Journal of Engineering Mechanics

Underground structures provide more effective protection against air blast and surface explosions compared with their aboveground counterparts, but their safety is threatened by subsurface detonations due to the strong coupling between the explosion energy and the surrounding soil. For a certain standoff distance between the explosion center and buried structure, the inside equipment may be damaged by the strong vibration within the structure, while the structure itself experiences minor or even no damage. This strong vibration, not damaging the main structure, but damaging the contained equipment, is termed in-structure shock. In the present study, a theoretical model is established to evaluate the in-structure shock environment of a buried arch–wall structure subjected to overhead subsurface detonation. Dynamic soil-structure interaction, as well as different response modes including local deflection and global rigid body motion, are incorporated to determine the response of the concerned structural member. A small-scale field test was conducted to validate the proposed model. Subsequently, shock response spectra are employed to characterize the in-structure shock level within the structure. Furthermore, a parametric study is conducted to examine the influence of governing parameters on the structural response and consequent in-structure shock level, including soil parameters, ground shock characteristics, scaled distance, and location. The present study not only provides a method for quick assessment of the in-structure shock level of underground arch–wall structures subjected to overhead ground shock in preliminary design but also extends the theoretical prediction of buried structure response from the directly loaded members to opposite ones.

In this paper, new fundamental solutions for dynamic analysis of plane elastodynamics are developed. The governing dynamic differential equations are rewritten by replacing the accelerations with the corresponding displacements at different time steps via a suitable finite difference scheme. The known displacements in initial conditions or from previous time steps are treated as generalized new inertia terms. The unknown displacements at the current time step are added to the governing differential operator to form a new operator. The new time-dependent fundamental solutions are then derived with respect to the new differential operator. The required mathematical derivations are presented in detail. The corresponding integral equations and domain load treatments are also presented. Singular integrals of the derived fundamental solutions are also treated. Several numerical examples are solved to demonstrate the validity and the accuracy of the developed new solutions. The results demonstrated the accuracy of the developed new solutions compared to traditional time domain fundamental solutions.

The fractional viscoelastic model has been applied to characterize the viscoelasticity of asphalt concrete (AC), but it rarely is adopted in pavement structure analysis due to the complicated calculating process. Therefore, simple methods of applying the fractional viscoelastic models in the pavement mechanic analysis are proposed. First, based on the derived complex modulus expressions of the typical fractional viscoelastic model of AC, combined with the particle swarm optimization and interior-point algorithm, a novel global optimization algorithm for the parameter identification of fractional viscoelastic models is proposed. Then, based on the dynamic modulus and phase angle data obtained in laboratory experiments, the viscoelastic parameters of AC were identified, and the performance of different viscoelastic models was evaluated. Subsequently, based on the Grünwald–Letnikov definition of the fractional operator and the Newton–Raphson integration scheme, the numerical implementation algorithm of some typical fractional viscoelastic models of AC in finite element analysis is proposed, followed by compiled user material subroutines (UMATs). Finally, the thermoviscoelastic analysis of an asphalt pavement structure under impact load was conducted, and the mechanical response laws revealed by different viscoelastic models were investigated. The results showed that the fractional viscoelastic model could yield a more accurate prediction of the viscoelasticity of AC in a wider frequency domain compared with the integer-order viscoelastic model. Moreover, due to the ability to simulate the mechanic behavior of the pavement structure in all temperature ranges with fewer parameters, the modified fractional Zener model is recommended for pavement mechanics analysis.

The analysis of long-term rheological consolidation behaviors of soft soils is the research focus in geotechnical and geological engineering. This paper develops an analytical theory to explore such behavior within layered viscoelastic sediments in a three-dimensional (3D) Cartesian coordinate system. Starting from the governing equations of 3D consolidation problems and introducing the displacement functions, the state vectors between the surface and an arbitrary depth of a finite soil layer are established in the transform domain. With the aid of this relationship and continuity conditions between adjacent layers and the boundary conditions of the layered system, an analytical solution for viscoelastic soils is then obtained. Detailed comparisons are given to confirm the applicability of the theory, followed by typical examples examining the effect of types of viscoelastic model, fractional order, and soil layered properties on the coupled rheological and consolidation responses. In the present theory, the state space equation containing eight coupling state vectors is uncoupled into two sets of equations of six and two state vectors based on three displacement functions and a decoupling transformation, which has the advantage of cutting the computation amount and proves to be remarkably efficient and practicable in solving the 3D rheological consolidation problems.

