Journal of Engineering Mechanics

This paper considers some historical aspects of engineering mechanics with emphasis on the long historical development of mechanics from the evolution of mathematics and tool making before the Common Era to modern genomic and nanoengineering research. To focus, the discussion is divided into five periods of development: (1) engineering mechanics before the Common Era B.C., (2) development between the first and sixteenth centuries; (3) acceleration in the seventeenth and eighteenth centuries; (4) glory of the nineteenth and twentieth centuries; and (5) window in the twenty-first century. The paper also attempts to project a personal view on the future development in the next 50 years in engineering mechanics. This is given in a section of science fiction and fact at the end of the paper.

A brief history of developments in the field of low-speed aeroelasticity is provided in the context of application to long-span bridge structures. The paper begins with summary of some of the significant developments in aeroelasticity for low-speed aeronautical applications in the early 20th century. The role of the pivotal Tacoma Narrows failure and subsequent investigation is introduced. The development of formal experimental and analytical tools for the prediction of long-span bridge response to wind is presented, and their roots in—but differences from—classical low-speed aeroelasticity are presented and discussed (e.g., aerodynamic admittance). The important issue of Reynolds number scaling is discussed and posed as a problem that requires resolution in future research. Details of analytical and experimental techniques are not provided herein; readers are referred to the references for developments in these areas. The intent of the paper is to emphasize the parallels between these two strongly related fields, and in so doing, highlight the role of classical aeronautical engineering in the development of state-of-the-art bridge wind engineering.

A variational approach for the nonlinear free vibration of shallow shells having a quadrilateral boundary is presented in this paper. Natural coordinates ξ and η are used to map the prescribed geometry in the $x-y$ plane. Displacement fields corresponding to u, $v\text{,}$ w, ${\beta }_1\text{,}$ and ${\beta }_2$ are expressed in terms of the product of two algebraic functions, the form of which is so chosen that the displacement boundary condition can be imposed by manipulating the coefficients. In arriving at the stiffness matrix, no simplification is applied to the nonlinear strains and the variation of the complete energy equation is considered. For the plate problems numerical results are obtained and compared with approximate analytical results by other researchers. Numerical results for the shallow shells are also presented and their characteristics are found to be significantly different from the results for the plates.

A new exact approach for forced vibration analysis of single-degree-of-freedom (SDOF) systems with nonperiodically time-varying parameters (mass and stiffness) is presented. In this paper, the variations of mass and stiffness, relative to time, are described by the selection of suitable expressions such as power functions and exponential functions. More general cases, such as the variation of mass is described by an arbitrary continuous real-valued function and the variation of stiffness is expressed as a functional relation with the variation of mass and vice versa, are also considered in this study. Using appropriate functional transformation, the governing differential equations for vibrations of SDOF systems with nonperiodically time-varying parameters are reduced to Bessel’s equations or other solvable equations for several important cases. Thus, classes of exact solutions for the free and forced vibrations of SDOF systems with arbitrarily time-varying parameters (mass and stiffness) are obtained. Numerical examples show that the proposed procedure is a simple, efficient, and exact method.

Real-time substructure testing is a method for establishing the dynamic behavior of structural systems. The method separates a complex structure into physical and numerically modeled substructures, which interact in real-time allowing time-dependent nonlinear behavior of the physical specimen to be accurately represented. Displacements are applied to the physical specimen using hydraulic actuators and the resulting measured forces are fed back to the numerical substructure. This feedback loop is implemented as a time-stepping routine. One of the key factors in obtaining reliable results using this method is the accurate compensation of the delayed response of the actuator. If this is not accounted for, instability of the feedback loop is likely to occur. This paper presents a method for estimating the delay while a test is in progress and accurately compensating for it during the test. The stability of both linear and nonlinear single-actuator systems is examined and the behavior of twin-actuator systems controlling two degrees-of-freedom at the substructure interface is presented. The effectiveness of the method is clearly demonstrated by comparisons between experimental and theoretical behavior.

Sandwich and bimetallic plating significantly enhance many engineering applications within the civil engineering, marine engineering, and naval architecture fields due to its high strength-to-weight ratio. However, the design of sandwich plates requires an assessment of how they react to environments in which elevated temperatures are probable. A simple model, consisting of a layer bonded to a half plane, is used to predict the thermoelastic stability of such sandwich and bimetallic plating. It is found that the conduction of heat between the two dissimilar elastic bodies can cause thermoelastic instabilities within the system. The characteristic equation governing the thermoelastic stability of the layer bonded to a half plane exhibits instabilities dependent on the material properties of the layer and half plane. These instabilities are categorized, based on the ratio of the material properties, into three types.

A study is presented of saturation effects of subsoil on seismic motions at the free surface of a half space due to an inclined (SV) wave. By treating the soil as a partially water-saturated porous medium that is characterized by its degree of saturation, porosity, permeability, viscosity, and compressibility, a theoretical formulation is developed for the computation of free-surface amplitudes in both the horizontal and vertical components, which are defined as a function of the degree of saturation, the angle of incidence, and the frequency. Numerical results are presented using typical sand properties. It is shown that even a slight decrease of full saturation may lead to a substantial influence on the free-surface amplitudes in both the components and the amplitude ratios between them, and this influence is dependent on the angle of incidence. Significant phase shift between the horizontal and vertical components may also occur due to this slight change in saturation. At small incident angles, partial saturation of subsoil generally may cause a greater vertical-to-horizontal ratio compared with a fully saturated model. It is suggested that one may need to carefully take into account the saturation condition in the interpretation of field observations on seismic ground motions.

