Journal of Engineering Mechanics

This paper describes the wave-propagation behavior of multilayered structures and proposes an optimization procedure for designing layered stress wave attenuators. Two types of stress wave attenuators were investigated, straight and nonstraight configurations, and their wave behaviors were analyzed using the concept of longitudinal waves in rods and flexural waves in Timoshenko beam formulations. The underlying concept in this research relies on the reflection and transmission of waves at different types of discontinuities, such as boundaries, impedance mismatches, and angled joints. Therefore, the effects of these discontinuities were explored thoroughly, and their attenuation capacity was investigated using explicit formulas. These concepts then were used to develop a heuristic optimization procedure to obtain efficient layered stress wave attenuators by properly tuning the length and material of each layer. It was assumed that the stress wave attenuators were subjected to impulsive transient loadings with similar duration as that of blast waves. The results obtained demonstrate that it is very difficult to attenuate the amplitude of transient loadings with the duration of blast waves in structures using straight layered configurations having small thickness, whereas symmetric nonstraight architectures can be rather effective for achieving the desired attenuation of impulsive loadings.

The dynamic response of an elastic pounding oscillator subjected to harmonic excitation is investigated with dimensional analysis. To model the pounding process, a linear viscoelastic model is used to simulate the contact force. Through dimensional analysis, the peak structural response parameters of the pounding oscillator, including structural displacement, velocity, and penetration displacement, are characterized by a set of dimensionless terms (denoted by the Buckingham notation $\mathrm{\Pi }$). The reduced $\mathrm{\Pi }$-set explicitly describes the interaction between the oscillator and the rigid barrier. Analytical solutions to dimensionless contact time, displacement, and velocity response are derived in this study and are further verified against the numerical simulation. The effect of pounding on the oscillator’s response is illustrated using three well-divided spectral regions (i.e., amplified, deamplified, and unaffected regions), which are defined based on the dimensionless system frequency parameter ${\mathrm{\Pi }}_{\omega }$. Parametric studies show that the penetration displacement for different levels of contact stiffness is insensitive to the dimensionless gap size ${\mathrm{\Pi }}_d$ but is affected significantly by changes in the coefficient of restitution ${\mathrm{\Pi }}_r$.

The article presents a new approach based on a strain gradient damage constitutive law for modeling quasi-brittle materials such as concrete. The authors use a weak type nonlocal formulation of the problem, relying on Mindlin’s Form II strain gradient elasticity theory. Gibbs free energy is used and the influence of the positive and negative principal strains to damage evolution is separated. Additional energy dissipation due to the gradient of the positive principal strains is introduced. The model requires an internal length, which is treated as an internal variable dependent on the level of damage. The study shows that the internal length increases with damage, corroborating available experimental results. Calibration of the gradient internal length evolution with damage is established through experimental data from two independent tests: a uniaxial tension or compression test to establish the evolution of damage, and a four-point bending (loading-unloading) test to relate the variation of the internal length with the accumulated level of damage. A numerical analysis of the response of a concrete beam specimen under four-point bending is presented to describe the calibration procedure.

An accurate three-dimensional (3D) elasticity solution is presented for static analysis of flat laminated panels with interlaminar bonding imperfection under arbitrary boundary conditions exhibiting edge effects. The recently developed mixed-field multiterm extended Kantorovich method (MMEKM) for 3D solution of perfectly bonded laminates is generalized to include the interfacial compliance characterized by displacement jumps. A general variationally consistent framework using the Reissner-type mixed variational principle is proposed to treat the imperfect interfacial conditions. It is shown through numerical studies on composite and soft-core sandwich panels under different boundary conditions that, similar to the perfect bonding case, the MMEKM yields accurate results with just two or three terms and in two or three iterations for the weakly bonded laminates also. The roles that the boundary conditions, locations of the imperfect interfaces, and span-to-thickness ratios play on the effect of weak bonding on the response of laminated structures are investigated for a wide range of values for the imperfection compliance.

