Journal of Engineering Mechanics

In this article, the transformation of linear first-order models to second-order models is investigated for cases in which the system is excited by unknown inputs and ground excitations. It is shown that the second-order coefficients lie in the null space of a matrix, which is constructed from the partitions of the state matrix using the Kronecker product. The conditions that determine the size of this null space are discussed and solutions are developed for various cases.

Vibration reduction or damping capability is highly desired for structural stability when hazardous impact loads are applied to a concrete structure. Damping capability of concrete structures depends primarily on the viscoelastic response of concrete material to the magnitudes and frequencies of impact loads, which in turn requires a minimum level of stiffness and damping capacity of concrete. A common industrial byproduct material—silica fume that showed certain antishock potential when mixed with concretes—was modified with silane in this study toward improved capabilities in both stiffness and damping. To evaluate the effectiveness of the modified silica fume (MSF), a series of dynamic flexural tests and numerical analyses were conducted, of which the results are presented. A three-dimensional micromechanical model was developed based on the discrete element method (DEM), which was then employed to study the stiffness and damping behavior of the admixed concrete. A 10% usage of MSF (by weight of cement) was found to significantly enhance the storage and loss moduli and the loss tangent of concrete. The DEM model developed can be used for evaluating and designing energy-absorbing concretes for general military and civil uses.

The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange’s equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function.

Real-time hybrid simulation provides an economical and efficient experimental technique for performance evaluation of structures under earthquakes. A successful real-time hybrid simulation requires accurate actuator control in order to achieve reliable experimental results. The time delay as a result of servohydraulic dynamics, if not compensated for properly, would lead to inaccurate or even unstable simulation results. However, the nonlinearities in servohydraulic systems and experimental substructures make the actuator delay difficult to accurately estimate in practice. Therefore, actuator control presents a challenge for the application of the real-time hybrid simulation technique to earthquake engineering research. This paper presents an improved adaptive inverse compensation technique for real-time hybrid simulation. Two adaptive control laws based on a synchronization subspace plot are introduced to adjust the compensation parameters in order to minimize both phase and amplitude errors in the servohydraulic actuator response. The improved adaptive inverse compensation method is experimentally evaluated through real-time tests involving a large-scale magneto-rheological damper subjected to band-limited white noise–generated random displacements and variable current inputs. The experimental results are compared with the command displacements, with the error assessed using various evaluation criteria. The improved adaptive inverse compensation is compared with an existing adaptive inverse compensation method to demonstrate the improvement that the newly developed compensation method offers in minimizing actuator delay. The proposed improved adaptive inverse compensation method is demonstrated to further improve actuator control by reducing not only actuator tracking errors but also associated energy errors.

Strength anisotropy in soils needs to be characterized by proper anisotropic failure criterion. This paper presents a novel yet simple methodology to generalize an isotropic failure criterion to account for strength anisotropy in soils. A salient ingredient of the method involves the introduction of the degree of cross anisotropy and an anisotropic variable, defined by the joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, into the frictional characteristic of the isotropic criterion. The well-received Lade’s failure criterion is taken as an example to demonstrate the generalization. Predictions using the newly generalized Lade’s criterion for a number of soils, including completely decomposed granite, glass beads (virtual sand), natural clays, sand, as well as silty sand, show good agreement with test data. The proposed approach has proved to be simple and generic, and can be effortlessly applied to many existing isotropic failure criteria to adapt them to account for strength anisotropy. The treatment also requires very few parameters, which can be conveniently calibrated from conventional laboratory tests in most cases.

Because of large pronounced deformation in the compressive creep process of soft sand asphalt, it is necessary that both the true stress and true strain are measured. Accordingly, instead of fictitious creep compliance (FCC), true creep compliance (TCC) relating the true strain to the true stress is used to characterize the viscoelastic properties of sand asphalt in this paper. The relationship between TCC and FCC is described by a second-kind Volterra integral equation (VIE). A prediction method of long-term mechanical behavior of largely deformed sand asphalt with constant loading creep tests is proposed. In this method, the FCC master curves are constructed based on the time-temperature superposition principle, and then the linear VIE from the FCC to the TCC is solved with the collocation method, and the nonlinear VIE from the TCC to the FCC is solved with an iterative formula. Unconstrained compressive creep tests for 3,600 s were conducted on sand asphalt mixture samples in various temperature and nominal stress conditions. As an application example, the long-term creep behavior of sand asphalt at the given reference temperature is predicted with the proposed method.

A cable-braced grid shell is a new type of single-layer latticed shell suitable for glass roofs. Compared with traditional single-layer latticed shells, this new type of shell has a unique mesh shape (planar quadrilateral mesh), mesh form (steel and crossing cables), and surface shape (from the translation surface method). The grid shell is a single-layer latticed structure, and therefore stability is one of the key factors in the structural design. Therefore, in this paper, an elliptic paraboloid cable-braced grid shell with imperfections is used as an example with which to determine the formulas for the buckling load based on the continuum analogy. The main contents of this paper include the formula for the linear buckling load of an elliptic paraboloid cable-braced grid shell with imperfections, which is determined based on the continuum analogy. The equivalent rigidity for the cable-braced grid shell is then determined, and the effect of the cables on the shear rigidity is discussed. Finally, the formula for the linear buckling load is verified with numerical examples, and the errors are analyzed and a corresponding correction factor is given.