Journal of Engineering Mechanics

Importance ranking of rock properties is important in allocating investigation resources, and then performing probabilistic analysis efficiently. Traditional global sensitivity analysis (GSA) can be employed to perform this ranking; however, it neglects (1) the epistemic uncertainties in the probability models and their parameters due to small sample sizes of inputs, and (2) the mutual dependence of inputs. This paper overcomes these limitations by introducing a stratified Bayesian multimodel inference (BMMI) coupled with moment independent GSA to estimate the imprecise sensitivity indexes (SIs) with complex copula-dependent inputs. The methodology initially identifies candidate marginal models and the uncertainties in their parameters by BMMI, which is employed to construct a model set comprising an ensemble of marginals estimated via the reweighting approach. Subsequently, this model set is used to quantify the uncertainties in the copula-based dependent structure using BMMI. The final step is to estimate the inaccurate SIs using the Monte Carlo–based moment independent GSA framework, which propagates an ensemble of joint densities to represent the overall uncertainty. The methodology is generalized in a way that it can be used for any number of complexly dependent inputs and eliminates the need to estimate conditional probability density functions (PDFs) and a precise copula otherwise required in mapping-based and traditional GSA. The methodology is demonstrated for two slopes, i.e., an infinite soil slope (two inputs) and a rock slope (four inputs). The methodology was accurate for both examples, and more informative than traditional GSA because it estimates the bounds of SIs reflecting the effect of epistemic uncertainties associated with dependent inputs with their point estimates from traditional GSA lying in their bounds.

The potential of a finite-element technique based on an egalitarian meshing of the space–time domain $\mathcal{D}$ of physical problems described by parabolic or hyperbolic differential equations is explored. A least-squares minimization technique is applied in the meshed domain $\mathcal{D}$ to obtain stiffness-like matrices associated with various linear differential operators. Applications discussed include problems of boundary growth, and diffusive coalescence, in which $\mathcal{D}$ cannot be regarded as the Cartesian product of two independent domains in space and time.

The Hermite polynomial model based on the first-four central moments of non-Gaussian distribution is widely applied to simulate non-Gaussian stochastic processes due to its simplicity and efficiency. Although a variety of expressions have been developed to approximate the coefficients of the Hermite polynomial model, unsatisfactory accuracy and limited applicability could still be encountered. Compared to the central moments, probability-weighted moments possess abundant characteristics of probability distribution. In this paper, a new form of Hermite polynomial model is proposed based on probability-weighted moments for simulating non-Gaussian stochastic processes. The coefficients of the Hermite polynomial model can be conveniently determined via a linear system of equations, leading to a wide application range of the model. More importantly, the sample accuracy for simulating non-Gaussian processes can be significantly improved, and the incompatibility problem can be avoided to some extent by using the proposed model. In addition, a fast strategy for determining the Gaussian auto-correlation function is also suggested, which avoids the complicated manipulations of cubic equations of Gaussian and non-Gaussian auto-correlation functions. A classical example is investigated to demonstrate the better accuracy and applicability over conventional Hermite polynomial models for simulating non-Gaussian stochastic processes. Two engineering cases are also investigated to demonstrate practical applications of the proposed model.

Negative Poisson’s ratio (NPR) auxetic metamaterials are attracting significant attention because of their peculiar and interesting mechanical features. Using geometrically von-Karman nonlinear factors and Mindlin plate theory, a smart multiscale hybrid (GPL/CF/PVDF) sandwich plate with a unique two-type functionally graded graphene origami auxetic (FG-GOA) is investigated here for its nonlinear vibrational behavior. The present properties of the electro-elastic layers were established using the Halpin–Tsai (HT) model and rule of mixing (ROM). Hamilton’s principle, Maxwell’s law, and the nonlinear factors of von Karman are used to determine the governing equations for the piezo plate. The subsequent step is to use the generalized differential quadrature (GDQ) technique to discretize the equations of motion for the sandwich plate. Results show that smart FG-GOA plates exhibit hardening nonlinearity. Nonlinear ratios of frequencies and natural frequency of the intelligent plate are also measured by electric voltage, the weight fraction of GPL, and the volume fraction of carbon fibers. Furthermore, the effect of the porosity coefficient, GOri folding degree, the FG-GOA core height, and the smart hybrid nanocomposite (SHNC) layer’s height on frequency ratio and nonlinear natural frequency were calculated and displayed for each figure.

