Journal of Engineering Mechanics

A Wiener path integral (WPI)-based approximate technique is developed for determining the joint response probability density function (PDF) of a class of one-dimensional stochastic mechanics problems. Specifically, employing a variational formulation and relying on the concept of the most probable path, the original stochastic problem is recast into a number of deterministic boundary value problems (BVPs) to be solved numerically. Next, it is shown that by employing a Rayleigh-Ritz solution scheme for the BVP, and potentially combining with an appropriate expansion for the joint response PDF, the total computational cost of the technique is kept at a minimal level. In particular, the system response PDF at a specific point in space is determined by solving only very few deterministic systems of algebraic equations. The developed WPI technique can account for nonhomogeneous stochastic fields modeling the material properties as well. Further, it can be construed as a local technique due to the fact that the response PDF at a specific point of interest can be directly determined without the need for obtaining the global solution first. This feature renders the technique particularly well-suited for determining efficiently statistics of effective material properties in homogenization problems, which, in many cases, require knowledge of response statistics at few points/regions only. Finally, the stochastic beam bending problem is considered in detail as an illustrative example. In this regard, a specific case is included as well where, notably, the exact beam joint response PDF coincides with the WPI approximate solution. Comparisons with pertinent Monte Carlo simulation data demonstrate the reliability of the technique.

A finite element based single-shear nail-connection model has been developed based on an existing computer model which idealizes dowel-type wood connection as an elastoplastic beam surrounded by a compression-only wood medium. Both the new and base models predict the lateral hysteresis response of the connection considering the nonlinear material behavior of the surrounding wood medium and the connector and the formation of gap between the wood and the connector which leads to pinched-hysteresis loops during cyclic loading. The base model assumes the compressive strength of the wood medium decreases after the connections reach certain lateral displacements. The new model assumes that the strength of the wood medium does not decrease at any compressive displacement. Instead, it is assumed that the loss of load carrying capability of the nail connection is primarily caused by the decrease in the vertical contact length of the wood medium against the nail. The new model has been validated using reversed-cyclic nail connection test data in terms of stiffness, strength, and energy dissipation.

This paper presents the poroelastic dual-porosity dual-permeability analytical solutions simulating the pressure transmission test on chemically active shale, taking into account shale anisotropy and electrokinetic effects. Laboratory data from pressure transmission tests on a shale sample with high clay content were also simulated by using both single-porosity and dual-porosity dual-permeability analytical solutions. The matching provides estimates of crucial shale parameters, including hydraulic permeabilities, membrane coefficient, ions diffusion coefficients, and electroosmotic permeability. The matches between analytical solutions and laboratory data included not only pore pressure, which had been the focus of previous studies, but also axial strain. Such double matches provided additional confidence in the estimations compared with conventional simulations of only pore-pressure measurements. It was found that the single-porosity simulation could not match pore pressure and axial strain simultaneously. In particular, if all measured properties were honored, the simulation yielded higher pore-pressure and lower axial strain predictions than laboratory data. To obtain a good match in both pore pressure and axial strain by using the single-porosity simulation, some parameters such as Young’s moduli and cation exchange capacity (CEC) had to be changed substantially from measured values. Therefore, it was postulated that most of the volume change occurred within the clay grains and in between the clay layers, which cannot be captured by the single-porosity model. This hypothesis was further supported by the fact that the dual-porosity dual-permeability simulation was able to model the pressure transmission test very well for both pore pressure and axial strain. Sensitivity analysis was also conducted to identify parameters with the most influence on the outcomes of the pressure transmission test. This paper highlights the importance of accounting for shale dual-porosity dual-permeability and chemically active natures when simulating shale responses.

