Journal of Engineering Mechanics

In this paper, the moment-curvature behavior of a steel column under constant axial loading is implemented into a computationally efficient one-dimensional finite-element approach, utilizing Timoshenko beam theory, to determine the dynamic response of steel columns subjected to blasts. Then, a new single-degree-of-freedom (SDOF) approach is provided for determining pressure impulse curves for steel columns under constant axial loading. This SDOF approach relies on the newly defined concept of the reduced resistance-deflection function to accurately simulate the $P\mathrm{\Delta }$ effects and the global instability failure mechanism, which are both caused by the axial load. The aforementioned finite-element approach is then used to thoroughly validate the newly proposed SDOF approach for deriving pressure impulse curves. It is shown that, despite the inherent simplicity of the approach, the newly proposed SDOF approach provides accurate and reliable results.

The influence of the initial stretching of a simply supported plate containing two neighboring circular inclusions on the forced vibration analysis of the plate caused by the time-harmonic bending forces on the upper face plane is studied in the plane-strain state. The corresponding boundary-value problem is formulated using the three-dimensional linearized theory of elastic waves in initially stressed bodies and is solved numerically by the FEM. The materials of each component of the plate (i.e., the circular inclusions and the matrix) are selected to be isotropic. Numerical results on the dynamic stress concentrations around the inclusions and the influence of the initial stretching on those concentrations are presented and compared with the corresponding numerical values of plates with two neighboring circular holes and a plate without holes.

Structural health monitoring (SHM) using dynamic response measurement has received tremendous attention over the last decades. In practical circumstances, outliers may exist in the measurements that lead to undesirable identification results. Therefore, detection and special treatment of outliers are important. Unfortunately, this issue has rarely been taken into systematic consideration in SHM. In this paper, a novel outlier-resistant extended Kalman filter (OR-EKF) is proposed for outlier detection and robust online structural parametric identification using dynamic response data possibly contaminated with outliers. Instead of definite judgment on the outlierness of a data point, the proposed OR-EKF provides the probability of outlier for the measurement at each time step. By excluding the identified outliers, the OR-EKF ensures the stability and reliability of the estimation. In the illustrative examples, the OR-EKF is applied to parametric identification for structural systems with time-varying stiffness in comparison with the plain EKF. The structural response measurements are contaminated with outliers in addition to Gaussian noise. The proposed OR-EKF is capable of outlier detection, and it can capture the degrading stiffness trend with more stable and reliable results than the EKF.

Transverse galloping is a type of aeroelastic instability characterized by large amplitude, low frequency, normal to wind oscillations that appear in some elastic two-dimensional bluff bodies when subjected to a fluid flow, provided that the flow velocity exceeds a threshold critical value. Such an oscillatory motion is explained because of the energy transfer from the flow to the two-dimensional bluff body. The amount of energy that can be extracted depends on the cross section of the galloping prism. Assuming that the Glauert–Den Hartog quasi-static criterion for galloping instability is satisfied in a first approximation, the suitability of a given cross section for energy harvesting is evaluated by analyzing the lateral aerodynamic force coefficient, fitting a function with a power series in $\tan \alpha$ ($\alpha$ being the angle of attack) to available experimental data. In this paper, a fairly large number of simple prisms (triangle, ellipse, biconvex, and rhombus cross sections, as well as D-shaped bodies) is analyzed for suitability as energy harvesters. The influence of the fitting process in the energy harvesting efficiency evaluation is also demonstrated. The analysis shows that the more promising bodies are those with isosceles or approximate isosceles cross sections.

Research on damage detection is commonly carried out in the frequency domain using methods based on the modal data, transfer function or frequency response function, and transmissibility. The motivation for using transmissibility to detect damages relies on the fact that transmissibility measurements are local quantities that suggest high sensitivity. Nevertheless, the measurement of transmissibility requires external harmonic forces as the known input and sensors directly attached to the structure. There is a need for methods that can perform damage detection without attaching sensors and knowing the details of the input excitations. In a vehicle-bridge coupled (VBC) system the vehicle can serve as a force exciter and its dynamic response can be easily measured. In this paper, to make use of the vehicle response the transmissibility of a VBC system was first theoretically derived in a system consisting of a simply supported beam and a single-degree-of-freedom vehicle. Then, a numerical study was conducted to investigate the feasibility of detecting bridge damages using the vehicle transmissibility of the VBC system. In the numerical analysis, several damage indicators were constructed based on the transmissibility from both the bridge and vehicle responses, and compared to each other to select a proper one for damage detection. A parametric study was conducted on factors such as the measurement numbers, road roughness, and vehicle speeds and numbers to analyze the effectiveness of using such indicators for damage detection. To make use of the mobility of moving vehicles, two methods were finally proposed to measure the transmissibility of vehicle responses by using two vehicles. Method I used one reference vehicle and one moving vehicle; Method II used two moving vehicles at a constant distance in the longitudinal direction along the bridge. Using these two methods, the modal information such as natural frequencies and modal shape squares was successfully extracted for damage detections.