This study quantitatively investigates the influences of the $P\text{-}\mathrm{\Delta }$ effect on the statistics of ductility demand and cumulative dissipated energy of a hysteretic system under bidirectional seismic excitations. An improved biaxial Bouc-Wen model incorporating the $P\text{-}\mathrm{\Delta }$ effect as well as the strength and stiffness degradations was used to represent the hysteretic behavior of an inelastic two-degrees-of-freedom (2DOF) system. The influences of both the strength/stiffness degradation and the $P\text{-}\mathrm{\Delta }$ effect on the statistics of the ductility demand and cumulative dissipated energy of the hysteretic 2DOF system were quantitatively investigated using a series of strong ground motion records. Based on the numerical results, the preferred empirical probability distribution types and prediction equations for the ductility demand and normalized cumulative dissipated energy of the hysteretic 2DOF system including the $P\text{-}\mathrm{\Delta }$ effect and under bidirectional seismic excitations were recommended, while the potential statistical correlation between the ductility demand and commonly used seismic parameters were also discussed. The analyses show that the strength/stiffness degradation and $P\text{-}\mathrm{\Delta }$ effect can significantly impact the probabilistic characteristics of the ductility demand and cumulative dissipated energy of a hysteretic system under bidirectional seismic excitations, especially for a system with a short natural vibration period and/or small yield strength. The ductility demand of an inelastic 2DOF system under bidirectional excitations can be approximated by the square root of the sum of squares of the ductility demands of a single-degree-of-freedom (SDOF) system under unidirectional excitation, while the normalized cumulative dissipated energy of a 2DOF system can be expressed as the approximate sum of the normalized cumulative dissipated energies of the SDOF system.

In the present paper, stress intensity factor (SIF) analyses and fatigue-crack-growth simulations of corner cracks emanating from loaded pinholes of attachment lugs in structural assemblies are carried out for different load cases. A three-dimensional (3D) symmetric Galerkin boundary-element method (SGBEM) and FEM alternating method is developed to analyze the nonplanar growth of these surface cracks under general fatigue. The 3D SGBEM-FEM alternating method involves two very simple and coarse meshes that are independent of each other: (1) a very coarse FEM mesh to analyze the uncracked lug, and (2) a very coarse SGBEM mesh to model only the growing crack surface. By using the SGBEM-FEM alternating method, the nonplanar growth of cracks in 3D (surfaces of discontinuity) up to the failure of structures are efficiently simulated, and accurate estimations of fatigue lives are made. The accuracy and reliability of the SGBEM-FEM alternating method are verified by comparing them to other FEM solutions, as well as experimental data for fatigue-crack growth available in the open literature. The SIF calculations, crack surface evolutions, and fatigue-life estimations are all in good agreement with other detailed FEM solutions and experimental observations. It is noted that for fracture and fatigue analyses of complex 3D structures such as attachment lugs, a pure FEM requires several hundreds of thousands or even millions of elements, whereas the present 3D SGBEM-FEM alternating method requires only up to 1,000 FEM elements and $\sim 100$ SGBEM elements. It thus demonstrates that the present SGBEM-FEM alternating method, among the many Schwartz-Neumann-type alternating methods developed in the past 20–30 years are suitable for analyzing fracture and fatigue-crack propagation in complex 3D structures in a very computationally efficient manner, as well as with very low human labor costs.

This study develops four finite elements (FEs) for the analysis of wide-flange steel beams reinforced with a glass fiber–reinforced polymer (GFRP) plate bonded together via an adhesive layer. The formulations treat each of the steel beams and GFRP plates as Vlasov-Gjelsvik thin-walled beams. Two elements are based on shear-deformable kinematics, whereas the other two are based on non-shear-deformable kinematics. The formulations capture the longitudinal-flexural and lateral-torsional responses of the system. Results are then compared with three-dimensional FE analysis solutions based on a current computer program, and the importance of incorporating shear-deformation effects is illustrated, particularly when predicting predominantly torsional responses. The formulation is used to investigate the interaction effect of the shear modulus of the adhesive layer and the length of the GFRP plate.

