinary
Rupesh Kumar Mahendran, Hirshikesh, Sundararajan Natarajan
Summary: This paper studies the effect of stress-diffusion interactions on the localization of plastic strain in an elastoplastic material using a fully coupled chemo-mechanical system. The transient coupled system is solved using a finite element formulation in the open-source finite element solver FEniCS. The role of geometric discontinuities and stress concentrations as well as plastic yielding on the diffusion-deformation process are investigated.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2022)
Article
Mathematics, Applied
Dibyendu Adak, Sundararajan Natarajan
Summary: This paper introduces a virtual element method for the time-dependent Stokes equation, where the velocity and pressure are approximated using different techniques based on the order of convergence. The method involves modifying the velocity space while maintaining the same dimension, and ensures stability and convergence for different values of k.
MATHEMATICS IN COMPUTER SCIENCE
(2021)
Article
Mathematics, Applied
Shaima M. Dsouza, Tittu Mathew Varghese, P. R. Budarapu, S. Natarajan
Article
Engineering, Biomedical
Thirunindravur Mannan Balaramakrishnan, Sundararajan Natarajan, S. Sujatha
JOURNAL OF BIOMIMETICS BIOMATERIALS AND BIOMEDICAL ENGINEERING
(2020)