A nonlinear finite-element formulation for the static and dynamic behavior of flexible beams was developed by appropriately modifying and extending the three-dimensional (3D) finite-deformation beam model originally developed by Simo. By introducing energy dissipation in a physically consistent way through a linear viscoelastic constitutive equation, the main contribution in this paper lies in the derivation of a tangent stiffness operator that includes the effect of damping. Moreover, a solution to issues concerning the interpolation of total rotation vectors of magnitude greater than $\pi$ is proposed, along with an alternative approach for the update of curvatures based on total rotation vectors, taking advantage of special features of Lie groups and of the notion of right-trivialized derivative. Both two-dimensional (2D) and three-dimensional (3D) numerical examples are presented. In particular, static and dynamic analyses of an electrical conductor commonly used in power substations were performed. Energy balance calculations and the convergence rate of Newton’s method illustrate the accuracy of the computed solutions.

A new type of nonlinear energy sink (NES), termed a track NES, is proposed in this paper. The shape of the track over which the auxiliary mass moves determines the character of the nonlinear restoring force for the NES. After deriving the equations of motion for the track NES, numerical optimization is carried out for the system implemented in a two-degree-of-freedom primary structure. The optimization results are in the track shape of a fourth-order polynomial. The performance of the track NES is compared with an equivalent tuned mass damper (TMD) and the Type I NES, which utilizes a cubic restoring force. The results of this comparison show that the attenuation observed with the track NES is competitive with the Type I NES and is more robust against changes in the underlying structure than the TMD. Moreover, the track NES is more scalable and offers greater flexibility in prescribing the associated nonlinear restoring force.

This paper studies the dynamic geometrically nonlinear behavior of walls that are strengthened with fiber-reinforced polymer (FRP) composite materials but include preexisting debonded regions. For that purpose, two specially tailored finite elements corresponding to the perfectly bonded regions and debonded regions within the layered wall are formulated under the umbrella of a dynamic analysis. The two finite elements are based on a high-order multilayered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains. The convergence and validity of the geometrically nonlinear dynamic model are studied for the case of a locally debonded FRP-strengthened wall under in-plane shear loads applied at a constant rate. The unified model of the strengthened wall with a local delamination is then used for studying the dynamic nonlinear behavior under different levels of shear loading rate. The dynamic results and the comparison with static analyses reveal the impact of the geometrical nonlinearity on the dynamic behavior of the debonded composite layer and the evolution of interfacial stresses at its perimeter. At the same time, they reveal the impact of the dynamic effects on the geometrical nonlinearity and critical points it involves.

Strut-and-tie models (STMs) are widely used by RC designers. However, selection of a viable model is a challenging task, especially in complex three-dimensional (3D) design domains with irregular cutouts, which are common in building cores and shear walls. Therefore, topology optimization has been promoted as a means of automating the development of minimum strain energy STMs, which can lead to improved structural behavior. Current drawbacks of such methods are that solutions may be difficult to construct and may fail to properly account for tensile stresses resulting from force spreading. A two-dimensional hybrid truss-continuum topology optimization scheme was recently developed to overcome these challenges with the goal of reconfiguring traditional reinforcement layouts to automatically follow principal tensile stresses, reducing cracking at service loads and increasing strength and ductility at an ultimate limit state. That work is generalized and extended herein to 3D domains and mechanics models. Stiffness is formulated such that truss elements carry only tensile forces and thus represent straight steel rebar, while the continuum elements carry only compressive forces and thus represent concrete compression load paths. The latter is achieved using a stress-dependent orthotropic material model. The algorithm is demonstrated on several benchmark design examples.

A multiple scales asymptotic analysis is developed to describe the attenuation of a water hammer pressure wave initiated by a time-varying valve closure. The analytical results expose a simple rule-of-thumb relationship between water hammer pressure wave attenuation and the periodic average of the absolute flow velocity that is predicted by a quasi-steady friction model. The effect of flow reversals on the pressure wave attenuation is examined through comparison with a similar method applied to the water hammer generated during flow establishment, wherein flow reversals do not occur and there is a nonzero net flow. Although the analytical description is based on the assumption that the water hammer is generated by a sudden valve closure, its practical usefulness is extended by using the numerical solution as a guide to demonstrate its validity for a range of valve closure durations. A qualitative upper limit on closure times to which the analytic results may be applied is also found. All results are numerically verified using the method of characteristics.

