Journal of Engineering Mechanics

Fiber Bragg grating (FBG) sensors have attracted a considerable amount of interest for their superior characteristics. However, the FBG sensors made on bare fibers are easily damaged. For their safe use in engineering, the glass core of optical fibers is coated with softer low modulus protective coatings. A portion of the host material strain is absorbed by the protective coatings when the strain transfers from the host material to the fiber core, and hence only a segment of structural strain is sensed. By introducing the shear modulus of the host material, a novel analytical model is developed for evaluating the sensing strain of the embedded FBG sensors in composite structures based on the strain in a host material. The average strain transfer ratio is deduced to describe the percentage transferred to the optical fiber core from the host material. It is concluded that the shear modulus of the host material influences strain transmission, especially when it is much lower than the modulus of the fiber core. Then, the strain transfer ratio of an optical fiber sensor embedded in a multilayered structure is developed in a similar way. The factors that affect the efficiency of strain transfer on the optical fiber sensor are deduced and discussed in detail based on the theoretical analysis. Finally, the theoretical results are verified through laboratory experimentation with the FBG sensors.

In this paper the elastic nonuniform torsion analysis of composite cylindrical bars of arbitrary cross section consisting of materials in contact, each of which can surround a finite number of inclusions, taking into account the effect of geometric nonlinearity is presented employing the boundary element method (BEM). All of the cross section’s materials are perfectly bonded together, that is separation is not allowed. The torque-rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain.” The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross section is evaluated directly employing the primary warping function of the cross section depending on its shape. Three boundary value problems with respect to the variable along the beam axis angle of twist, to the primary and to the secondary warping functions are formulated. The first one, employing the Analog Equation Method (a BEM based method), yields a system of nonlinear equations from which the angle of twist is computed by an iterative process. The rest two problems are solved employing a pure BE method. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization.

In this paper, a three-member tensegrity structure is used as a conceptual model for the dendritic actin network in living cells. The pre and postbuckling behavior of the tensegrity is analyzed basing on the energy method. Analytical simulations are carried out on the tensegrity by using the experimentally obtained scales and mechanic properties of actin-filaments for the structural members of the tensegrity. The model exhibits a stress stiffening regime followed by a stress softening regime in the load-stiffness relationship, which qualitatively tallies with the experimentally observed response of actin networks. Due to the simplicity of the model, there is only a single compressed member and the structure buckles abruptly, which results a softening regime much steeper than that observed in the actin network. To take the member length variety into account, we propose a conceptual large-scale tensegrity system with various member lengths, and its behavior is approximately estimated by the mean response of a large number of three-member tensegrity cells with their member length varying in the range of filament lengths. The obtained mean response exhibits a much better fitness to the response of actin networks than those exhibited by the single tensegrity model. The findings reported in this paper indicate that the dendritic actin network may work as a complex tensegrity system, when it is subjected to a stress.

Piped water is used to remove hydration heat from concrete blocks during construction. In this paper we develop an approximate model for this process. The problem reduces to solving a one-dimensional heat equation in the concrete, coupled with a first order differential equation for the water temperature. Numerical results are presented and the effect of varying model parameters shown. An analytical solution is also provided for a steady-state constant heat generation model. This helps highlight the dependence on certain parameters and can therefore provide an aid in the design of cooling systems.

Knowing the ability of reinforced concrete (RC) bridges to withstand future seismic demands during their life-cycle can help bridge owners make rational decisions regarding optimal allocation of resources for maintenance, repair, and/or rehabilitation of bridge systems. The accuracy of a reliability assessment can be improved by incorporating information about the current aging and deterioration conditions of a bridge. Nondestructive testing (NDT) can be used to evaluate the actual conditions of a bridge, avoiding the use of deterioration models that bring additional uncertainties in the reliability assessment. This paper develops probabilistic deformation and shear capacity models for RC bridge columns that incorporate information obtained from NDT. The proposed models can be used when the flexural stiffness decays nonuniformly over a column height. The flexural stiffness of a column is estimated based on measured acceleration responses using a system identification method and the damage index method. As an application of the proposed models, a case study assesses the fragility (the conditional probability of attaining or exceeding a specified capacity level) of the column in the Lavic Road Overcrossing for a given deformation or shear demand. This two-span concrete box-girder bridge located in Southern California was subject to the Hector Mine Earthquake in 1999. Pre- and postearthquake estimates of the univariate shear and deformation fragilities and of the bivariate shear-deformation fragility are computed and compared. Both displacement and shear capacities are found to decrease after the earthquake event. Additionally, the results show that the damage due to the Hector Mine Earthquake has a larger impact on the shear capacity than the deformation capacity, leading to a more significant increment in the shear fragility than in the deformation fragility.