Horizontal jet grouting columns (HJGCs) are commonly adopted to reinforce weak ground ahead of the tunnel excavation face. However, the dynamic mechanical response of the HJGCs during tunneling remains unclear. To provide a comprehensive understanding of HJGC reinforcement mechanisms and a basis for optimal design, a mechanical shell model for the HJGCs based on the two-parameter Pasternak foundation is initially established, and the analytical solutions for deflection and internal force are derived. Furthermore, the feasibility of the proposed model is validated through comparisons with numerical simulations based on an actual project. Subsequently, the mechanical behavior of the HJGCs and the sensitivity of the design parameters on the HJGCs deformation are examined. Additionally, the influence of various factors on tunnel face stability is deliberated. The findings suggest that the analytical solution derived from the proposed model aligns closely with the results obtained through numerical simulation. The longitudinal deflection pattern of the HJGCs is categorized into the airside impact zone, excavation disturbance zone, and forward stability zone. Significantly, the transverse deflection at the vault exhibits the greatest magnitude and gradually diminishes toward the arch foot. Longitudinally, the HJGCs reinforcement effectively serves as a spatial leverage mechanism, facilitating the redistribution of pressure within the spatial domain. In addition, the sequence of the impact levels of the discussed parameters or factors is presented individually.

Extreme waves pose one of the major threats to marine structures. Furthermore, their non-stationary nature makes proper stochastic analysis of their responses a challenging problem. To address this issue, this paper proposes a method based on a novel linear filter wave model incorporated into the dimension-reduced probability density evolution equation (DR-PDEE). The linear filter system is capable of simulating random background waves conforming with the Joint North Sea Wave Project (JONSWAP) spectrum of any arbitrary sea state by adjusting the parameters of filters directly related to the parameters of the JONSWAP spectrum without reidentification. In particular, by conducting the digital filtering, wave kinematics at different depths below the sea surface can be reproduced conveniently, and therefore only one filter is adequate for the depthwise wave kinematics field. Extreme ocean waves are treated as the superposition of background waves and extreme crests according to the constrained quasi-determinism method, with randomness from both parts. Incorporating the filter into the equation of motion of the offshore structure of interest leads to an augmented high-dimensional stochastic system with multiple random variables. The DR-PDEE then is employed to reduce the dimensions of the equation governing the evolution of probability density of responses of the original complex system to two. Solving the DR-PDEE using the path integral method yields the probability function of the response at each time step. A numerical example involving the response of a National Renewable Energy Laboratory (NREL) 5-MW spar-type floating offshore wind turbine (FOWT) subjected to extreme waves was studied to assess the reliability of the proposed method. The method provides an effective tool for the determination of the stochastic extreme response of offshore structures, and provides a foundation for further dynamic analyses.

We develop randomized neural networks (RNNs) with Petrov–Galerkin (RNN-PG) methods to solve linear elasticity and Navier–Stokes equations. RNN-PGs use the Petrov–Galerkin variational framework, where the solution is approximated by randomized neural networks and the test functions are piecewise polynomials. Unlike conventional neural networks, the parameters of the hidden layers of randomized neural networks are fixed randomly while the parameters of the output layer are determined by the least-squares method, which can effectively approximate the solution. We also develop mixed RNN-PG (M-RNN-PG) methods for linear elasticity problems to ensure symmetry of the stress tensor and avoid locking effects. For the Stokes problem, we present various M-RNN-PG methods that enforce the divergence-free constraint by different techniques. For the Navier–Stokes equations, we propose a space-time M-RNN-PG that uses Picard or Newton iteration to deal with the nonlinear term. Using several examples, we compare RNN-PG methods with the finite-element method, the mixed discontinuous Galerkin method, and the physics-informed neural network. The numerical results demonstrate that RNN-PG methods achieve higher accuracy and efficiency.

