Journal of Engineering Mechanics

The welded hollow spherical joint (WHSJ) is one of the most commonly used joints in reticulated shell structures. Corrosion at the surface of WHSJs has significantly different influences on the compression capacity of WHSJs, depending upon its location. Pit corrosion is a typical corrosion type for steel structures, but the influence of pit corrosion at different locations on the loading capacity of WHSJs has not been quantified. This study determined the influence of corrosion located in different places on the compression capacity of WHSJs. The influence of corrosion location on compression capacity was systematically investigated. The accuracy of the finite-element (FE) model was validated. The influence of corrosion and geometrical parameters on the random distribution of compression capacity was analyzed. A simplified method to predict the compression capacity is proposed.

The goal in this research was to investigate harvesting energy from a nonlinear functionally graded beam with bonded piezoelectric patch under multiple moving loads. The material of the harvester was considered to be varied in the thickness direction. The generalized Hamilton’s principle and von Kármán nonlinear theory were used to obtain a coupled system of differential equations considering nonlinear geometry as well as electromechanical coupling. The Newmark time integration scheme as well as the finite-element method were used to obtain the numerical results. Numerical study was also performed to investigate the effects of velocity of the moving loads, time lags between the moving loads, beam length, material distribution, and piezoelectric patch location on the harvested power. Results indicate that the aforementioned parameters have significant effects on the harvested power. The results show that ignoring the nonlinear effects especially for considerable values of moving loads results in erroneous large values for the harvested power. To the best of authors’ knowledge, there is no other study about energy harvesting from nonlinear vibrations of beams under moving loads.

An often-used tool for describing the strength of geotechnical materials is the Mohr strength envelope, which has been used for more than 100 years. For simple problems, analytical bearing capacity solutions can be found and numerical methods exist for finding bearing capacities for more complicated geometries and nonlinear Mohr envelopes. Despite their long history, Mohr envelopes have never been used in elastoplastic calculations, meaning that displacement magnitudes cannot be found. This paper presents the implementation of nonlinear Mohr envelopes in an elastoplastic numerical framework. This allows the use of materials with plasticity behavior described by Mohr envelopes to be used on an equal basis with materials whose plasticity behavior is described by the traditional yield surfaces and plastic potentials. This opens up its use with both failure load calculation and displacement estimates. Mohr envelope elastoplasticity is particularly useful with the use of safety factors as in shear strength reduction methods, where no simple, consistent methods so far exist for nonlinear yield criteria formulated in Cartesian stresses. Several computational examples are given.

Concrete is a complex heterogeneous material. Its internal structure controls its mechanical behavior through crack localization, branching, and coalescence. As a result, only models that represent its failure through fracture-mechanics-based formulations can physically account for such phenomena. Among these models, the lattice-discrete particle model (LDPM) has great success. By representing concrete through an assemblage of interacting coarse aggregate pieces, LDPM can successfully model concrete multiaxial behavior under various static and dynamic loading conditions. However, this fine detailing results in a large computational cost that hampers the use of LDPM in large structural scale applications. In this work, the formulation of a calibration-free coarse-graining technique is presented. In this technique, fictitiously larger aggregate pieces are used to replace the original concrete aggregate pieces, with linear scaling of aggregate diameters. The formulation accounts for the effect of coarse graining on the amount of energy dissipated during deformation under combined tension and shear (tension-shear). Because of coarse graining, less distributed cracking is represented during tension-shear deformation at the coarse scale. The proposed formulation recovers this energy-dissipating mechanism by introducing a transition function in the tension-shear constitutive law based on the coarse-graining factor and geometry, which eliminates the need to recalibrate the LDPM parameters for the coarser scale. The formulation is developed and initially validated using simulations of uniaxial compression and notched three-point bending tests, with coarse-graining factors up to 5. Then, using the same identified function without any change, extensive validation of the technique is demonstrated by simulating size effect tests of notched three-point bending tests, uniaxial compression of ultrahigh-performance concrete (UHPC) with various scaling factors, and flexural behavior of RC beams with different reinforcement ratios. The results show that the proposed technique is capable of replicating the same fine-scale response and failure patterns at a fraction of the fine-scale computational cost.