Braided, inflatable structural members with axial reinforcing cords have the ability to accommodate loading with a low mass and small storage volume. These members are particularly attractive for space-based applications. There is currently a need to develop computationally efficient structural design methodologies for these unique, compliant, inflatable structural members so that engineers can more-effectively perform structural analyses and conduct structural-optimization studies. In this paper, an analysis methodology is developed for the three-dimensional, large-displacement, materially nonlinear behavior of these inflatable, slender members that includes the effect of the internal inflation pressure. A three-dimensional, corotational, flexibility-based fiber-beam element is employed to handle geometric and material nonlinearities. Comparisons are made with the in-plane and out-of-plane response of component-level testing of inflatable straight tubes, as well as to higher-fidelity shell-based finite-element models. The model results show good agreement with both shell-based finite element (FE) models (with a significantly decreased number of degrees of freedom), and results of component-level tests well past the point where test specimens lose internal prestress due to bending and exhibit a nonlinear response.

Loss of support as a result of voids underneath concrete slabs can initiate and propagate slab cracking in jointed plain concrete pavements. This paper investigates the hypothesis that foundation voiding occurs because of localized plastic deformation of the depressurized foundation as a result of slab curling and repeated application of traffic loads. Plane strain and three-dimensional (3D) nonlinear finite-element models of the subgrade foundation are presented. The analysis shows that voids underneath concrete slabs usually occur along the edge of slabs adjacent to the shoulder. The sizes of voids are primarily determined by foundation properties (cohesion stress and internal friction angle), slab properties, axle loads, and temperature gradients. Voids along the edge of slabs adjacent to the shoulder lead to high transverse tensile stresses on the top surface, which may result in top-down longitudinal cracking close to the outer wheel path. These same voids increase the longitudinal tensile stresses on the bottom surface at the edge of the slabs, which can increase the potential for bottom-up transverse cracking at the middle of the slabs.

Long slender elastic structures, such as railroad tracks, pipelines, and pavements, may experience buckling owing to axial compressive forces developed in them as a result of thermal or other effects, and in many cases these structures can be simplified as a beam on an elastic foundation. This paper presents an investigation of the critical buckling and postbuckling of such an elastic structure on a nonlinear foundation that has softening and restabilizing effects. The method of minimization of the total potential energy of the beam-foundation system is invoked to develop a differential equation of equilibrium and a differential equation of critical buckling (or bifurcation) of the beam. The analysis shows that critical buckling may be in a symmetric or in an antisymmetric mode, depending on the length of the beam, and when the length is extremely large, the two buckling modes are indistinguishable. The equations of the postbuckling equilibrium of the beam are highly nonlinear. To elucidate the response of the beam, a multiple-scale perturbation technique as used in modal analysis and a numerical solution based on a shooting technique are developed. It is shown that the postbuckling equilibrium of the beam has two stages after its critical buckling: a postbuckling localization stage that is unstable, and a subsequent postbuckling snaking stage characterized by a zigzag of the equilibrium configuration, and this snaking stage is dependent on the relative effects of the softening and restabilizing parameters. Comparisons of the perturbation solutions with the results of the numerical formulation show that the former semianalytical technique is accurate in the initial stages of postbuckling during which localization develops, but not in the subsequent snaking stage. The effect of the foundation parameters is also investigated in the paper.

Model-based crack identification in beam-like structures has been a classic problem. The authors have recently developed a framework to identify crack damage in beams based on a cracked beam element model, which stems from the local flexibility and fracture mechanics principles. This paper presents an experimental study on the cracked beam element model for crack damage identification in a physical testing environment. Five solid beam specimens were prepared with different numbers of cracks, and they were subjected to a modal testing and analysis procedure to extract the natural frequencies and mode shapes. The extracted modal data were then compared with the predicted counterparts using the cracked beam element model to verify the accuracy of the model. The extracted modal data were also employed to inversely identify the cracks with the cracked beam element model through a model updating procedure. Results indicate that all the cracks can be identified correctly with accurate crack depth and location information. To enhance the modal dataset for finite-element (FE) model updating, the artificial boundary condition (ABC) technique has also been applied on the test beams, and the incorporation of such frequencies proves to enhance the identification of cracks from the FE model updating.