A new approach to describe the maximum strength criterion of concretes with different strength capacities is formulated. The proposed failure criterion incorporates the so-called “performance parameter” $\left({\beta }_P\right)$ that controls the dependence of the maximum strength on the concrete quality. To assure the feasibility of the solution procedure for any possible set of known data, different methods are proposed to determine ${\beta }_P$ according to the available material data. The performance dependent strength criterion presented in this work is expressed in terms of the Haigh Westergaard stress coordinates and as a function of four material parameters that fully define the compressive and tensile meridians of the failure criterion. The variation of the shear strength between these two meridians follows an earlier elliptic interpolation. The proposal includes approximating functions that define the dependence of the above mentioned four material parameters on the two fundamental mechanical properties of concrete: the uniaxial compressive strength $f_c^{\prime }$ and the performance parameter ${\beta }_P$ . The capability of the proposed criterion to predict peak stresses of both normal- and high-strength concretes is verified with experimental data available in the literature corresponding to uniaxial, biaxial, and triaxial compression tests.

A theory that accurately describes tensile strength of wet sand is presented. A closed form expression for tensile strength unifies tensile strength characteristics in all three water retention regimes: pendular, funicular, and capillary. Tensile strength characteristically increases as soil water content increases in the pendular regime, reaches a peak in the funicular regime, and reduces with a continuing water content increase in the capillary regime. Three parameters are employed in the theory: internal friction angle (at low normal stress) ${\varphi }_t$ , the inverse value of the air-entry pressure $\alpha$ , and the pore size spectrum parameter $n$ . The magnitude of peak tensile strength is dominantly controlled by the $\alpha$ parameter. The saturation at which peak tensile strength occurs only depends on the pore size spectrum parameter $n$ . The closed form expression accords well with experimental water retention and tensile strength data for different sands.

A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions.

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.

This paper presents an extended polynomial dimensional decomposition method for solving stochastic problems subject to independent random input following an arbitrary probability distribution. The method involves Fourier-polynomial expansions of component functions by orthogonal polynomial bases, the Stieltjes procedure for generating the recursion coefficients of orthogonal polynomials and the Gauss quadrature rule for a specified probability measure, and dimension-reduction integration for calculating the expansion coefficients. The extension, which subsumes nonclassical orthogonal polynomials bases, generates a convergent sequence of lower-variate estimates of the probabilistic characteristics of a stochastic response. Numerical results indicate that the extended decomposition method provides accurate, convergent, and computationally efficient estimates of the tail probability of random mathematical functions or reliability of mechanical systems. The convergence of the extended method accelerates significantly when employing measure-consistent orthogonal polynomials.

The characteristics of shear layer structure between the sliding jet and the pool for skimming flows over a vertical drop pool were investigated experimentally, using flow visualization technique and high speed particle image velocimetry. Four series of experiments having different end sill ratios ( $h/H=0.12$ , 0.43, 0.71 and 1.0, where $h$ =end sill height and $H$ =drop height) with various approaching flow discharges were performed to measure the detailed quantitative velocity fields of the shear layer. The mean velocities and turbulence properties were obtained by ensemble averaging the repeated measurements. From the velocity profiles, it is found that the growth of the shear layer in the downward direction as the jet slides down the pool represents the momentum exchange. Analyzing the distribution of measured velocity, the similarity profile of the mean velocity at different cross sections along the shear layer was obtained. The proposed characteristic scales provided unique similarity profiles having promising regression coefficient. The selection of these characteristic scales is also discussed. Further, the spatial variations of mean velocity profiles, turbulence intensities, in-plane turbulent kinetic energy, and Reynolds shear stress were also elucidated in detail. The imperative observation is that the Reynolds shear stress dominates the major part along the shear layer as compared to the viscous shear stress. The study also provides an insight into the flow phenomena through the velocity and turbulent characteristics.

In 1946, L. A. Galin proposed an ingenious solution to the problem of analytically determining the plastic region completely surrounding a circular hole in a thin initially elastic plate subject to tensile stress at infinity. The results of Galin’s analysis are recovered by a simple collocation, provided an elliptical elastic-plastic boundary is assumed. This elementary procedure is then applied to treat the case, unresolvable by Galin’s method, in which the plastic domain does not completely surround the hole.

There is a growing interest in the development of procedures for the design of structures exposed to multiple hazards. The goal is to achieve safer and/or more economical designs than would be the case if the structures were analyzed independently for each hazard and an envelope of the demands induced by each of the hazards were used for member sizing. We describe an optimization approach to multihazard design that achieves the greatest possible economy while satisfying specified safety-related and other constraints. We then present an application to illustrate our approach.

This note describes the calculation of the optimal shape of a cantilever beam under two simple cases of transient loading.