Journal of Engineering Mechanics

In this paper, a direct simulation algorithm is presented for the generation of a class of non-Gaussian stochastic processes according to target lower-order moments and prescribed power spectral density (PSD) function. The proposed algorithm is to expand the autoregressive (AR) model and the autoregressive moving average (ARMA) model, which are available to generate Gaussian random process, to simulate directly non-Gaussian stochastic process. The coefficients of the AR or ARMA model are determined based on the prescribed PSD function. It is well known that outputting stochastic process is also non-Gaussian if inputting white noise is non-Gaussian. But the skewness and kurtosis of the outputting non-Gaussian random process are not identical to these of inputting non-Gaussian white noise. In this paper, the relationships of lower-order moments such as skewness and kurtosis between output and input are analyzed and close to linear transformations. To corroborate the feasibility and correctness of the present methodology, numerical examples involving simulation of fluctuating wind pressures are taken into consideration. Numerical results indicate that the skewness and kurtosis of generated wind pressures based on the AR or ARMA model closely match their targets. In addition, the PSD and correlation functions of simulated samples also show considerably good agreement with prescribed functions. Therefore, the proposed algorithm is effective to simulate directly the class of non-Gaussian stochastic process.

The paper presents two computational procedures to reconstruct the stiffness distribution and to detect damage in Euler–Bernoulli beams. A novel methodology of damage identification is developed using static deflection measurements. The first formulation is based on the principle of the equilibrium gap along with a finite-element discretization, and leads to an overdeterminate linear system. The solution is obtained by minimizing a regularized functional using a Tikhonov total variation (TTV) scheme. The second proposed formulation is a minimization of a data-discrepancy functional between measured and model-based deflections. The optimal solution is obtained using a gradient-based minimization algorithm and the adjoint method to calculate the Jacobian. Also discussed is a simple procedure to measure the deflection of beams using a close-range photogrammetry technique. An edge detection-based algorithm is devised for quasi-continuous deflection measurement. The proposed identification methodology is validated using experimental data. Four beams with predefined damage scenarios are tested. In each case, the location and damage levels are reconstructed with good accuracy. However, results show that, in general, the equilibrium gap-based formulation has greater success than the data-discrepancy method. The proposed methodology has the potential to be used for long-term health monitoring and damage assessment of civil engineering structures.

This study presents a numerical approach to predict the macroscopic behavior of parallelepiped elastomeric isolators undergoing large deformations. The model uses experimental data fitting performed through cubic splines on several rubber compounds. A nine-constant Mooney-Rivlin model and an exponential law proposed in previous studies are assumed to evaluate the energy density of the rubber pads within a finite-element discretization of the isolator. Having a few experimental stretch-stress data for each rubber compound in uniaxial tension and/or shear, cubic Bezier splines are utilized to generate a large number of data (or metadata) containing the original experimental data. The Mooney-Rivlin and exponential law constitutive parameters are estimated through the least squares method, assuming spline interpolations as data to fit. The uniaxial and shear response of each rubber compound are numerically compared and, when possible, their capability in reproducing experimental data is assessed. Full-scale rectangular seismic isolators are analyzed. The compression modulus, ${\mathrm{E}}_{\mathrm{c}}$, the shear-large displacement curves, and the hysteretic behavior are estimated. For hysteretic behavior, the model is compared with existing experimental data by modeling rubber with a recently presented overlay viscoplastic model.

In Bayesian model updating, parameter identification of structural systems using modal data can be based on the formulation of the likelihood function as a product of two probability density functions, one relating to modal frequencies and one to mode-shape components. The selection of the prior distribution of the prediction-error variances relating to these two types of data has to be performed carefully so that the relative contributions are weighted to give balanced results. A methodology is proposed in this paper to select these weights by performing Bayesian updating at the model class level, where the model classes differ by having different ratios of the two prediction-error variances. The most probable model class on the basis of the modal data then gives the best choice for this variance ratio. Two illustrative examples, one using simulated data and one using experimental data, point out the effect of the different relative contributions of the modal frequencies and mode-shape components to the total amount of information extracted from the modal data.

The rotation and shear property theory of rubber bearings is researched in the paper. On the basis of the nonlinear rotational stiffness and Haringx elastomer model, a simple mechanics model is provided to analyze the rotation, compression, and shear property for rubber isolators. The rotational stiffness analysis theories corresponding to different shear deformation state are established on the basis of the properties of rubber material and isolators. The tests of natural rubber bearings (RB) and lead plug rubber bearings (LRB) were conducted to testify the nonlinear rotational stiffness analysis model and the shear hysteretic model proposed in the paper. The test results show that both nonlinear rotational stiffness analysis model and shear hysteretic model proposed in the paper could be used effectively to analyze the mechanics properties.