A damage-plasticity model is extended to account for the effects of simultaneously occurring stiffness degradation, residual deformation, and creep. Assuming the additivity of small strains, the model combines damage mechanics, plasticity theory, and an improved version of the ACI model to characterize creep at low stress levels. The coupling between damage and creep produced by medium and high stress levels is accounted for by introducing a damage-dependent influence function. An explicit numerical algorithm is developed to implement the proposed model in the simulations of structural response. The proposed model is systematically validated by comparing its results with experimental data, suggesting that it offers promise for capturing the long-term mechanical behavior of reinforced concrete structures.

Nondestructive ultrasound-based methods have been applied to evaluate the elastic properties of concrete materials. Although the wave modulus of elasticity of concrete frequently is reported to be higher than the static counterpart, the microstructural and physical mechanisms are not well understood. This study conducted a computational micromechanics to investigate the effects of aggregates and voids on both the effective wave modulus of elasticity and the static modulus of elasticity, based on concrete microstructures resolved with X-ray microtomography. It was demonstrated that the existence of void defects plays a significant role in the elastic properties of concrete compared with the aggregates. It was shown that the wave modulus of elasticity of concrete is higher than the static modulus of elasticity because of the existence of crack-like voids with small aspect ratios.

A train-bridge system (TBS) is inevitably subjected to parameter uncertainty, which leads to variability in its dynamic responses. In practice, it is difficult to characterize parameter uncertainty using precise probability density functions due to lack of sufficient statistical information. In such situations, uncertain parameters are usually modeled as uncertain-but-bounded parameters; this is also known as interval uncertainty. This paper aims to determine the dynamic response bounds of a TBS subjected to interval uncertainty. In mathematics, estimation of dynamic response bounds can be pursued in the context of optimization, that is, the minimization or maximization of an objective function. The solver in this context shares common features of a black-box function, such as high computational cost and no closed-form solution. In view of this, the present study proposes an efficient Bayesian optimization approach for estimating the dynamic response bounds of a TBS. Specifically, a Bayesian modeling approach employing a Gaussian process prior is proposed to replace the current expensive-to-run original model solver, along with an acquisition function that trades off exploration and exploitation of the search space. By doing so, the optimization of a complex, intractable black-box function is converted to the maximization of a computationally efficient acquisition function that has a closed-form expression and is differentiable. Two test functions are provided in order to demonstrate the applicability of the proposed Bayesian optimization methodology for finding the global minimum. It is demonstrated that the Bayesian optimization methodology is efficient and effective in solving the optimization problem with a limited number of function evaluations. Next, the proposed Bayesian optimization approach is utilized for interval dynamic analysis (IDA) of the TBS. The computational accuracy and efficiency of the proposed method is compared with a direct Monte Carlo simulation (MCS) estimator, which is used as a reference solution because of its generality, robustness, and easy implementation. The comparison results show that the proposed Bayesian optimization method is feasible and reliable for IDA of the TBS in terms of both computational accuracy and efficiency. Last, the influence of the interval change ratios of the system parameters on dynamic responses is investigated. The results reveal that an increase in the parameter uncertainty level results in a higher uncertainty bound on the dynamic responses.

Recently, there has been a growing interest in studying cellular materials made of unit cells that take the topology of the mathematically known triply periodic minimal surfaces (TPMS). Architected foams based on the shell-based Schoen’s I-graph–wrapped package (I-WP) TPMS (i.e., IWP-foam) seems a promising mechanical metamaterial and might yield better mechanical properties than stochastic or strut-based foams. The IWP-foam has a cubic symmetry and is interconnected and intertwined in the three-dimensional (3D) space. Changing the thickness of the I-WP minimal surface can change the relative density of the IWP-foam. In this paper, the elastic properties (uniaxial, shear and bulk moduli, and Poisson’s ratio), elastic anisotropy, plastic properties (tensile, shear, and hydrostatic yield strengths), and anisotropic yield surfaces under different load combinations of IWP-foam, as a function of the relative density, are computed through conducting microscopic finite-element simulations. The anisotropic elastic and plastic properties of IWP-foam are compared with that of other common types of periodic cellular solids. Furthermore, computationally inexpensive closed-form macroscopic isotropic and anisotropic yield functions are used to predict the microscopic yield behavior of IWP-foam. It is found that the uniaxial elastic modulus and yield strength, as well as the shear elastic modulus and shear yield strength, scale with the Gibson-Ashby power-law, indicating a mixed stretching-dominated and bending-dominated deformation behavior. On the other hand, the bulk modulus and hydrostatic yield strength scale linearly with relative density, indicating a stretching-dominated behavior. It is shown that a modified version of Hill’s anisotropic yield function can better describe the macroscopic yield behavior of the IWP-foam under several different stress states than the isotropic Deshpande-Fleck model, especially for combinations of shear stress states. Finally, it is noticed from comparing the elastic and plasticity yield properties of the IWP-foam with several other common foams and lattices that, for a given relative density, the IWP-foam has the highest uniaxial stiffness and strength.