This paper presents a solution procedure based on the finite element method for the three-constituent coupled problem representing the behavior of unsaturated porous media. A formulation is derived from the theory of porous media considering the dynamic behavior, the balance of momenta of porous liquid, porous gas, and solid porous matrix. The hysteresis of the liquid retention behavior is also modeled. A retention model able to smoothly represent the transition from maximum saturation to partially saturated states, and vice versa, is considered. With these features, the resulting system of equations is fairly complex; however an efficient, stable, and accurate numerical method is developed for its solution. The derivation of consistent tangent operators of first and second order to obtain quadratic convergence is presented in addition to all details to properly implement the numerical solver, e.g., consistent treatment of initial conditions. Finally, a number of numerical experiments are studied in order to illustrate the model capabilities in particular with regard to the influence of gas pressure on the unsaturated porous media behavior.

Formation of ice plays a key role in the behavior of concrete materials at low temperatures in cold and wet regions. The internal stresses generated during the freeze-thaw process could cause serious damage and other durability problems to concrete structures. However, just concerning the stage while the temperature is below 0°C, ice could reduce the stress concentration in the porous matrix by filling the capillary pores and result in a significant increase of elastic modulus and strength, which is usually beneficial for concrete under mechanical loads (either static or fatigue). Meanwhile, pore pressures at low temperatures will also play an important role in either accelerating or delaying the microcracking. In order to establish a mesoscale approach [which usually treats concrete as a composition of coarse aggregate, mortar, and interfacial transition zone (ITZ) between them] based on the rigid-body spring method (RBSM) for the aforementioned issues, in the first stage, the ice-strengthened elastic properties of the mortar are estimated based on multiscale continuous micromechanics. Then a mesoscale model based on RBSM is developed to simulate the nonlinear mechanical behavior under uniaxial compression, tension, and splitting for concrete, in which the ice-strengthened elastic properties in mortar and ITZ, as well as the pore pressures caused by ice formation, are taken into consideration. The range and tendency of the simulated strength values agree well with experimental data.

Cation exchange capacity (CEC) has a significant influence on the physical and chemical behavior of soil. Quantification of the CEC is an essential yet challenging task. A new methodology for the determination of the CECs of soils by using the soil water retention curve (SWRC) in the extremely high suction range is presented. The methodology is based on a theoretical SWRC model that explicitly considers the contribution of the cation hydration on the matric potential. For a homoionic soil, the CEC governs the relationship among the type of exchangeable cations, matric potential, and the corresponding equilibrated soil water. Thus, the CECs of homoionic soils can be deduced from their SWRCs. For a natural soil with a multiple cation species, the CEC of bulk soil can be determined from the SWRC of the ${\mathrm{Na}}^{+}$-exchanged form of the soil. A suite of materials ranging from nonexpansive to expansive soils is used to demonstrate the validity of the proposed methodology. The CECs of these soils are also measured independently by using the ammonium acetate method for comparison purposes. The close match between the independently measured and the SWRC-based CEC values confirms the validity and illustrates the potential promises of the SWRC-based methodology in determining the CEC of soils.

In this paper the influence of bimoment, induced by external axial loads, on the global buckling of thin-walled Z-section beams, subjected to different boundary conditions, is studied. Since bimoment varies along the beam axis, the problem of torsional and torsional-flexural buckling of thin-walled beams is defined by linear homogeneous differential equations of the second-order theory with a variable coefficient. To obtain the buckling load numerically, a finite-difference method is employed for discretizing the governing differential equations. To verify the validity and the accuracy of this study, numerical solutions are presented and compared with those calculated by simulation software.

The flow characteristics around a pipeline partially buried in a rigid porous seabed of infinite depth are numerically examined using the classical boundary-element method. A simplified model, comprising an impermeable circular pipe with/without a permeable protective coating, is applied to analyze the oscillating-flow case. Darcy’s law and the potential-flow theory form the basis of this study. Taking advantage of the regular perturbation method prohibits the occurrence of the highly ill-conditioned linear systems because of substantial a difference in the order of magnitude among the flux and pressure continuity conditions across the soil- and coating-water interfaces. The computed results of uncoated cases reveal that the pore-fluid velocity rapidly increases in seabed areas close to the pipe. A remedy for this is to utilize a precoated permeable layer, which effectively eliminates the localized regions of the flow-induced pressure concentration. Numerical experiments show helpful results so far, which might lead to the development of cheap novel approaches to prevention of the piping effect.

