Journal of Engineering Mechanics

Because of its efficiency in analyzing complex viscoelastic problems, the finite-element (FE) analysis has been widely used to identify the time- and rate-dependent effects of viscoelastic materials on various structural conditions. When performing the FE analysis on a viscoelastic structure, most FE programs require fundamental material properties, shear and bulk moduli, of the given viscoelastic material as their input. However, the shear and bulk modulus tests are difficult to perform, so they have been commonly estimated from a single material test on the basis of the assumption that the Poisson’s ratio of viscoelastic materials is a time-independent constant. Such an assumption, however, might not be suitable because the Poisson’s ratio of the viscoelastic materials is also a function of time. Therefore, this study developed computation algorithms for determining the time-dependent Poisson’s ratio and shear and bulk moduli of asphalt mixtures, which have been well recognized as a viscoelastic material, by employing the indirect tension testing system. The shear and bulk moduli determined by the developed approach appear to be reasonable and realistic. Their applicability and reliability were also verified by comparing experimental data to the results of the FE analysis performed on the same circular specimen as that used in the indirect tension creep test.

In this study, we conduct a combined experimental and micromechanical investigation into the strain-rate sensitivity of concretes, with a special reference to the effect of aggregate concentration. We first measured the stress-strain relations of Type I portland cement with 0.45 water-to-cement ratio (w/c), and then those of the mortar containing sand aggregates of up to 50% volume concentration, over six orders of magnitude of strain rate, from $5\times {10}^{-6}/\text{s}$ to $1\times {10}^{-1}/\text{s}$ under compression. It was found that, at a given strain rate, the peak stress increases with the aggregate concentration but the peak strain tends to decrease with it. At a given aggregate concentration, the peak stress also increases with strain rate whereas the peak strain generally decreases with it. We then developed an inclusion-matrix type micromechanical model to simulate the behavior of the concrete. In this process the nonlinear viscoelastic behavior of the portland cement was modeled by a modified Burger's model with strain-rate dependent spring and dashpot elements, and the stress-strain relations of the mortar at various aggregate concentrations and strain rates were calculated from a two-phase composite model with a secant-moduli approach. It is shown that the measured data could be sufficiently well predicted by the developed micromechanics composite model.

This paper presents the temperature dependence of the mechanical properties of structural high-strength low-alloy (HSLA) ASTM A709 Gr50 steel (En10025: S355 JO; DIN: ST 52-3U). Engineering stress-strain diagrams at lowered and elevated temperatures are presented. Creep responses for selected constant stresses at selected temperatures are also presented and are fit with a rheological model. Additionally, a relation between impact toughness and fracture toughness is proposed and is validated using results from notch impact tests on a Charpy pendulum impact machine.

Stochastic wind velocity fields are usually simulated as $N$ -variate stationary Gaussian processes by using the spectral representation method (SRM). However, the temporal statistics estimated from one SRM-simulated sample wind process cannot coincide with the target characteristics; the disagreements can be described by the bias and stochastic errors. For controlling the errors efficiently, this paper assesses the errors produced by both the Cholesky decomposition-based SRM (CSRM) and the eigendecomposition-based SRM (ESRM). The SRM is revisited first, followed by computing the temporal mean value, correlation function, power spectral density (PSD), and standard deviation of the SRM-simulated wind process. It is shown that the temporal correlation function and standard deviation are Gaussian, while the temporal PSD is non-Gaussian. Further, as mathematical expectations and standard deviations of the corresponding temporal estimations, the bias errors and stochastic errors of all the first- and second-order statistics are obtained in closed form for both the CSRM and the ESRM; the closed-form solutions are then verified in the numerical example. More importantly, this example is employed for taking a clear look at and making a comparison between the stochastic errors produced by the CSRM and by the ESRM; observations suggest that (1) in sum, the ESRM produces smaller stochastic errors than the CSRM and (2) if the ESRM is employed, stochastic errors will be distributed to each component of the wind process in a more uniform pattern. Moreover, some practical approaches are proposed to control the stochastic errors.

