Journal of Engineering Mechanics

Reliable evaluation of the fatigue crack growth rates in different kinds of specimen is necessary for the design of engineering components working in fatigue-load conditions. In this study, a new numerical model for evaluation of the fatigue crack growth rate in a three-point-bend specimen was proposed on the basis of compliance method. A three-point-bending fatigue test machine with a displacement-controlled loading system was developed to measure decrease of the fatigue load due to increase of the compliance of the specimen caused by crack growth. Evaluation of the fatigue crack growth rates of hot-rolled 16Mn steel was carried out using the test machine and the numerical model. The analysis results of the crack growth rates revealed different tendencies of slope for the former and latter processes of the subcritical propagation. Paris’s constants of hot-rolled 16Mn steel for the former process were obtained as $c=1.17\times {10}^{-9}$ and $m=4.47$, whereas the same parameters for the latter process were obtained as $c^{\prime }=3.09\times {10}^{-5}$ and $m^{\prime }=0.84$. The threshold value of the stress-intensity factor range for the material was determined as $\mathrm{\Delta }{K}_{th}=10.8\mathrm{MPa}\surd \mathrm{m}$.

A novel nonlinear isolation system designed for buildings is proposed to isolate vibrations in the vertical direction. The system is characterized by quasi-zero stiffness (QZS) obtained by combining linear springs in parallel with disk springs having nonlinear stiffness, including a region with negative stiffness. Static analysis was first applied to establish the force-displacement relation of the bearings and then determine the dynamic equations of motion. Two approximate analytical methods, the average method (AM) and harmonic balance method (HBM), were applied to solve this nonlinear vibration problem, and their suitability was examined. Based on the theoretical response, the transmissibility function was defined to gain insight into the system’s dynamic characteristics and evaluate the isolation properties. The resulting curves show that the QZS system can be effective for vertical isolation, with results dependent on external input magnitude and the damping level. Larger-amplitude excitation and higher damping level tend to increase the isolation starting frequency above which the transmissibility reduces the vibration of the superstructure. Finally, the nonlinear transmissibility curves were compared with equivalent linear curves, and a numerical comparison between a traditional building and a QZS vertically isolated building under seismic excitations was conducted. The comparison revealed significant advantages to adopting the QZS system in vertical isolation.

This work aims at the unconstrained optimization of laminate plate problems by introducing a methodology that uses a decomposition method along with regularized Newton method. The framework is applied to fiber orientation optimization in laminated thin plates regarding the minimization of the maximum displacement of specific plate regions. First, the problem’s domain is divided into isotropic and remainder parts, with the latter grouping laminar anisotropic behavior. This leads to an evaluation of the gradient and Hessian of the objective function in such fashion that inverses are defined only at the first step of the procedure and they are related to the isotropic part only, although the Hessian is updated each step. The fiber orientation sensibility on a plate’s solution can be evaluated separately, leading to an analytic and straightforward way of deriving the first and second derivatives of the design variables. The pb-2 Rayleigh-Ritz Method is used to approximate the solution space and to determine the problem’s semianalytical response. The results obtained are discussed and compared to those found in the literature.

A new method, optimal step-by-step tuning (OSST), is presented for the frequency adjustment of variable stiffness semiactive tuned mass dampers (SATMDs). In this method, the external excitation of the system fitted with a SATMD is divided into several time steps, and the response components are expressed as polynomial functions of the SATMD’s stiffness. An objective function is defined, the minimization of which leads to the desired SATMD’s stiffness in each time step. In order to assess the efficiency of the OSST method, a single-degree-of-freedom (SDOF) system equipped with an innovative SATMD under transient vibrations is considered. The system’s response is obtained and compared with the following cases: (1) unity tuning ratio (UTR) method, in which the frequency of the SATMD is equal to the excitation frequency, and (2) constant tuning ratio (CTR) method, in which the ratio of the SATMD frequency to excitation frequency is a constant value close to unity. The results reveal the superiority of the OSST method in transient response reduction in comparison with the UTR and CTR methods.

A statistical linearization technique is developed for determining second-order response statistics of beams with in-span elastic concentrated supports. The nonlinearities considered relate both to the support restoring forces, and to the assumption of relatively large beam displacements. A significant novel aspect of the technique is the utilization of constrained modes involving generalized functions in their definition; thus, shear-force discontinuities at the support locations can be readily accounted for. Overall, a set of nonlinear modal equations is derived and replaced by a set of equivalent linear ones based on an error minimization scheme in a mean square sense. This yields a set of algebraic nonlinear equations for the beam response second-order statistics, which can be readily solved in a computationally efficient manner via a simple iterative scheme. It is noted that the technique applies to an arbitrary number of supports yielding accurate and computationally efficient solutions for the second-order statistics of the response. Two illustrative numerical examples are considered for assessing the reliability and accuracy of the technique as compared with pertinent Monte Carlo simulation data. The latter are generated based on a boundary integral solution methodology in conjunction with a Newmark numerical integration scheme.