The nonlinear analysis of shape memory alloy (SMA) hybrid composite beams under in-plane thermal load is presented in this paper. The properties of the constituents are assumed to be temperature dependent. The initial imperfection of the beam is also taken into account as an initial deflection function prior to heating. Geometrical nonlinearity is formulated in the von Karman sense. It is assumed that the kinematics of the beam obeys the Timoshenko first-order beam theory and the SMA fibers follow the one-dimensional Brinson constitutive law. These basic assumptions are inserted into the static version of the virtual displacements principle to derive the nonlinear equilibrium equations. The resulting system of equations is uncoupled and solved exactly. Closed-form expressions are presented to trace the equilibrium path of the beam as a function of the uniform heating parameter. It is shown that, in special cases, the induced tensile recovery stress of the SMA fibers may stabilize an imperfect beam that has bent during heating.

The first two moments of the steady-state response of a dynamical random system are determined through a polynomial chaos expansion (PCE) and a Monte Carlo simulation that gives the reference solution. It is observed that the PCE may not be suitable to describe the steady-state response of a random system harmonically excited at a frequency close to a deterministic eigenfrequency: many peaks appear around the deterministic eigenfrequencies. It is proved that the PCE coefficients are the responses of a deterministic dynamical system—the so-called PC system. As a consequence, these coefficients are subjected to resonances associated to the eigenfrequencies of the PC system: the spurious resonances are located around the deterministic eigenfrequencies of the actual system. It is shown that the polynomial order required to obtain some good results may be very high, especially when the damping is low. These results are shown on a multidegree-of-freedom (DOF) system with a random stiffness matrix. A 1-DOF system is also studied, and new analytical expressions that make the PCE possible even for a high order are derived. The influence of the PC order is also highlighted. The results obtained in the paper improve the understanding and scope of applicability of PCE for some structural dynamical systems when harmonically excited around the deterministic eigenfrequencies.

The use of a membrane to mitigate the extreme pressure loads on the roof of a surface-mounted prism is investigated. The fluid-structure interaction problem is solved by coupling the unsteady Navier-Stokes equation with the membrane equation. The minimum number of membrane modes required for the solution is determined through a convergence study. The results show that this passive control technique can be used to reduce the extreme pressure coefficients by approximately 25%. This reduction is explained by investigating the effects of the membrane on the flow field.

This paper presents a novel method of data-based probabilistic seismic hazard analysis (PSHA) and ground motion simulation, verified using previously recorded strong-motion data and machine-learning techniques. The procedure consists of three parts: (1) selection of an orthonormal set of basis vectors called eigenquakes to represent characteristic earthquake records; (2) estimation of response spectra for the anticipated level of shaking for a scenario earthquake at a site using Gaussian process regression; and (3) optimal combination of the eigenquakes to generate time series of ground acceleration consistent with the response spectral ordinates obtained in the second part. The paper discusses the benefits of applying such machine-learning methods to strong-motion databases for PSHA and ground motion simulation, particularly in large urban areas where dense instrumentation is available or expected. The effectiveness of the proposed methodology is exhibited using four scenario examples for downtown Los Angeles. Advantages, disadvantages, and future research needs for this machine-learning approach to PSHA are discussed.

This study presents the thermal buckling of a radially solid sandwich circular plate made of a piezoelectric actuator and porous material. The porous material properties vary through the thickness of the plate for a specific function. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The geometrical nonlinearities are considered along with the higher-order shear deformation plate theory. The problem is simplified to an axisymmetric one, and then closed-form solutions for circular plates subjected to temperature load are obtained. The buckling temperatures that are derived for solid circular plates under uniform temperature rise through the thickness for an immovable clamped edge of the boundary conditions. The effects of the porous plate thickness, piezoelectric thickness, applied actuator voltage, and variation of porosity on the critical temperature load are investigated. In this paper, the stability of the plate is compared through saturated and unsaturated porous layers, and the effect of the fluid’s thermal expansion coefficient on the stability of the plate is investigated.