Modeling and simulation are being relied upon in many fields of science and engineering as computational surrogates for experimental testing. To justify the use of these simulations for decision making, however, it is critical to determine, and when necessary mitigate, the biases and uncertainties in model predictions, a task that invariably requires validation experiments. To use experimental resources efficiently, validation experiments must be designed to achieve the maximum possible increases in model predictive ability through the calibration of the model against experiments. This need for efficiency is addressed by the concept of optimally designing validation experiments, which constitutes optimizing a predefined criterion while selecting the settings of experiments. This paper presents an improved optimization criterion that incorporates two important factors for the optimal design of validation experiments: (1) how well the model reproduces the validation experiments, and (2) how well the validation experiments cover the domain of applicability. The criterion presented herein selects the appropriate settings for future experiments with the goal of achieving a desired level of predictive ability in the computer model through the use of a minimal number of validation experiments. The criterion explores the entirety of the application domain by including the effect of coverage, and exploits areas of the domain with high variability by including the effect of empirically defined discrepancy bias. The effectiveness of this new criterion is compared with two well-established criteria through a simulated case study involving the stress-strain response and textural evolution of polycrystalline materials. The proposed criterion is demonstrated as efficient at improving the predictive capabilities of the numerical model, particularly when the amount of experimental data available for validation is low.

A new class of interval-based computational algorithms for parameter identification under uncertainty in structural engineering problems is presented. The iterative method allows passing directly from uncertain raw measurements to sharp (tight) bound estimates of the unknown parameters by exploiting interval FEMs and adjoint-based optimization techniques. Overestimation in interval width is handled successfully using the inclusion isotonicity property of interval arithmetic. First, an update of the iterative solution proceeds in a degenerated interval form until it becomes insignificant, and then the update is switched to full interval form, allowing uncertainty propagation and sensitivity analysis. A new containment-stopping criterion, which is intrinsic to intervals, is used. Example problems are then presented and discussed to show the effectiveness of the proposed inverse method in estimating the range of Young’s moduli from given ranges in displacements.

This paper considers the minimum buckling load and mode shape of a simply supported beam on an elastic foundation. Solutions are obtained by solving the eigenvalue problem delivered by a finite-element formulation and by using the analytical solutions involving (1) trials and (2) rounding of real numbers to integers as described by Hetényi [Hetényi, M. (1946). Beams on Elastic Foundations, University of Michigan Press, Ann Arbor, MI]. The comparison shows that the solution by rounding can lead to overestimation of the buckling load close to the transition zone between mode shapes. The paper explains the reason for the overestimation and offers a simple direct algorithm that always leads to the correct mode shape and minimum buckling load.

The presence of unknown complex boundary conditions usually imposes difficulties in estimating the cable forces in cable-stayed bridges when using conventional model-based force identification methodologies. Therefore, there exists a need for new methodologies that can overcome these challenges while achieving acceptable force identification accuracy. This paper presents an innovative method to estimate the forces within stay cables with complex boundary conditions. The proposed approach transforms the cable force estimation problem from the common procedure of constructing and solving the equation of motion of the cable to a simpler problem of finding the zero-amplitude points of its mode shapes. Ultimately, the presented methodology yields accurate cable force estimations regardless of the complexity of the boundary conditions. An equivalent segmental model whose length is given by the distance between these points is used next to find an estimate of the cable tension force. A stay cable under axial force and constrained by end rotational springs is employed to analytically investigate the force identification accuracy of the proposed method. It is observed that with mode orders lower than 18, the proposed method achieves a maximum relative error less than 5% regardless of the end-restraint condition. Therefore, the proposed method has great potential for practical application because of its theoretical simplicity, accuracy, and feasibility.

This article presents a novel extended limit analysis approach that determines the sharp maximum and minimum bounds on the collapse load of rigid perfectly plastic structures simultaneously subject to uncertain but bounded loading magnitudes and plastic material capacities. The governing formulation is cast as a linear programming problem with interval coefficients. Linearity is achieved by a suitable piecewise linearization of nonlinear yield surfaces. The proposed algorithm is founded on a characteristic formula concept and an appropriate interval arithmetic interpretation to transform the interval limit analysis problem into two deterministic linear programming problems that can be solved by any available linear programming solver.