The nonzero-mean probability density function (PDF) solutions of nonlinear stochastic oscillators under the excitation of Poisson impulse process are obtained with exponential-polynomial closure (EPC) method. The excitations are assumed to be external Poisson impulse process and parametric Poisson impulse process on displacement. The PDF of the oscillator response is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation, which is solved with the EPC method. The nonlinear oscillator with external and parametric excitation on displacement is analyzed when the mean of oscillator response is nonzero. Different levels of oscillator nonlinearity and nonzero means of the impulse amplitude are considered in the analysis. The analytical results show that the PDF solutions given by the EPC method are in good agreement with the simulated results when the complete sixth-degree polynomial of state variables is taken in the EPC procedure. The good agreement is also observed in the tail regions of the PDF solutions. The numerical analysis further shows that the PDF of displacement is not symmetrical about the mean of displacement.

A failure analysis of composite plates accounting for localized loadings is presented in this work. A unified formulation is adopted to derive classical, higher order, layerwise, and mixed theories. A closed form, Navier-type solution is assumed. Simply supported, cross-ply laminates are investigated. Plates are subjected to a stepwise loading, an off-centric localized one and a localized moment. First-ply failure loading and index are obtained via several failure criteria. The influence of the side-to-thickness ratio is accounted for investigating thin and very thick plates. Symmetric and asymmetric stacking sequences are investigated. The accuracy of the proposed theories is assessed. On the basis of the obtained results, it can be concluded that higher order models are required for a correct failure analysis in which the three-dimensional stress state attributable to the localized loadings is accurately described.

The inelastic nonlinear behaviors of preloaded steel trusses undergoing heating and cooling cycles, a problem not well treated previously, are studied in this paper. A bilinear elastoplastic model with a kinematic strain-hardening rule is adopted for steel at varying temperatures. The material softening effects at elevated temperatures are taken into account via the Eurocode 3 reduction factors. The plastic strain resulting from strain reversal upon unloading at a given temperature is considered in updating the stress-strain curve for the next temperature increment. Two simple trusses are adopted to illustrate the physical phenomena involved. All the equations are presented in incremental form, consistent with the updated Lagrangian formulation. The results for the trusses are believed to be new and can be adopted as the benchmarks for validating other numerical approaches used in treating problems involving the heating and cooling stages.

Decentralized data processing has the benefit of improving wireless monitoring system scalability, reducing the amount of wireless communications, and reducing overall power consumption. In this study, a system identification strategy for single-input multi-output (SIMO) subspace system identification is proposed based on Markov parameters. The method is specifically customized for embedment within the decentralized computational framework of a wireless sensor network. By using the computational resources of wireless sensors, individual sensor nodes perform local data processing to identify the Markov parameters of a structural system. The data storage and wireless communication requirements of Markov parameters are significantly less than that required by the original raw data, resulting in the preservation of scarce system resources such as communication bandwidth and battery power. Then, the estimated Markov parameters are wirelessly communicated to a wireless sensor network base station where the global structural properties are assembled by execution of the eigensystem realization algorithm, an indirect subspace system identification method. The proposed strategy is evaluated using input-output and output-only data recorded during dynamic testing of a cantilevered balcony in a historic building (Hill Auditorium, Ann Arbor, MI).

The effect of seepage (injection and suction) on the dynamics of vortices and large-scale structures in a rough open channel flow was examined experimentally. The velocity measurements in the open channel flow were carried out using particle image velocimetry. A swirling strength-based vortex identification algorithm was used to extract the location, size, and strength of vortices in the flow. Proper orthogonal decomposition (POD) was used to analyze the dynamics of large-scale structures in the flow. The results indicate that suction induces a greater change compared with an equivalent amount of injection on the open channel flow. Suction dampens the size and strength of the vortices compared to the no-seepage case. POD analysis indicates that seepage tends to introduce more small-scale structures in the flow and destroys the large-scale organized motion present otherwise in the flow.

The purpose of this study is to find analytic solutions for the accurate computation of the shear stresses in sandwich beams under flexure. Specifically, the Jourawski approach for treating the shear problem is applied to the structural beam model on the basis of the piecewise linear (i.e., zigzag) warping. This approach is shown to work very well for sandwiches in which one may neglect the normal deformation component along the core thickness. The focus is limited to sandwiches whose cross section is symmetric with respect to the neutral axis. For such a case, general expressions are obtained for the shear stresses in terms of the rotations of skins and core. By resorting to the description of the zigzag warping developed in the 1970s an explicit analytic expression is obtained for the case of simply supported sandwich beams subject to uniform transversal loading. The comparison with finite-element simulations shows the excellent accuracy and wide range of applicability of the proposed method.