Laminar radial flow between two parallel disks is a fundamental nonlinear fluid mechanics problem described by the Navier-Stokes (NS) equation, but is unsolved because (1) an exact solution is not found even with extensive references, and (2) it is unclear why radial flow remains laminar at high Reynolds numbers. This paper first presents exact velocity distribution solutions for developed radial inflows and outflows, proving that both flows are described by brief Jacobi elliptic sine-squared functions but with different characteristics. For inflow, a stable velocity distribution forms; for outflow, the velocity distribution may have an inflection point inducing flow instability or separation. Both velocity distributions become the classic parabolic law at low Reynolds numbers, but uniform (similar to turbulent velocity distributions) at high Reynolds numbers. Furthermore, both pressure and boundary shear stress follow an inverse-square law, but the friction factor is invariant. These results are instructive for studying nonuniform open-channel flow for which nonlinear inertia is of importance.

Strain localization refers to the formation of narrow zones of intense deformation in materials as a result of bifurcation in the stress-strain response during loading. Bifurcation occurs before the theoretical peak strength is reached and is then followed by strain softening. Theories and criteria have been developed to predict the point of this bifurcation in stress-strain relations. Two bifurcation criteria have been proposed for geomaterials: the complex Rudnicki-Rice criterion and the simple Vermeer criterion. The Rudnicki-Rice criterion is for strain-controlled loading, whereas the Vermeer criterion is for stress-controlled loading. This paper reviews and presents a rigorous and theoretical comparison of the two bifurcation criteria in the context of the flow theory of strain hardening elastoplasticity and shows that the simple Vermeer’s criterion is equivalent to the more complicated Rudnicki-Rice criterion for two-dimensional (2D) loading conditions. However, important differences between the two criteria exist for three-dimensional (3D) loading conditions. This paper also shows that the Rudnicki-Rice criterion provides a more realistic prediction of strain localization in geomaterials during 3D loading than does the Vermeer criterion. The paper is envisioned to offer an improved understanding of strain localization in geomaterials.

In optimal control design, two of the most popular strategies used are linear quadratic regulator (LQR) control and the $H_2$ norm optimization. This paper obtains a mathematical equivalence between the performance index of an LQR control algorithm and the $H_2$ norm of a linear system. For a single-input excitation such as an earthquake, the optimal gain for an LQR control algorithm is the same as that of an $H_2$ norm minimization of the system. This observation leads to the inference that for a linear system, quadratic optimal gain for a free vibration of the system can also be used as an optimal gain for the forced vibration of the system. However, the same results are not true for multi-input excitations, such as wind or blast loads. In these cases, optimal gains must be obtained separately for the two algorithms.

The efficient vibration control of complex multibody systems is an important issue in engineering design and has drawn substantial attention in the field of multibody system dynamics and control engineering. In this paper, by combining the transfer matrix method for multibody systems and modal space control, an active vibration control design method is presented for the dynamic modeling and vibration control design of multibody systems. The state-space equations in terms of generalized coordinates in modal space can be obtained easily. Based on the independent modal space control method, a robust independent modal space controller is presented for active vibration control of general linear multibody systems. The proposed method has low memory requirements, high computational efficiency, and additional advantages for dynamic design and real-time control of general multibody systems. A numerical simulation example of vibration control of a multiple-launch rocket system is given, validating the method and the control performance.

Complex mechanical (e.g., multibody) systems with different types of constraints are generally performed through analytical dynamics methods. In some cases, however, it is possible that the (augmented) mass and/or stiffness matrices may derive to be singular; consequently, modal analysis, which is used extensively in the classical dynamics literature, fails. In this paper, if the uniqueness condition is satisfied by the constraints, a properly modified modal analysis is elucidated into analytical dynamics leading to the evaluation of the natural frequencies in a simple and straightforward way. Under that framework, advances of both classical and analytical dynamics are taken into consideration for evaluating the structural response.