Machine Learning Aided Stochastic Elastoplastic and Damage Analysis of Functionally Graded Structures

The elastoplastic and damage analyses, which serve as key indicators for the nonlinear performances of engineering structures, have been extensively investigated during the past decades. However, with the development of advanced composite material, such as the functionally graded material (FGM), the nonlinear behaviour evaluations of such advantageous materials still remain tough challenges. Moreover, despite of the assumption that structural system parameters are widely adopted as deterministic, it is already illustrated that the inevitable and mercurial uncertainties of these system properties inherently associate with the concerned structural models and nonlinear analysis process. The existence of such fluctuations potentially affects the actual elastoplastic and damage behaviours of the FGM structures, which leads to the inadequacy between the approximation results with the actual structural safety conditions. Consequently, it is requisite to establish a robust stochastic nonlinear analysis framework complied with the requirements of modern composite engineering practices. In this dissertation, a novel uncertain nonlinear analysis framework, namely the machine leaning aided stochastic elastoplastic and damage analysis framework, is presented herein for FGM structures. The proposed approach is a favorable alternative to determine structural reliability when full-scale testing is not achievable, thus leading to significant eliminations of manpower and computational efforts spent in practical engineering applications. Within the developed framework, a novel extended support vector regression (X-SVR) with Dirichlet feature mapping approach is introduced and then incorporated for the subsequent uncertainty quantification. By successfully establishing the governing relationship between the uncertain system parameters and any concerned structural output, a comprehensive probabilistic profile including means, standard deviations, probability density functions (PDFs), and cumulative distribution functions (CDFs) of the structural output can be effectively established through a sampling scheme. Consequently, by adopting the machine learning aided stochastic elastoplastic and damage analysis framework into real-life engineering application, the advantages of the next generation uncertainty quantification analysis can be highlighted, and appreciable contributions can be delivered to both structural safety evaluation and structural design fields

Material-based design computation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 306-328).The institutionalized separation between form, structure and material, deeply embedded in modernist design theory, paralleled by a methodological partitioning between modeling, analysis and fabrication, resulted in geometric-driven form generation. Such prioritization of form over material was carried into the development and design logic of CAD. Today, under the imperatives and growing recognition of the failures and environmental liabilities of this approach, modern design culture is experiencing a shift to material aware design. Inspired by Nature's strategies where form generation is driven by maximal performance with minimal resources through local material property variation, the research reviews, proposes and develops models and processes for a material-based approach in computationally enabled form-generation. Material-based Design Computation is developed and proposed as a set of computational strategies supporting the integration of form, material and structure by incorporating physical form-finding strategies with digital analysis and fabrication. In this approach, material precedes shape, and it is the structuring of material properties as a function of structural and environmental performance that generates design form. The thesis proposes a unique approach to computationally-enabled form-finding procedures, and experimentally investigates how such processes contribute to novel ways of creating, distributing and depositing material forms. Variable Property Design is investigated as a theoretical and technical framework by which to model, analyze and fabricate objects with graduated properties designed to correspond to multiple and continuously varied functional constraints. The following methods were developed as the enabling mechanisms of Material Computation: Tiling Behavior & Digital Anisotropy, Finite Element Synthesis, and Material Pixels. In order to implement this approach as a fabrication process, a novel fabrication technology, termed Variable Property Rapid Prototyping has been developed, designed and patented. Among the potential contributions is the achievement of a high degree of customization through material heterogeneity as compared to conventional design of components and assemblies. Experimental designs employing suggested theoretical and technical frameworks, methods and techniques are presented, discussed and demonstrated. They support product customization, rapid augmentation and variable property fabrication. Developed as approximations of natural formation processes, these design experiments demonstrate the contribution and the potential future of a new design and research field.by Neri Oxman.Ph.D

A new mixed model based on the enhanced-Refined Zigzag Theory for the analysis of thick multilayered composite plates

