Elasto-plastic analysis of functionally graded metal-ceramic beams under mechanical loading

The elasto-plastic analysis of functionally graded (FG) metal-ceramic beams under mechanical loading by using the finite element method is presented. A bilinear stress-strain relation with isotropic hardening is assumed for elasto-plastic behaviour of metal, and the effective elasto-plastic properties of the functionally graded material are evaluated by using Tamura-Tomota-Ozawa (TTO) model.  A nonlinear beam element based on the classical beam theory is formulated and employed in the analysis. The element employed nonlinear von K\'am\'an strain-displacement relationship is derived by using the neutral surface as reference plane. The layer beam approach, in which the plastic rate equation is solved at Gauss points,  is adopted in updating the stress and evaluating the element nodal force vector and tangent stiffness matrix. Numerical examples are given to show the accuracy of the derived formulation and to illustrate the effect of the material distribution and plastic deformation on the behavior of the beams. The formation and propagation of plastic zone during the loading process is also examined and highlighted

LARGE DEFLECTION OF CANTILEVER FUNCTIONALLY GRADED SANDWICH BEAM UNDER END FORCES BASED ON A TOTAL LAGRANGE FORMULATION

A two-node beam element for large deflection analysis of cantilever functionally graded sandwich (FGSW) beams subjected to end forces is formulated in the context of total Lagrange formulation. The beams consist of three layers, a homogeneous core and two functionally graded layers with material properties varying in the thickness direction by a power gradation law. Linear functions are adopted to interpolate the displacement field and reduced integral technique is applied to evaluate the element formulation. Newton-Raphson based iterative algorithm is employed in combination with arc-length control method to compute equilibrium paths of the beams. Numerical investigations are given for the beam under a transverse point load and a moment to show the accuracy of the element and to illustrate the effects of material inhomogeneity and the layer thickness ratio on the large deflection behavior of the FGSW beams

Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation

Peer reviewedPostprin

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

Thermal Buckling of Metal Foam Sandwich Panels for Convective Thermal Protection Systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77175/1/AIAA-9741-678.pd

Machine learning assisted coupled frequency analysis of skewed multi-phase magnetoelectric composite plates with temperature and moisture dependent properties

In this article, the application of an artificial neural network (ANN)-based machine learning (ML) strategy to predict the coupled frequency of geometrically skewed multiphase magnetoelectric (MME) composite plate exposed to hygrothermal environment is presented. The ANN model is trained using a dataset comprising more than one million simulations conducted using an in-house developed finite element formulation. The underlying multiphysics governing equations are derived using Hamilton’s principle and higher-order shear deformation theory (HSDT). The influence of the hygrothermal environment on the elastic stiffness of MME composites is defined by the empirical constants in the constitutive relations. Four prominent combinations of the empirical constants leading to different elastic stiffness relations have been considered in this study. Alongside, the influence of geometrical skewness on the coupled fundamental frequency is also assessed. For the training of the ANN model, the Levenberg–Marquardt optimization algorithm with 30 neurons along with a tangent sigmoid activation function is used. The trained ANN model is tested on an unseen dataset, different from the training data, and it is shown to accurately predict the natural frequency of MME plate with a maximum error of 2.3%. Further, excluding the training time and considering the computational time alone, the ANN model is found to be 6.3 times faster than the FE simulations. It is anticipated that such ML-based reduced order models can be effective in the design process, especially in complex multiphysics problems, such as the one considered in the work, involving a multitude of geometric, loading and material parameters

Advanced Mechanical Modeling of Nanomaterials and Nanostructures

This reprint presents a collection of contributions on the application of high-performing computational strategies and enhanced theoretical formulations to solve a wide variety of linear or nonlinear problems in a multiphysical sense, together with different experimental studies

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Research and Technology, 1994

This report selectively summarizes the NASA Lewis Research Center's research and technology accomplishments for the fiscal year 1994. It comprises approximately 200 short articles submitted by the staff members of the technical directorates. The report is organized into six major sections: Aeronautics, Aerospace Technology, Space Flight Systems, Engineering and Computational Support, Lewis Research Academy, and Technology Transfer. A table of contents and author index have been developed to assist the reader in finding articles of special interest. This report is not intended to be a comprehensive summary of all research and technology work done over the past fiscal year. Most of the work is reported in Lewis-published technical reports, journal articles, and presentations prepared by Lewis staff members and contractors. In addition, university grants have enabled faculty members and graduate students to engage in sponsored research that is reported at technical meetings or in journal articles. For each article in this report a Lewis contact person has been identified, and where possible, reference documents are listed so that additional information can be easily obtained. The diversity of topics attests to the breadth of research and technology being pursued and to the skill mix of the staff that makes it possible

The Deformation Response of Polycrystalline MAX Phases Under High Strain-Rate Loading.

Mn+1AXn phase ternary compounds (or MAX phases) are a relatively newer class of nano-layered, ternary compounds (carbides or nitrides) which exhibit unique combination of properties typical of ceramics and metals. Hence, they are attractive candidates for use in structural applications. However, the responses of MAX phases under dynamic loading conditions have not been characterized extensively. In this dissertation, experimental protocols to characterize representative MAX phases (Ti2AlC and Ti3SiC2) under high strain-rates are developed using a Split Hopkinson Pressure Bar (SHPB) set-up. It is observed that Ti2AlC shows significant inelastic deformation and relatively higher strains before fracture, even at very high strain-rates (~up to 4700 s-1), underlying cause of which is attributed to kink banding of the nano-layered structure at sub-grain length scale. On the other hand, Ti3SiC2 exhibits a response more typical of ceramics and therefore additional modification to the experimental set-up and protocols are necessary. Local strain field analysis using Digital Image Correlation (DIC) shows that strain evolution is heterogeneous, underlying origins of which can be related to existence of grain clusters. The clusters span several grains that are identified as discrete homogeneous patterns on the strain distribution maps. The geometric properties of a grain and neighboring grain effects by virtue of its position in polycrystalline MAX phase are of relevance in dictating the deformation modes. A computational model is developed to capture the effect of grain geometry and multi-axial stress state experienced by a grain in a polycrystalline material due to its neighbors and applied external loading.PhDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133363/1/ribh_1.pd