Closed-form solutions for buckling of long plates with flexural/twist anisotropy with the short edges simply supported and with the longitudinal edges simply supported, clamped, or elastically restrained in rotation under axial compression are presented. An energy method (Rayleigh–Ritz) is employed to obtain the critical buckling loads. The critical buckling loads are expressed in terms of minimum nondimensional buckling coefficients and stiffness parameters. The new closed-form solutions show an excellent agreement when compared to existing solutions and finite-element analysis. Due to their simplicity and accuracy, the new closed-form solutions can be confidently used as an alternative to computationally expensive structural analysis to assess buckling in the preliminary design phase of composite structures.

A finite-element method considering the interaction of the bending and shear-lag deformation of a box girder was established. Meanwhile a shear-lag-induced stiffness matrix was defined. The stiffness matrices considering the effect of the shear lag were deduced. At each node of the beam element, two shear-lag degrees of freedom were used as boundary conditions for the box girders. The proposed formulations were then applied to analyze the effects of the shear lag on the deflection, the internal forces, and the shear-lag coefficients in the simply supported cantilever and continuous box beams under uniformly distributed and concentrated loads. The numerical results obtained using the proposed procedure were in good agreement with those using the finite-shell-element method, the finite-stringer method, the analytical method based on the variational principle, and the model tests. The proposed method is reliable and more effective for the analysis of the shear lag in the actual box-girder structures.

Current models to determine the local buckling stress of inelastic plates under in-plane loading are based on plastic deformation theory and semirational or empirical relationships. A successful $J_2$ flow theory describing inelastic local buckling of initially perfect plates needs to avoid two well-known pitfalls known as the “inelastic column buckling paradox” and the “plastic buckling paradox.” While the former problem, which found its origin in 1895 in Engesser’s double modulus approach, was resolved by Shanley in the late 1940s, a convincing solution of the plastic buckling paradox has not yet been presented. This paper proposes a modification to the $J_2$ flow theory which hinges on the determination of the shear stiffness from second-order considerations. A differential equation is derived which describes the incremental plate deformations at the inelastic local buckling load. The differential equation is studied for two cases of boundary conditions: a plate simply supported along four edges and a plate simply supported along three edges with one longitudinal edge free.

Linear response surface (RS) models are used to represent the relationship between samples of response time histories measured by sensors placed across a structure. Different structural states of a general time-variant system are considered for short intervals capturing a linearized model of each state. Within this framework, the error associated with each RS model is sensitive to a modification of the structural state. A method that relates the changes of the statistical characterization of the error to the occurrence of a structural modification is developed for damage detection. The localization of damage is then pursued by identifying the largest discrepancies resulting from the comparison between the statistics of the sum of the squares of the error obtained at each sensor location. The generality of the method is shown by applying it to the experimental data of a realistic structure, which is representative of a continuous body affected by distributed cracking.

This paper proposes a multiresolution based wavelet controller for the control of linear time varying systems consisting of a time invariant component and a component with zero mean slowly time varying parameters. The real time discrete wavelet transform controller is based on a time interval from the initial until the current time and is updated at regular time steps. By casting a modified optimal control problem in a linear quadratic regulator (LQR) form constrained to a band of frequency in the wavelet domain, frequency band dependent control gain matrices are obtained. The weighting matrices are varied for different bands of frequencies depending on the emphasis to be placed on the response energy or the control effort in minimizing the cost functional, for the particular band of frequency leading to frequency dependent gains. The frequency dependent control gain matrices of the developed controller are applied to multiresolution analysis (MRA) based filtered time signals obtained until the current time. The use of MRA ensures perfect decomposition to obtain filtered time signals over the finite interval considered, with a fast numerical implementation for control application. The proposed controller developed using the Daubechies wavelet is shown to work effectively for the control of free and forced vibration (both under harmonic and random excitations) responses of linear time varying single-degree-of-freedom and multidegree-of-freedom systems. Even for the cases where the conventional LQR or addition of viscous damping fails to control the vibration response, the proposed controller effectively suppresses the instabilities in the linear time varying systems.