Although a complete unified theory for elasticity, plasticity, and damage does not yet exist, an approach on the basis of thermomechanical principles may be able to serve as the foundation for such a theory. With this in mind, as a first step, a mixed formulation is developed for fully coupled, spatially discretized linear thermoelasticity under the Lagrangian formalism by using Hamilton’s principle. A variational integration scheme is then proposed for the temporal discretization of the resulting Euler-Lagrange equations. With this discrete numerical time-step solution, it becomes possible, for proper choices of state variables, to restate the problem in the form of an optimization. Ultimately, this allows the formulation of a principle of minimum generalized complementary potential energy for the discrete-time thermoelastic system.

This paper presents a new algorithm for evaluating impulse response functions for the convolution integrals of the aerodynamic forces of bridge decks. The impulse response functions formed by measured flutter derivatives are modified to satisfy causality conditions through optimization. The error function in the object function is defined as the least square errors between the measured and the modified transfer function, and the causality condition is imposed as a penalty function. The modified transfer functions are interpolated with the cubic spline. The selection of the optimal penalty number is presented for obtaining a balanced solution between the effects of the error function and the penalty function. The proposed method is verified using two numerical examples. Time-domain aeroelastic analyses are performed with the proposed method for a thin rectangular section and a bluff H-type section, and the results are compared to values obtained by the rational function approximation (RFA) and the analytical particular solution of the equation of motion. The proposed method yields accurate and stable solutions for both types of sections, whereas the rational function approximation results in erroneous solutions for a bluff H-type section.

In this work, a new concrete model that strongly couples continuum-damage-mechanics to elastoplasticity is presented. The model incorporates a plasticity yield criterion written in terms of the nominal/damaged, rather than effective, stress space. Tensile and compressive behaviors are modeled through the damage-affected-multi-hardening nature of the plasticity yield criterion and the introduction of two (tensile and compressive) plasticity-affected isotropic damage initiation/growth criteria, where plasticity variables are added to the definition of the tensile and compressive growth functions of damage. A nonassociative plastic flow rule is used to control inelastic dilatancy. Specific expressions of the elastic/damage and plastic/damage components of the Helmholtz free energy function are presented. The constitutive equations of the model are consistently derived within a sound framework of irreversible thermodynamics. These free energy expressions are used to define three plasticity and damage interconnected dissipation mechanisms, one plasticity mechanism and two damage mechanisms. The elastic-plastic-damage, elastic-plastic, and elastic-damage tangent operators are also derived. A computational algorithm for the numerical integration of the constitutive equations is proposed on the basis of the doubly passive predictor–plastic-damage corrector approach. The model is implemented in the Finite Element (FE) analysis software ABAQUS through a user defined material subroutine (UMAT). Two- and three-dimensional verification examples are carried out to demonstrate the effectiveness and robustness of the proposed model in producing results that depict experimentally observed concrete behaviors. The results of the proposed model are compared with those of a weak coupling concrete model recently presented by the authors, in which damage was incorporated in the elastic formulation whereas plasticity remained in the effective stress space. The comparison shows the effect of strong-coupling on increasing/accelerating the degradation of concrete when the same material parameters of the weak coupling model are used. The results of the proposed model are also compared with those of well known strong-coupling models available in contemporary literature. To reduce the sensitivity of the nonlinear FE analysis of concrete structures to the refinement of the FE meshes, the damage density parameters are defined to include embedded dimensionless coefficients that are related to concrete’s fracture energies (in tension and compression) and to the geometrical characteristic length provided by ABAQUS software during the analysis. The conclusions drawn from this work clearly indicate the adequacy of the model to describe the different stages of concrete behavior and stiffness and strength degradations attributable to elastoplasticity-affected damage growth. They also show that the model can be further improved and equipped with nonlocal measures to enhance its future performance.

This work presents the principle of virtual work and reciprocal theorem of partial-interaction composite beams. The principle of minimum potential energy is also obtained and proved along with the variational formulae for the frequency of free vibration and the critical load of buckling of partial-interaction composite beams. Approximate solutions for bending, vibration, and buckling are finally given to demonstrate their applications. It is shown that the deflections, resonant frequencies, and critical loads of buckling of composite beams under different boundary conditions can be readily obtained with enough accuracy by using these variational principles.