An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstration example.

A multiscale crack iteration and remeshing model was proposed and implemented to predict the low-cycle crack propagation behavior for steel. Crack propagation behavior was quantified by fatigue indicator parameters (FIPs) in the crystal plasticity model. Once the crack propagation rate and direction were determined in the grain, the crack seam was inserted into the model by remeshing in postprocessing. To further relax the fatigue driving force and reduce the impact of FIP variation, an iteration procedure, in which sufficient computational cycles were preselected and iterated during the simulation, was applied to the mesoscale model. Additionally, the boundary conditions of the mesoscale model were obtained from the macroscale model by the multiscale simulation method. A three-point bending fatigue test was carried out to validate the iteration and remeshing model. The experimental results showed two cracks generated from the upper and lower surfaces during the fatigue test, and the crack propagation rate increased as the crack grew toward the center region. Meanwhile, the numerical model, including two initiated cracks, was implemented corresponding to the central region in the experimental specimen. By applying the boundary condition from the macroscale simulation associated with the experiment, the two cracks grew during the iteration and remeshing. The simulation results showed two cracks growing gradually toward the region with a reasonable number of cycles. The zigzag pattern simulated from the mesoscale model also qualitatively correlates well with the observation from experimental results.

In the framework of recent research on Fourier’s heat conduction law with fractional orders, a novel model of Green-Naghdi of type II (GN II) thermoelasticity has been devised. The uniqueness theorem has been established for a unified heat transport equation. As limit instances, certain theories are presented. The problem is solved using the Laplace and Fourier transform techniques. By using a complex transform reversal formula, Fourier expansion techniques are utilized to quantitatively build the reverses of Fourier transforms and Laplace processes. For temperature, displacement, and stress distributions, numerical findings are presented and visually displayed. The findings obtained for various choices of time-fraction parameters create certain correlations.

In this study, the use of submerged dual poroviscoelastic barriers with finite depth enclosing a floating compliant platform that supports utility systems, such as a solar photovoltaic system, on top is investigated as a protection measure against surface wave action. An analytical analysis of the wave interaction with the barrier-platform configuration is performed using eigenfunction expansion with least square approximation that takes full account of the hydroelastic behavior of the barriers. The results show that the platform displacement decreases as the barrier hydroelastic regime shifts from plate-like to membrane-like with increasing tension. In addition, a longer barrier at the incident front side of the platform yields better performance than an equal length on both sides given the same total barrier dimension. An increase in the porosity of the barriers reduces the displacement and wave loading on the barriers but leads to simultaneous higher wave transmission and larger platform displacement. The higher transmission is reduced by the internal dissipation properties of the barrier material. Overall, the dual barriers with sufficient length and appropriate poroviscoelastic properties can significantly improve the stability of the floating platform, and its performance can be tuned through varying the hydroelastic regimes and barrier-length combinations.

The nonlinear dynamic deflection and stress responses of a multilayered shallow shell structure with cutout subjected mechanical pulse load were investigated. The theoretical model was developed using equivalent single-layer theory in the context of third-order midplane displacement polynomials. The geometrical nonlinearity was introduced using Green-Lagrange (retaining higher-order small strain terms) and von-Karman strain (neglecting the small-strain terms of higher order) to account for large-amplitude oscillation of the shell structure. Hamilton’s variational principle was used to derive the equation of motion. The nonlinear solution was calculated using the direct iterative method. Following the derived mathematical expressions, a computational program was prepared using the isoparametric finite-element (FE) approach in the MATLAB version 2018a platform. The computational model cogency has been confirmed by relating the results to previously published results. Besides, experimentally obtained dynamic deflection values were compared with computational results. The results highlight the importance of the nonlinear terms in the Green-Lagrange strain, which are neglected under the von-Karman assumptions. The critical dynamic behavior of the laminated shallow shell structure with the cutout of variable shapes and sizes was examined by varying geometrical, boundary support, and loading conditions.