A solution to the problem of a plane-strain fluid-driven crack propagation in elastic permeable rock with resistance to fracture is presented. The fracture is driven by injection of an incompressible Newtonian fluid at a constant rate. The solution, restricted to the case of zero lag between the fluid front and the fracture tip, evolves from the early-time regime when the fluid flow takes place mostly inside the crack toward the large-time response when most of the injected fluid is leaking from the crack into the surrounding rock. This transition further depends on a time-invariant partitioning between the energy expanded to overcome the rock fracture toughness and the energy dissipated in the viscous fluid flow in the fracture. A numerical approach is used to compute the solution for the normalized crack length and crack opening and net-fluid pressure profiles as a function of two dimensionless parameters: the leak-off/storage evolution parameter and the toughness/viscosity number. Relation of this solution to the various available asymptotic solutions is discussed. Obtained mapping of the solution onto the problem parametric space has a potential to simplify the tasks of design, modeling, and data inversion for hydraulic fracturing treatments and laboratory experiments.

This study elucidates the water well resonance induced by preearthquake signals using an analytic approach. Weak pressure waves passing through a confined aquifer are considered as the incoming preearthquake signal. Owing to the hardness of the porous skeleton, the pressure waves are simply the limiting case of the second kind of dilatational waves of poroelasticity. Because the driving signals of a weak preearthquake pressure wave transmitting through a confined aquifer are too weak to significantly affect the solid skeleton, we believe that this phenomenon is attributed to the effect of resonant amplification of water levels in wells. The flow inside the well is assumed to be incompressible, inviscid, and irrotational, while that outside the well is treated as a porous-media flow with a rigid skeleton. The flows inside and outside the well are analyzed using the potential flow theory under the assumption of small-amplitude waves and Darcy’s law of porous-media flow, respectively. The well-posed boundary value problem is solved using the regular perturbation expansion based on a small gauge function $k_{0}R$ , where $k_0=\text{wave}$ number and $R=\text{well}$ radius. The results of this study demonstrate that the weak preearthquake longitudinal pressure wave is only a triggering mechanism for the resonance of transverse gravity surface water waves inside the well.

In this note it is shown that the combination of conventional laminas (possessing positive Poisson’s ratio) and auxetic laminas (possessing negative Poisson’s ratio) gives rise to effective in-plane composite laminate Young’s modulus that surpasses the rule-of-mixture formula. To enable comparison between the developed model with the rule-of-mixture, the former is presented in such a way that two correction functions exist distinctively for multiplication into the two terms of the rule-of-mixture formula. Each of the two correction functions reduces to a minimum of 1 when all laminas possess equal Poisson’s ratio, and the correction functions are greater than one when there exists mismatch in the Poisson’s ratios among the laminas in the laminate. Plotted results show that the overshooting of the laminate’s effective in-plane modulus is significant for semiauxetic laminates but not for conventional and fully auxetic materials.

This note presents the results of an experimental study of circular sand jets in air from three nozzles of diameter of 19.2, 31.1 and 63.8 mm. It was found that the frontal speeds of the sand jets and the steady sand jet velocity accelerate due to gravity with negligible air resistance. The sand velocity does not appear to be affected by sand particle sizes for the three sizes tested. The diameters of sand jets, as they travel downwards, decrease and gradually approach an asymptotic value after a distance of 120 times of the initial jet diameter. The sand concentration in the jet decreases as the distance from the nozzle increases. Waves were observed at the periphery of the sand jet and some preliminary results of wave speed and wavelength are reported.

This technical note presents an extension of a previous study where two methods for detecting structural damage have been developed by using displacement and velocity measurements. In this study, acceleration feedback is used in detecting changes in global structural stiffness coefficients of lumped-mass-shear-beam models. The previously developed method relies on the decoupling of effects of changes in stiffness at different locations and the use of displacement or velocity feedback has proven to be effective. Extension to the use of acceleration feedback using existing formulation is not trivial in that the desired decoupling effect cannot be achieved by simple coordinate transformation because the acceleration itself is directly related to the stiffness coefficients. An approach to circumvent this difficulty is presented and it involves increasing the order of time derivatives of the linear system so that the acceleration becomes the “velocity” of the new system. The performance of the proposed method is demonstrated using an illustrative example of a three-story model with stiffness changes at different floors. Numerical studies are also conducted to evaluate the time horizons required to normalize monitor outputs for the effective and efficient detection of stiffness changes.