The Refined Zigzag Theory (RZT) has been widely used in the numerical analysis of multilayered and sandwich plates in the last decay. It has been demonstrated its high accuracy in predicting global quantities, such as maximum displacement, frequencies and buckling loads, and local quantities such as through-the-thickness distribution of displacements and in-plane stresses [1,2]. Moreover, the C0 continuity conditions make this theory appealing to finite element formulations [3]. The standard RZT, due to the derivation of the zigzag functions, cannot be used to investigate the structural behaviour of angle-ply laminated plates. This drawback has been recently solved by introducing a new set of generalized zigzag functions that allow the coupling effect between the local contribution of the zigzag displacements [4]. The newly developed theory has been named enhanced Refined Zigzag Theory (en- RZT) and has been demonstrated to be very accurate in the prediction of displacements, frequencies, buckling loads and stresses. The predictive capabilities of standard RZT for transverse shear stress distributions can be improved using the Reissner’s Mixed Variational Theorem (RMVT). In the mixed RZT, named RZT(m) [5], the assumed transverse shear stresses are derived from the integration of local three-dimensional equilibrium equations. Following the variational statement described by Auricchio and Sacco [6], the purpose of this work is to implement a mixed variational formulation for the en-RZT, in order to improve the accuracy of the predicted transverse stress distributions. The assumed kinematic field is cubic for the in-plane displacements and parabolic for the transverse one. Using an appropriate procedure enforcing the transverse shear stresses null on both the top and bottom surface, a new set of enhanced piecewise cubic zigzag functions are obtained. The transverse normal stress is assumed as a smeared cubic function along the laminate thickness. The assumed transverse shear stresses profile is derived from the integration of local three-dimensional equilibrium equations. The variational functional is the sum of three contributions: (1) one related to the membrane-bending deformation with a full displacement formulation, (2) the Hellinger-Reissner functional for the transverse normal and shear terms and (3) a penalty functional adopted to enforce the compatibility between the strains coming from the displacement field and new “strain” independent variables. The entire formulation is developed and the governing equations are derived for cases with existing analytical solutions. Finally, to assess the proposed model’s predictive capabilities, results are compared with an exact three-dimensional solution, when available, or high-fidelity finite elements 3D models. References: [1] Tessler A, Di Sciuva M, Gherlone M. Refined Zigzag Theory for Laminated Composite and Sandwich Plates. NASA/TP- 2009-215561 2009:1–53. [2] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. Assessment of the Refined Zigzag Theory for bending, vibration, and buckling of sandwich plates: a comparative study of different theories. Composite Structures 2013;106:777–92. https://doi.org/10.1016/j.compstruct.2013.07.019. [3] Di Sciuva M, Gherlone M, Iurlaro L, Tessler A. A class of higher-order C0 composite and sandwich beam elements based on the Refined Zigzag Theory. Composite Structures 2015;132:784–803. https://doi.org/10.1016/j.compstruct.2015.06.071. [4] Sorrenti M, Di Sciuva M. An enhancement of the warping shear functions of Refined Zigzag Theory. Journal of Applied Mechanics 2021;88:7. https://doi.org/10.1115/1.4050908. [5] Iurlaro L, Gherlone M, Di Sciuva M, Tessler A. A Multi-scale Refined Zigzag Theory for Multilayered Composite and Sandwich Plates with Improved Transverse Shear Stresses, Ibiza, Spain: 2013. [6] Auricchio F, Sacco E. Refined First-Order Shear Deformation Theory Models for Composite Laminates. J Appl Mech 2003;70:381–90. https://doi.org/10.1115/1.1572901

Tracking and analysis of flamelet structures in turbulent non-premixed combustion

In this thesis, two approaches to analyze flamelet structures in turbulent non-premixed combustion are presented. The analyses are based on a highly resolved direct numerical simulation (DNS) of a temporally evolving turbulent syngas jet flame that was conducted to this end. First, the simulation is analyzed by means of a novel on-the-fly tracking procedure to assess the model assumptions of a recently published extended flamelet formulation, which in contrast to the classical flamelet model, explicitly accounts for flame-tangential transport effects. After the extended model is modified to describe flamelets in a Lagrangian manner, flamelets are tracked in the DNS with the help of tracer particles that are attached to the iso-surface of stoichiometric mixture fraction. At each time step, gradient trajectories (flamelets) are emitted from these particles and are traced along the ascending and descending gradient until a local extremal point is reached. The on-the-fly tracking procedure thus allows a detailed analysis of single flamelets in turbulent flames and a full reconstruction of flamelet histories for the first time. In a second step, the history of flamelet identities is recomputed by means of a flamelet solver and a distinction is made between three different approaches (i) the classical flamelet (FLT), (ii) the curvature-affected flamelet (FLT-C) and (iii) the multi-dimensional flamelet (FLT-MD). Comparing the results of the recomputed histories with the DNS, it turns out that the FLT and FLT-C approaches mostly fail to reproduce the DNS results. On the other hand, the full extended FLT-MD approach agrees very well with the DNS for all identities considered, indicating that curvature-induced flame-tangential transport is an important aspect to consider in flamelet modeling. The study is complemented by a budget analysis of instantaneous flamelet identities, with which it is possible to quantify transient effects for the first time. The second approach analyzing flamelet structures consists in decomposing the mixture fraction field into small subunits called “dissipation elements”. Dissipation elements are defined as the ensemble of all gradient trajectories that end at the same local extremal points (minimum and maximum). However, in contrast to the on-the-fly tracking this procedure is applied during the postprocessing of the DNS and allows to identify all gradient trajectories. Originally developed for the statistical analysis of non-reacting flows, this methodology promotes novel flamelet-based modeling strategies. Classifying dissipation elements according to the location of their extremal points, statistics are computed and analyzed for two instants of time, considering the Euclidean distance l of the extremal points, the scalar difference ∆Z, the arithmetic mean Zm and an approximate gradient g = ∆Z/l . These statistics lead to further conclusions regarding the location of dissipation elements in mixture fraction space and how they are affected by turbulent mixing. Last, joint statistics of the temperature and the species mass fraction of OH with respect to g are inspected. It turns out, that there exists a strong correlation between the approximated gradient g and the quantities T and YOH, respectively

Mathematical Modeling and Simulation in Mechanics and Dynamic Systems

The present book contains the 16 papers accepted and published in the Special Issue “Mathematical Modeling and Simulation in Mechanics and Dynamic Systems” of the MDPI “Mathematics” journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering. It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”