Journal of Engineering Mechanics

The transient coupling between the vessel motion and liquid sloshing in multiple tanks is investigated. External disturbance factors (e.g., spring constraint or force field) that might affect the oscillation characters of the coupling system are not involved so that the vessel motion is only excited by the liquid sloshing in tanks. The analytical solution for this coupling problem has been derived based on the potential flow theory, which converts the problem to a linear system of ordinary differential equations. The approach to determine natural frequencies of the coupling system is also given. The vessel with one or more rectangular tanks is considered for cases studies. Effects of factors, such as vessel mass, number of tanks, tank configuration and free-surface deformation on the vessel motion, liquid sloshing, and mechanical-energy components of the system are studied systematically.

In this paper, an upper-bound solution for the FCEM is proposed to study the effect of the plastic behavior of soil on the interpretation of a flat dilatometer test. Kinematically admissible displacement fields for the FCEM are derived from Zhou’s elastic solutions for an incompressible material. These displacement fields are then used to obtain an upper-bound solution for a FCEM based on energy conservation principles that the sum of the plastic and elastic work of soil is equal to the flat cavity expansion work, with yield being defined using the Tresca yield criterion. The upper-bound solution is validated by comparing the calculated list-off pressure for the flat dilatometer test using both the proposed upper-bound solution to an elastic solution and a series of field test data. The results show that the proposed upper-bound solution is better than the elastic solution in interpreting the flat dilatometer test.

A new state-space model is formulated for the dynamic analysis of sandwich beams that are made of two thin elastic layers continuously joined by a shear-type viscoelastic (VE) core. The model can accommodate different boundary conditions for each outer layer and accounts for the rate-dependent constitutive law of the core through additional state variables. The mathematical derivation is presented with the Standard Linear Solid (SLS) model (i.e., a primary elastic spring in parallel with a single Maxwell element) and then extended to the generalized Maxwell (GM) model. The kinematics equations are developed by means of Galerkin-type approximations for the fields of axial and transverse displacements in the outer layers, and imposing the pertinent compatibility conditions at the interface with the core. Numerical examples demonstrate the accuracy and versatility of the proposed approach, which endeavors to represent the effects of the VE memory on the vibration of composite beams.

This paper presented new analytical solutions for the elastic buckling of Eringen’s nonlocal columns with allowance for selfweight. A discrete column model on the basis of the central finite difference formulation and the equivalent Hencky bar-chain model also were presented for this buckling problem. The discrete column model allows one to determine the buckling solutions of columns constructed from repetitive cells. In addition, one may use the discrete buckling solutions to calibrate the small-length scale coefficient $e_0$ in the Eringen’s nonlocal column model. It was found that $e_0$ values varied from 0.289 to 0.373 with respect to increasing selfweight for clamped-free column case, from 0.289 to 0.276 for the pinned-pinned column case, and from 0.289 to 0.281 for the clamped-clamped column case.

An analytical model is proposed in this paper to evaluate the residual flexural strength for corroded RC beams. The steel slipping caused by bond degradation is included in the proposed model. Various failure modes of beams caused by different types of steel bar anchorage are also incorporated in the model. The bond degradation is considered as a function of the corrosion rate of steel. Bond degradation transfers prematurely the effective bond force, resulting in incompatible strain within the slipping region. A new method is developed to quantify the slipping region based on the transfer theory of effective bond force. Next, a new strain-incompatibility analysis method is proposed to determine the deteriorated flexural strength. The accuracy of the model is validated by experimental observations on the beams with different steel anchorage under corrosive environments. Results show that the proposed model can provide a reasonable prediction for the flexural strength and failure modes. The strain incompatibility of the corroded beams is sensitive to corrosion loss and loading position. It becomes very significant for the beams with a corrosion loss greater than 7% and the beam with a concentrated load at the midspan.

This paper introduces a novel gradient inelastic beam theory and a corresponding flexibility-based (FB) frame element formulation to treat major weaknesses of existing FB formulations in the presence of softening section constitutive relations (or softening material response). These weaknesses include (1) strain localization and loss of objectivity and (2) instabilities and convergence failures of the numerical solution algorithms. These weaknesses are shown to emanate from the pathogenies of Navier’s beam theory in the presence of softening section constitutive relations. These pathogenies include (1) loss of solution uniqueness; and (2) loss of spatial continuity of the strain field, under a continuous force field. The proposed gradient inelastic beam theory is derived by enriching Navier’s beam theory with nonlocal section deformation variables through gradient-based equations. For the proposed theory, a FB formulation is developed. This FB formulation (1) results in a single set of algebraic equations, which, in its discretized form, can be solved by a Newton-Raphson iterative algorithm, as opposed to other formulations that use complicated solution algorithms employing nested iterative loops; (2) does not impose any restrictions on the type/form of the selected stress-strain constitutive laws, which are solely expressed in terms of local variables; and (3) is general, such that Navier’s (local) beam theory is a special case of it. The proposed FB formulation is shown to alleviate strain localization and loss of objectivity, and reduce instabilities and convergence failures of the numerical solution algorithm. However, solution uniqueness is not achieved.