This paper presents an experimental study on how the crack-parallel stress affects the fracture properties of fiber-reinforced concrete (FRC) using the gap test—a new simple fracture test invented and used for concrete at Northwestern University in 2020. First, it was conducted for plain concrete and was successfully applied to cross-ply carbon-fiber composite and to aluminum. An advantage of this test is that it is unambiguous because the test setup changes from one statically determinate configuration to another. The gap test, combined with the standard notched three-point-bend test, is now applied to geometrically scaled FRC specimens to determine how the fracture energy, $G_f$, and the effective size, $c_f$, of the fracture process zone (FPZ), are changed by the crack-parallel stress, ${\sigma }_{xx}$. For ${\sigma }_{xx}$ equal to about $2/3$ of the standard uniaxial compression strength, the increase in $G_f$ is 64% and 78% for the two FRCs, respectively, which is large but not as large as the 126% increase observed in tests of plain concrete. This indicates that the fiber reinforcement mitigates the effect of ${\sigma }_{xx}$, while introducing some degree of ductility into the fracture process. The compressive ${\sigma }_{xx}$ also increases the effective size of the FPZ by about 81% and 64% while such increase is 134% in plain concrete. Because crack-parallel stresses are ubiquitous in practice, the implications for design are significant.

This paper presents a new discretize-then-optimize (DTO) method for dynamic force inversion in a two-dimensional (2D) linear elastic, damped solid based on Runge–Kutta (RK) explicit time integration. Previous literature on DTO modeling for force or material inversion has predominantly focused on inversion methods based on Newmark implicit time integration. However, because implicit time integration may not be suitable for a problem with a large number of degrees of freedom [e.g., third-dimensional (3D) wave problems], there is a need to study an alternative DTO force-inversion formulation that centers around the RK explicit time integration, leveraged by a diagonal mass matrix. This paper attempts to fill this gap and present the full detail of the new RK-DTO formulation for dynamic force inversion. Our computational examples demonstrate that the new RK-DTO inversion simulator effectively reconstructs moving dynamic forces on the upper surface of the solid. It excels in efficiency when dealing with a higher number of degrees of freedom (DOFs) and maintains accuracy even with increased DOFs and observation durations. A smaller sensor spacing enhances the accuracy of the inverted force profile in the RK-based inversion. The presented inversion method can effectively identify the profiles of dynamic moving loads even when measurement data include noise or when the values of material properties are not deterministic.

The morphological origin of sand shear modulus at small strains ($G_{\max }$) remains poorly understood. This paper introduces spherical harmonic analysis to define multiscale particle morphologies of two typical natural sands: calcareous sand (CS) and Fujian sand (FS). Three distinct scale levels were taken into consideration: general form (large), local roundness (medium), and surface roughness (small). The 3D printing technique was employed to produce uniformly graded sand analogs with independent control of grain shape. Bender element tests were subsequently conducted on these analogs after isotropic consolidation in triaxial apparatus to obtain their shear wave velocities and small-strain shear moduli. The results highlight the substantial enhancement of $G_{\max }$ through irregular particle morphologies within uniformly graded sand. Notably, the general form (large scale) emerges as the primary morphological determinant of the enhanced $G_{\max }$. Parameters of Hardin’s equation—material coefficient $A$ and stress exponent $N$—are demonstrated to reflect the comprehensive $G_{\max }$ pattern and its sensitivity to confining stress, respectively. The reduction of $N$ with diminishing overall regularity indicates the weakening effect of morphological irregularity on $G_{\max }$’s sensitivity to confining stress. Remarkably, the medium-scale level yields the lowest $N$ value, emphasizing the pivotal role of local roundness as the predominant morphological factor in this effect.