A new approach to a geometrically nonlinear (GN) static two-dimensional (2D) beam-cable problem is given. It has four new features. First, the search for the ultimate solution (US) is presented as sum of basic (BS) and smoothing (SS) solutions, where BS is discontinuous and SS is to ensure geometrical continuity and forces equilibrium in each point of the structure. Second, BS establishes the constant curvature reference geometry, in which basic bending moment and basic axial force are already embedded together with the resulting basic elongation and curvature. BS geometry gives the local system of coordinates according to which SS has to be determined. Third, a number of analytically exact SS for distributed loading are derived in a form convenient for applying the transfer matrix method. These exact SS are given for four different elements: a cable, a linear curved beam, and geometrically nonlinear tensed or compressed curved beams. Fourth, the efficient procedure of correction of BS based on SS derived at each iteration is proposed, taking into account whether or not SS is oscillating to slow down or speed up this correction. Four elaborated examples are investigated. They explore the optimal number and length of elements, as well as ranges of application of particular SS. It is shown that the GN beam element is the best choice able to reduce the required number of elements and iterations in tens of times. For tensed geometries, combined application of GN beam and cable elements is found to be very effective. The method is very stable, and its convergence is insensitive not only to the initial geometry configuration, but also to the order and position of each particular element. The advantage of special meshing is discussed, where the size/number of elements is controlled by sections where the bending moment is nearly constant.

A partially embedded gradient metabarrier (PEGM) for seismic Rayleigh waves was designed and studied using the finite-element method (FEM). Investigations on the partially embedded periodic metabarrier (PEPM) were carried out first, and relations between band gaps (BGs) and some sensitive parameters were examined in detail. A PEGM and piecewise PEGM were then designed and discussed based on these investigations. It was found that BGs at ultralow frequencies can be obtained by the PEPM and effectively tuned by the geometrical parameters, especially the embedded depth. The PEGM broadens the frequency attenuation zone significantly, and the piecewise PEGM further extends the zone to cover the main frequency range of seismic waves from 1 to 20 Hz. Surface wave with tens of meters wavelength can be successfully controlled by the designed meter-scaled metabarrier. Simulations of the transmission spectra of El Centro and Taft waves showed that the piecewise PEGM exhibits high efficiency of earthquake shielding.

This study presents a directional constitutive model to predict the nonproportional cyclic behavior of undrained soft clay. A novel strategy consisting of a combination of directional dilation and the damage microplane model is used. Inherent cross-anisotropy is addressed via the modification of the integrated stress through an initial fabric tensor. The evolution of material microstructure is considered using the strain-dependent damage functions at the scale of microplanes. The variation of material stiffness is considered as a function of effective hydrostatic stress. The results were verified with available experimental data. The model accurately accounts for the effects of contributing factors, including the intermediate principal stress parameter.

The spectral representation method is widely used to generate nonstationary processeses. However, the operations of Cholesky decomposition in two directions and double summations are fairly time consuming. Moreover, the effectiveness of only frequency interpolation schemes is limited, and existing proper orthogonal decomposition (POD) schemes have their own limitations. An efficient approach to decomposition for a time-varying coherence matrix based on time-frequency interpolation has been proposed to accelerate Cholesky decomposition. The key idea is that the decomposition of a coherence matrix is continuous in both time and frequency directions and changes slowly, which is suitable for interpolation approximation. Naturally, conducting interpolation in both directions can greatly reduce the operations of a Cholesky decomposition. Then a diagonal POD strategy is taken into account to further factorize the diagonal elements of interpolated decomposition results, combined with accurate evolutionary spectra. Furthermore, each group of time functions is fully utilized to take into account the dissimilar spectra in different component processes. The efficiency and accuracy of the proposed method are evaluated in a numerical example. The results show that the simulation is very efficient, and both time-frequency interpolation approximation and POD reconstruction–based results agree well with target curves.