To investigate the interface mechanics and fracture properties and establish an interface tension-softening constitutive law between concrete and rock for analyzing fracture failure of rock-concrete structures, uniaxial tension and three-point bending tests are conducted on rock-concrete composite specimens with artificial grooving or natural interfaces. Tensile strength, fracture energy, and initial fracture toughness of a rock-concrete interface are obtained from experimentation. Based on the load-displacement curves measured in the three-point bending test, the energy dissipation at a rock-concrete interface is derived using the modified J-integral method. In addition, through enforcing a balance between energy dissipation and energy generated by fictitious cohesive forces acting on the fracture process zone (FPZ), the tension-softening constitutive law of a rock-concrete interface is established, which takes into account the effects of fracture energy and tensile strength of an interface. For the sake of practical applications, the tension-softening constitutive expression is simplified as a bilinear function. Finally, the crack propagation process of a series of concrete-rock composite beams is simulated numerically based on a nonlinear fracture mechanics theory by introducing a crack-propagation criterion. The predicted load versus crack mouth opening displacement (P-CMOD) curves show a reasonable agreement with the experimental ones, verifying the tension-softening constitutive law for the rock-concrete interface derived in this study.

As the importance of wind-induced internal pressure for building safety has continually been highlighted, increasing attentions have been paid to numerical methods for estimating fluctuating internal pressures, leading to the emergence of numerous second order nonlinear governing equations with two ill-defined parameters, namely inertial coefficient ($C_I$) and loss coefficient ($C_L$). Because resonance frequency and damping ratio of fluctuating internal pressures are susceptible to the values of inertial and loss coefficients, respectively, a correct understanding, and reasonable estimates, of these two parameters are required before using the governing equations to predict internal pressure responses. Compared with the inertial coefficient, which can be easily obtained from the Helmholtz frequency, a wider range of values of loss coefficient is in use, therefore this study focuses on the more uncertain parameter $C_L$ and presents an alternative method to identify loss coefficients of measured internal pressures without the onerous fitting works required by the current method. The reliability of this method is then verified using both wind tunnel tests and random excitation experiments using a loudspeaker specially designed for internal pressure studies. Potential influence factors for loss coefficient $C_L$ including opening size, opening shape, and magnitude of external pressure at the opening are investigated. The results indicate that (1) loss coefficient increases with opening area and depth, but decreases when external pressure strengthens; (2) the opening shape has a limited effect on the loss coefficient; and (3) $C_L$ is estimated to be in the range of 19–234 for varying opening sizes.

The evaluation of seabed response around an offshore pipeline has been studied since the 1980s. Most previous investigations considered full backfilled conditions. However, partial backfill is normally used in engineering practice, rather than full backfill. In this study, a two-dimensional (2D) integrated numerical model (PORO-WSSI-PIPE) is proposed to investigate the wave-induced residual liquefaction in a seabed around a partially backfilled trenched pipeline. The present model is validated through the comparison with previous laboratory experiments to ensure its accuracy and effectiveness. Sensitivity analysis indicates that the thickness of backfills significantly affects the wave-induced pore pressure around a trenched pipeline, and liquefaction may occur in the underlying trench layer with shallow backfill under large waves and in shallow water. Based on the numerical examples, a simplified approximation for the design of the thickness of backfills ($H_b$) with given wave and soil parameters is suggested for engineering practice, in which the pipeline can be prevented from seabed liquefaction.

Higher-order elements frequently render accurate results and allow the reduction of the total number of elements required to represent a given structure. However, element order also affects the efficient time-history integration of the associated equations of motion in Lagrangian dynamics by an explicit method, which is only conditionally stable. The integration time step is affected by element type and must be sufficiently small to avoid instability of the computed solution and, simultaneously, should be sufficiently large for an economic analysis. The upper bound to the size of this step in an analysis is rigorously obtained from the solution of the eigenvalue problem to the global system of equations of the entire finite-element model. Common alternatives to this computation are to approximate the time step by much simpler one-dimensional node-to-node or individual elemental eigenvalue approaches. Robust higher-order finite-element formulations have recently been developed for explicit integration, but time-step determinations have been primarily limited to the one-dimensional approach. In this paper, the individual elemental eigenvalue approach is further used to study the critical time step for several practical higher-order element types (27-node bricks, 16-node thin plates, 15-node tetrahedra, and 21-node wedges). Parametric studies on the variables controlling their critical time steps are discussed.

Flexible pavements are multilayer structures, typically with a viscoelastic asphalt layer followed by nonlinear unbound/bound layers. Conventionally, multilayered elastic analysis is performed to obtain the response of flexible pavements for design and inverse analyses; however, assuming asphalt pavement to be a linear elastic material is an oversimplification of its actual behavior. It is well known that the responses of asphalt pavements are both rate and temperature dependent. In the present work, a computationally efficient model has been developed to analyze flexible pavements, considering the top layer of linear viscoelastic asphalt concrete (AC), followed by a stress-dependent (nonlinear) base layer, and an elastic subgrade. Constitutive equations are formulated for layered viscoelastic–nonlinear axisymmetric systems. It is shown that the developed model can be used to simulate pavement response under stationary or transient loading. A comparison between the model responses and results obtained using a finite-element (FE) model shows that the model could be used to simulate both deflections and stress responses in multilayer viscoelastic nonlinear structures. The primary advantage of the model, as opposed to FE models, is its computational efficiency. This makes it viable for use in backcalculation algorithms.

This paper carries out the numerical simulation of tsunami propagation based on the fully nonlinear and highly dispersive Boussinesq model. The numerical results indicate that the waveforms of a tsunami are quite different on steeply and mildly sloping beaches, which cannot be predicted by the analytical solution of the nonlinear shallow water equations. Long wave trains form on the steeply sloping beaches while undular bores emerge on the mildly sloping beaches. The simulation of hypothesized tsunamis in the China Seas provide different wave patterns in the near shore regions, including long wave trains, undular bores, and solitons. In order to study the propagation and run-up of undular bores, a series of undular bores is proposed by sinusoidal and attenuation functions. The properties of the run-up and energy budget of these undular bores are investigated.