Journal of Engineering Mechanics

We investigate the generalization of a convolutional neural network (CNN)-based surrogate for the phase field model in predicting both damage and peak load under uniaxial tension, given the two-dimensional (2D) microstructure image of a unidirectional fiber–reinforced composite. We first discuss the phase field model and the numerical procedure to generate training and test data from synthetic microstructures with different volume fractions and fiber radiuses. We next present a two-stage approach for predicting peak load, achieved by first transforming a given fiber-encoded microstructure image to a continuous damage field; and second, predicting peak load from the damage field. A key finding is that the direct approach for predicting peak load from the microstructure image using a standard regression model fails to generalize. Instead, the damage field, even if imperfectly predicted, provides valuable cues for the CNN in generalizing across new microstructures within the range of parameters used in training. We describe several case studies to demonstrate the capability of the surrogate model to predict damage and peak load, and to interpolate over fiber radiuses and volume fractions.

In this paper, thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) are investigated within the framework of third-order shear deformation theory (TSDT). CNT distribution along the thickness direction of the plate is uniformly or functionally graded. The equivalent properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations of motion are derived using the Hamilton principle. Obtained governing differential equations are analyzed by utilizing Fourier series expansion along the longitudinal and latitudinal direction for simply supported edges boundary conditions whereas for other edges boundary conditions we used the differential quadrature method (DQM) to solve numerically. Validation of the present formulation is assessed by comparing the results with those reported in the open literature. The effect of CNT volume fraction, the different patterns of CNT distribution, temperature difference, aspect ratio, and thickness-to-length ratio on buckling and vibration behavior of carbon nanotube-reinforced composite (CNTRC) plate is studied. The numerical illustration reveals that in the FG-X pattern of CNT distribution natural frequency and thermal buckling load is more significant compared with the other patterns of CNT distribution.

An exact analytical solution, in terms of Bessel functions, was derived for the dynamic response of a shear beam with uniform cross section and mass density, and shear modulus that varies exponentially in the axial direction. The solution was generalized to a chain of such beam elements. The model may be appropriate for frame structures, which deform predominantly in shear, with gradually increasing rigidity toward the base. The results of a parametric study are presented for the frequencies of vibration and their ratios, mode shapes, transfer functions, and impulse response functions. The gradation affected the ratios between the frequencies of the higher modes of vibration and that of the fundamental mode, which were smaller than the corresponding ratios for a homogeneous shear beam and were progressively smaller for larger gradation constants. The mode shapes and the ratios of the amplitudes of the pulses in impulse response functions had amplitude amplification toward the top, which was larger for larger gradation constants, and suggests trapping of energy in the upper part of the structure. This effect may be responsible for observed damages and failure of structures in parts far from the base. The gradation also affected the symmetry and shape of the pulses in impulse response functions. The results of the parametric study may be useful for interpretation of the seismic response of full-scale structures. The model is intended for use as a simple surrogate model in structural system identification and health monitoring of frame structures.

This work investigates five different instability mechanisms that may occur and interact in straight-bladed H-rotor vertical-axis turbines. Specifically, it considers the static instabilities of divergence and centrifugal buckling as well as the dynamic instabilities of flutter, main resonance, and parametric resonance. This is done by applying Theodorsen’s model for unsteady aerodynamics with traditional finite element methods. The resulting model comprises bend-twist-coupled elements that inherently account for fluid and centrifugal effects. Comparisons with experimental results in the literature are used to assess the accuracy and limitations of the model. Eigenvalue analysis is used on time-averaged equations to predict divergence, flutter, and centrifugal buckling, as well as identify regions where main and parametric resonance may be excited. Time history analysis is used to provide further insight and show main and parametric resonance explicitly. Stability plots are constructed using both methods of analysis and presented in the forcing parameter space. Interaction between the different instability mechanisms is observed, including a region of parametric stabilization that is found to extend beyond the expected boundaries of both divergence and flutter.