Suppression of softening in the load-deflection diagram of concrete-filled tubular columns and spiral columns is proposed to serve as a design criterion helping to avoid the size effect and explosive brittle character of collapse. To this end, the recently developed “tube-squash” tests, in which a short concrete-filled steel tube is squashed to about a half of its original length and allowed to bulge, are conducted with tubes of different wall thicknesses. A finite-strain finite element computer code with a microplane constitutive model is used to simulate the tests. After its verification and calibration by tests, the code is used to analyze nonbuckling concrete-filled tubular columns and spirally reinforced columns. It is found that softening in the load-deflection diagram can be fully suppressed only if the reinforcement ratio (ratio of the tube volume or spiral volume to the total volume of column) exceeds about 14%. If mild softening is allowed, the reinforcement ratio must still exceed about 8%. These ratios are surprisingly high. If they are not used in design, one needs to pay attention to the localization of softening damage, accept the (deterministic) size effect engendered by it, and ensure safety margins appropriate for protecting against sudden explosive brittle collapse. This is of particular concern for the design of very large columns.

This paper presents a new constitutive model for fiber reinforced cementitious composite materials (FRCC), which is particularly suitable for High Performance Cementitious Composites (HP2C). The model is a two-phase composite model, one phase presenting the matrix, the other the composite fibers. In addition, the matrix–fiber interaction is taken into account as internal cross effects (i.e., thermodynamic couplings) between the irreversible deformations of the composite constituents. From one-dimensional thermodynamics, the partial stresses in the matrix and fibers are derived as thermodynamic forces associated with the irreversible deformations of matrix and fibers, respectively. Next, the identification of the model parameters from tensile data is detailed. In particular, it is shown that the model allows quantification of the ductility enhancement of HP2C in comparison with ordinary FRCC, through two material parameters derived from the constitutive model: a matrix–fiber coupling modulus and a friction-to-fracture strength ratio, to which we refer as ductility ratio. The physical significance of these model parameters is discussed in the context of micromechanical theory. The coupling modulus is found to depend mainly on the fiber volume fraction and the matrix quality. The ductility ratio depends on four material design parameters, which are intrinsic to the matter, and which are not affected by structural size effects. We conclude that any ductility gain, which can be obtained through the use of HP2C, is only related to the mix design, and not to structural dimensions.

An analytical study of local buckling of rectangular composite plates rotationally restrained elastically along unloaded edges and subjected to nonuniform in-plane axial action at simply supported loaded edges is presented. A variational formulation of the Ritz method is used to establish an eigenvalue problem, and by using combined harmonic and polynomial buckling deformation functions, which satisfy all the restrained boundary conditions, the explicit solution of plate local buckling coefficients is obtained. The explicit formulas for local buckling strength of orthotropic plates are simplified to the cases of isotropic plates, which are consistent with classical solutions. The elastically rotationally restrained plates are further treated as discrete plates or panels of fiber-reinforced plastic (FRP) box shapes, and by considering the effect of elastic restraints at the joint connections of flanges and webs, the local buckling strength of FRP box shapes is predicted. The theoretical predictions are in good agreement with transcendental solutions and finite-element eigenvalue analyses for local buckling of FRP box columns. The present explicit formulation can be applied to determine local buckling capacities of composite plates with elastic restraints along the unloaded edges and can be further used to predict the local buckling strength of FRP shapes.

Efficient numerical finite-element analysis of creeping concrete structures requires the use of Kelvin or Maxwell chain models, which are most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Bažant and Xi in 1995 but only for the case of a continuous retardation spectrum based on the Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published Microplane Model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context, the Maxwell chain is more effective than the Kelvin chain, because of the kinematic constraint of the microplanes used in M4. The paper shows how to determine the continuous relaxation spectrum for the Maxwell chain, based on the solidification theory for aging creep of concrete. An extension to the more recent microprestress-solidification theory is also outlined and numerical examples are presented.

This research examines the propagation of guided Lamb waves in fiber-reinforced polymer (FRP) bonded components, establishing the effectiveness of combining laser ultrasonic techniques with a time frequency representation (TFR) to experimentally measure the dispersion curves of a concrete component repaired with a FRP plate. A TFR is used to operate on experimentally measured, guided Lamb waves to resolve a FRP bonded component's individual modes and generate its dispersion curves. The objective of this research is to demonstrate that it is possible to develop the dispersion curves of FRP bonded components from a single, experimentally measured guided Lamb wave. The experimental results show that the stiffer the bond, the more deviation from the behavior of a free plate specimen, and the less modes that are present.

A new class of adaptive tuned vibration absorber, a variable effective inertia absorber, is presented to impart optimum vibration absorption. The tuning scheme has two facets: spectral analysis of the excitation and a concurrent in situ tuning of the absorber. The spectral analysis reveals the frequency content of the excitation. The online tuning uses the frequency content of the excitation to reposition a moving mass and change the damping coefficient of a variable rate damper for optimal (broadband) or tonal vibration suppression. The nonlinear differential equations of motion are linearized and then utilized to develop the online tonal and the broadband tuning of the variable effective inertia absorber. A case study is presented to demonstrate the novelty of the concept. The results show that the retuned absorber delivers considerable vibration suppression improvement over the detuned one.