Identifying the dynamic characteristics of structures under ambient conditions is very important for heath monitoring and damage assessment. In this study, an output-only recursive combined subspace identification technique is proposed for tracking the modal parameters of a time-varying structure under unknown and unmeasured nonstationary input. The technique consists of two parts: initial input estimation and online tracking. For initial input estimation, a short-duration input is first reconstructed through an iterative oblique projection and an orthogonal projection. The reconstructed input and the measured output are then used to form a cross-correlation matrix for initial estimation of modal parameters. An orthogonal projection and an instrumental variable approach are then incorporated in order to eliminate the effects of nonstationary input and measurement noise, respectively. A bi-iteration subspace tracker is applied to extract the unknown input and the structural modal parameters. The proposed technique was validated numerically on a four-degree-of-freedom structure and experimentally on a three-degree-of-freedom building model. Both results showed that the proposed technique can simultaneously reconstruct the unknown input and track the time-varying structural modal parameters using only output measurements.

This paper presents an elastoplastic solution for drained expansion of a cylindrical cavity in anisotropic critical-state soils. The large deformation theory and the advanced anisotropic critical-state soil model S-CLAY1, which is capable of reflecting the initial anisotropy and the development of anisotropy produced by the plastic volumetric and deviatoric strains, are employed to model the elastoplastic behavior of the soil during expansion. The problem considered is formulated as a system of seven first-order ordinary differential equations in terms of the Lagrangian description with three stress components, three anisotropic variables, and the specific volume as the basic unknown variables, and the system is then solved as an initial value problem. The results, including the distributions of the seven basic variables around the cavity, effective stress paths, anisotropic parameter paths, and evolution of the yield curve are presented and compared with those from FLAC3D numerical model and some other solutions to verify the current solution and emphasize the significant effects of plastic deviatoric strain-induced anisotropy on the cavity expansion responses. The results demonstrate that the present solution is more advanced than the other solutions, and the plastic deviatoric strain-induced anisotropy has pronounced effects on the expansion response, especially in overconsolidated soil. It is expected that more reasonable predictions could be made by the proposed solution when it is applied to practical geotechnical problems.

Fine-grained sediments containing large discrete gas bubbles are widely distributed in the five continents throughout the world. The presence of gas bubbles could either degrade or enhance the hardening behavior and undrained shear strength ($s_u$) of the soil, depending on the initial pore water pressure ($u_{w0}$) and initial gas volume fraction (${\psi }_0$). The existing constitutive models, however, can solely capture either detrimental or beneficial effect owing to the presence of gas. This study presents a new three-dimensional (3D) elastoplastic constitutive model that describes both the damaging and beneficial effects of gas bubbles on the stress–strain behavior of fine-grained gassy soil in a unified manner. This was achieved by incorporating (1) a versatile expression of yield function that simulates a wide range of yield curve shapes in a unified context, and (2) a dilatancy function capturing the distinct stress–dilatancy behavior of fine-grained gassy soil. Given the lack of direct experimental evidence on the shape of the yield curve of fine-grained gassy soil, new experiments were performed. This has led to the identification of three distinct shapes of yield curve—bullet, ellipse, and teardrop—as well as the formulation of the yield function considering the dependency of yield curve shapes on $u_{w0}$ and ${\psi }_0$. The new model was shown to reasonably capture both the damaging and beneficial effects of gas on the compression and shear behavior of three types of fine-grained gassy soils with a broad range of $u_{w0}$ and ${\psi }_0$ by using a unified set of parameters.

The Duffing oscillator represents an important example to describe, mathematically, the nonlinear behavior of several phenomena in physics and engineering. In view of its diverse applications in science and engineering, the current work investigates the stability analysis of the parametric Duffing oscillator. This equation represents a second-order ordinary differential equation with cubic nonlinearity and periodic coefficient. A coupling of the homotopy perturbation method (HPM) and Laplace transform ($L_T$), an approximate solution is derived. The HPM is adapted to find another accurate approximate solution. The latter analysis reveals the exact solution of the cubic Duffing equation. In addition, an expanded frequency parameter is achieved to find another approximate periodic solution. Therefore, this method is exercised to govern the stability criteria of the problem. Finally, the multiple time scales with the HPM is used to judge the stability criteria. The analyses include the resonance as well as nonresonance cases. Numerical estimations are performed to confirm, graphically, the perturbed solutions together with the stability examination. It is shown that the damped parameter and the cubic stiffness parameter have a destabilizing influence. In contrast, the natural and parametric frequencies are of stabilizing influences.