Previous studies have demonstrated that macroscopic liquefaction behavior is closely related to the evolution of the microstructure (fabric) of soils. Here we perform three-dimensional (3D) discrete-element method (DEM) simulations of soil liquefaction considering irregular shapes of Toyoura sand particles, which are approximated by 3D clumps. We introduce the Minkowski tensor to quantify the anisotropy of the particle-void cells around each clumped particle, and propose two void fabric proxies, $E_d$ and $A_d$. The evolution of $E_d$ and $A_d$ during the entire liquefaction process and their effects on pre- and postliquefaction behaviors are investigated. Specifically, $E_d$ quantifies the shape elongation of particle-void distribution, while $A_d$ represents anisotropy of the particle-void orientation, which is closely correlated with the flow strain accumulation. We further quantify irreversible changes in fabrics and anisotropic load-bearing structures developed in liquefaction processes, and propose fabric-based criteria for jamming transition in flow deformation. The volumetric strain during reconsolidation is well correlated with $E_d$ and $A_d$, whereas the jamming transition during liquefaction can only occur if $A_d$ becomes sufficiently large. The interplay between strain, stress, and fabric evolution during pre- and postliquefaction will improve fundamental understanding and modeling of liquefied soils.

This paper presents a new Bayesian approach for estimating input and state in linear structures using response-only measurements. The proposed approach benefits from a modally reduced state-space model, which circumvents the dimensionality of dynamical responses in complex structures through a low-dimensional subspace. It also substitutes unknown physical forces with a set of equivalent modal forces, which is beneficial when the magnitude and location of input forces are unknown. In this work, these forces are characterized through the conventional random walk model and a class of stationary Gaussian processes. Subsequently, an augmented state-space model is constructed to describe modal states and input loads. Based on this model, a Bayesian expectation-maximization (BEM) methodology is developed to identify the input, state, and noise parameters. This noise identification perspective activates uncertainty quantification in joint input-state estimation problems and enables quantifying the degree of confidence in the estimated quantities. When the proposed method is tested using numerical and experimental examples, accurate estimations and reasonable uncertainty bounds are acquired for the dynamical state and input forces. Although the literature reports the superiority of the Gaussian process latent force model over the random walk model without using a unified noise calibration strategy, this study, to our best knowledge, is the first effort to compare and interpret the results on a consistent basis where the noise and input characteristics are all identified from the data through BEM.

Shape sensing, which is the real-time monitoring of deformed shapes using discrete surface strain, is a fundamental approach to ensure structural safety, reliability, and affordability. Large deformation shape sensing is obviously more important because large deformations can result in structural damage and failure. Nevertheless, there are few effective methods for the shape sensing of large deformations. Based on Timoshenko beam theory, this paper establishes a new method, called analogy stiffness upgrading (ASU), to reconstruct nonlinear deformation. In this method, the inverse finite element method (iFEM) is used to predict the initial displacement field and compute the analogy stiffness matrix. Then, the analogy stiffness matrix is upgraded by using coordinate transformation from a co-rotational procedure. Through iterative computation, the real displacement field is finally obtained when the rotation angle calculated from the input strain data is the same as the integral result from the section strain data. Numerical examples and model tests are carried out to verify the ASU method. It is evident from the results that the ASU method can predict largely deformed shapes of beam structures with superior precision.

In this work, we present a multifidelity Bayesian optimization framework for designing architected materials with optimal energy absorption during compression. Data from both physical experiments (high fidelity) and numerical simulations (low fidelity) are fed in parallel to train the surrogate model, which iteratively decides the next sets of experiments and simulations to run in order to find the optimal structural parameters. We show that having multifidelity data sources allows the optimization framework to find the optimum after fewer iterations relative to using a single high-fidelity source. This saves both material costs and time in the optimization process. Finally, we also apply constraints (on relative density and stress variations) to the optimization process, finding optimal structures within the bounds of the constraints. This framework can be translated to other problems that require complex, high-fidelity, labor-intensive experiments while automating low-fidelity simulations.

Abstract

For landslide mitigation, stabilizing piles are widely adopted in geotechnical engineering practice. The formation of soil arching between stabilizing piles can greatly mitigate the lateral spreading of sandy soil, and complementarily, evidence demonstrates that the sandy soil properties have a significant influence on the soil arching process. Thus, this paper focuses on investigating the lateral arching evolution behaviors in both dense and loose sands. A discrete element method (DEM) involving the servo-mechanism that plays a role in quantitatively controlling the translational velocity of selected walls when a desired force is to be applied or maintained was carried out to simulate the dynamic evolutions of the lateral soil arching process. The double-arch model is proposed to illustrate the end-bearing arch and frictional arch to analyze soil arching effects separately. Results indicate that the macrobehaviors and microbehaviors of lateral soil arching in dense and loose sands are initially distinct but ultimately similar. The arching mechanism is also illustrated by fabric analysis and coordination numbers. In general, the lateral arching evolutions in both dense and loose sands can be divided into three evolutionary stages as the loading displacement increases, which are similar to the strain-hardening and strain-softening phenomenon, respectively. Similarly, a unique arching process of forming-breaking-forming is identified by the use of particle trace. Moreover, multiple two-dimensional DEM models at different depths are superimposed vertically to study the three-dimensional soil arching. Based on the parametric studies, the loading velocity and pile spacing ratio have a preponderant influence on the development of soil arching, whereas the influence of the depth and confining stress is almost negligible. Additionally, the distribution of horizontal thrust has been determined by monitoring the stabilizing pile-based arching foot at different locations and the distribution of shear resistance is found to be approximately triangular.

Practical Applications

To mitigate the lateral spreading of sandy soil slopes, the stabilizing piles have been widely adopted in geotechnical engineering practice. The lateral spreading forces of soils behind the stabilizing piles will create various forms of soil arching effect, which is a favorable phenomenon for conducting cost-effective engineering design. In this study, we employed the two-dimensional discrete element modeling method to study the dynamic evolution of the lateral soil arching effect. The influence of the soil-structure relative movement, stabilizing pile spacing ratio, and confining stress for both dense and loose sands on the arching evolution and performance has been systematically studied. We found that the frictional arching was always negligible compared with the end-bearing arching accounting for the dominant role of double-arch model. The development of the lateral soil arching for both sands discloses three evolutionary stages, which conforms to the generic rule of strain softening for dense sand and strain hardening for loose sand. It is anticipated that the results of this study will eventually provide a certain reference value for the design of pile-reinforced earth slopes.

In this article, an extended and more generalized method of homotopy analysis method (HAM), known as q-homotopy analysis transform method ($q$-HATM) is employed to develop solutions for highly nonlinear form of various time-fractional advection-dispersion models (TFADE). The proposed methodology of $q$-HATM is a conjunction of two different strong methodologies, that are HAM and Laplace transform technique (LTT) which makes the scheme much more capable to develop the convergent series solutions for differential equations with high nonlinearity. In this work, two different examples are constructed for the nonlinear time-fractional form of dispersion models corresponding to distance dependent dispersion and velocity components and also for the time dependent decay rate system and solutions are constructed by using $q$-HATM in generalized form. The graphical comparison is made for different types of variable functions and also for the different fractional order indexes. Prominent impact of fractional derivative indexes is significantly observed over both the examples of dispersion models. Hence, proposed examples shows that the $q$-HATM is much convenient to handle the nonlinear systems of fractional models.

We present a new convolutional neural network (CNN)-based element-wise classification method to detect a random number of voids with arbitrary shapes in a two-dimensional (2D) plane-strain solid subjected to elastodynamics. We consider that an elastic wave source excites the solid including a random number of voids, and wave responses are measured by sensors placed around the solid. We present a CNN for resolving the inverse problem, which is formulated as an element-wise classification problem. The CNN is trained to classify each element into a regular or void element from measured wave signals. Element-wise binary classification enables the identification of targeted voids of any shapes and any number without prior knowledge or hint about their locations, shape types, and numbers, while existing methods rely on such prior information. To this end, we generate training data consisting of input-layer features (i.e., measured wave signals at sensors) and output-layer features (i.e., element types of all elements). When the training data are generated, we utilize the level-set method to avoid an expensive remeshing process, which is otherwise needed for each different configuration of voids. We also analyze how effectively the CNN performs on blind test data from a non-level-set wave solver that explicitly models the boundary of voids using an unstructured, fine mesh. Numerical results show that the suggested approach can detect the locations, shapes, and sizes of multiple elliptical and circular voids in the 2D solid domain in the test data set as well as a blind test data set.

The accuracy of the optimally blended spectral-element method for wave propagation in a homogeneous transversely isotropic elastic medium was investigated. A nonstandard quadrature rule obtained by combining Gauss quadrature rule and Gauss–Lobatto–Legendre quadrature rule was used to compute elementary matrixes. The mass and stiffness matrixes were represented as the triple tensor-product of elementary matrixes as second-order tensors. The solution of the eigenvalue problem representing the semidiscretized version of elastic wave equation for plane harmonic wave propagation was obtained using the Rayleigh quotient approximation technique. The resulting eigenvalues subsequently were used to estimate the phase and group velocity of three bulk waves. The variations of the errors in these velocities of the bulk waves with the number of grid points per wavelength were depicted graphically. These variations were shown for different polynomial orders and various angles of deviation from the symmetry axis. The effect of a change in the order of time discretization on error variation also was shown. The solution obtained by the optimally blended spectral-element method was found to be more accurate than that from the classical spectral-element method for low-order polynomials. The improvement in solution accuracy was demonstrated through dispersion analysis.