Journal of Engineering Mechanics

In this paper, a mechanistic model for nanobeams with surface energy effects is developed by using a variational formulation. This work is motivated by the unusual response of nanocantilevers predicted by models based on the Young-Laplace equation for surface stress. The governing equation and boundary conditions derived from the variational methods are compared with the governing equations and boundary conditions used in the Young-Laplace models and other formulations. A key difference in the shear force boundary condition is noted. Analytical solutions for simply supported, cantilevered, and fixed-fixed beams are reexamined. It is shown that the unusual behavior of nanocantilevers predicted by the Young-Laplace models is due to the shear force boundary condition used. The current formulation leads to consistent solutions for beams under different boundary conditions.

The need to estimate the properties of layered elastic or viscoelastic media arises commonly in various engineering applications, including geotechnical site characterization and pavement condition assessment. The layered medium is usually probed with small-amplitude waves, and the medium’s response is used to drive an inverse medium problem leading to the identification of the properties. The property estimation problem is solved by a new methodology that seeks to minimize the misfit between measured and computed responses, constrained by the dispersion relation of the layered medium, the latter expressed in terms of the forward eigenvalue problem and the associated orthonormality condition. The medium’s properties are recovered upon satisfaction of the first-order optimality conditions of the system’s Lagrangian. The reported numerical results are based on synthetic records illustrating the methodology in the frequency domain, and demonstrating reconstruction of the medium’s material properties and geometric characteristics.

Simulation of fluctuating wind-speed fields is a critical task in determining the wind loads for wind-resistant design of high-rise buildings, long-span bridges, and large-size flexible structural systems such as latticed shells and wind turbines. Due to its simple algorithmic and rigorous theoretical basis, the spectral representation method (SRM) is a widely used simulation tool in practice. However, it may often exhibit low efficiency in its traditional procedure due to the involvement of decomposition of the cross-power spectrum density (PSD) matrix at each discretized frequency. Circumventing this challenge, a joint wave number–frequency power spectrum-based SRM associated with a one-spatial-dimension wind field was proposed recently, allowing an accurate simulation without the Cholesky decomposition. In this paper, the extension of SRM to wind fields in two spatial dimensions is done. Further, to reduce the computational costs associated with the threefold summation over one-dimensional frequency domain and two-dimensional wave-number domain, uneven discretization techniques by tensor-product and acceptance-rejection method are developed. Numerical examples relating to the simulation of fluctuating wind-speed fields in one spatial dimension and two spatial dimensions are included, showing the effectiveness of the proposed method.

Equivalent strut macromodels are largely used to model the influence of infill walls in frame structures due to their simplicity and effectiveness from a computational point of view. Despite these advantages, which are fundamental to carrying out seismic simulation of complex structures, equivalent struts are phenomenological models and therefore have to conventionally account for the influence of really large amounts of geometrical and mechanical variables with a relatively simple inelastic response. Mechanical approaches, generally used to evaluate the force–displacement curve of a strut, are based on hypothesizing the damage mechanism that will occur for an infill–frame system subject to lateral forces. This assumption has a great impact on the response of the system and is affected by large uncertainties that also propagate in seismic assessment results. Based on the aforementioned unknowns, this paper proposes a new stress–strain relationship to be used for fiber-section modeling of equivalent struts. The definition of the stress–strain model is based on an empirical approach rather than a mechanical one. The four parameters defining the stress–strain law (peak stress, peak strain, ultimate stress, and ultimate strain) are directly linked to geometrical and mechanical features of an infilled frame through analytical correlation laws, which are determined from an experimental data set enlarged with data from refined finite-element (FE) simulations. The analytical correlations provided in the paper are proposed as a tool for direct modeling of an infilled frame. Validation tests were carried out with experimental results different from those used to build the data set. The extension of the model to the prediction of cyclic behavior is finally proposed.

This paper aims to investigate and explain the influence of creep of concrete, insulation, and diagonal bars on the behavior of precast-concrete sandwich panels. A theoretical model is developed based on a layered structural modeling of the panel. Each reinforced concrete layer is modeled as an Euler-Bernoulli beam, and the insulation layer is modeled as two-dimensional linear viscoelastic continuum. For the analysis, the panel is divided into a number of regions through its length, and the diagonal bars are introduced via continuity requirements between different regions. Each region along the panel is divided into a number of layers in order to account for cracking, tension-stiffening, and different creep responses of each material point. Creep is accounted for using a convolution integral based on the modified principle of superposition that accounts for the material nonlinearity in tension. From the expansion of the relaxation moduli into a Prony series, an incremental exponential law is obtained, and a step-by-step time analysis was conducted. The results provide insight into the main parameters that control the creep response of composite concrete sandwich panels and provide a basis for the design and analysis of their time-dependent response.

In mathematics, the Woodbury formula is an efficient solution method for low-rank modifications that has been utilized by many researchers for the implementation of structural analyses with local material nonlinearity. The advantages of this method in local nonlinearity include the ability to avoid updating of the global stiffness matrix and to limit factorization to a matrix with a small dimension, which is known as the Schur complement. However, this matrix is generally dense, and its dimension depends on the scale of the nonlinear domains. When the condition of local nonlinearity is not satisfied, the problem becomes high-rank modifications and the Woodbury formula becomes inefficient. To overcome the limitation of the Woodbury formula and extend its high-efficiency advantage to more-general situations, an improved Woodbury method is proposed in which the dense Schur complement matrix is approximated using a banded and sparse matrix based on Saint Venant’s principle. To eliminate the error caused by this approximation and minimize its adverse effect on iterative calculations, a displacement modification process was developed in terms of the tangent response of the structure so that the iterative rate of the proposed method can be accelerated. Moreover, an adaptive iterative strategy was established to further improve the computational performance of the proposed scheme. A numerical example demonstrates that the proposed scheme can be implemented more efficiently than the classical approach for the nonlinear analysis of structures.

Atomistic simulations are performed to investigate the effect of length scale on the mechanical properties and associated plasticity of bioinspired brittle-matrix nanocomposites. The regularly staggered arrangements of stiff platelets reinforced in compliant matrix which is inspired by the nanostructure of nacre and bone is considered in the study. Although extensive studies have been done to understand the effect of length scale on nanocrystalline materials, studies on the size effect in nanocomposites are very limited. The results of the atomistic simulations are compared with those of the metallic matrix nanocomposites available in the literature. It is found that the number of lattice unit cells in the transverse gap between the platelets and the properties of the interface play significant roles in determining the critical length scale. Moreover, the critical length scale may not significantly depend on the constituent materials properties. These findings could provide guidelines in the design of tough ceramic–matrix composites.

This study proposes a new probabilistic framework, random isogeometric analysis (RIGA), combining isogeometric analysis (IGA) and random fields to numerically simulate seepage in unsaturated soils. The proposed framework benefits from computationally efficient IGA solutions and properly accounts for the variability of unsaturated soil parameters by using random field theory. Two constitutive models commonly used to describe the behavior of unsaturated soils, the soil water retention curve (SWRC) and hydraulic conductivity function (HCF), are considered under the proposed RIGA method. A database of unsaturated hydraulic properties is used to investigate the variability of SWRC and HCF model parameters for different soils. Random field concepts with statistical homogeneity (fixed mean, standard deviation, and spatial correlation) are implemented to generate SWRC and HCF model properties considering a joint lognormal distribution function among the model parameters. The joint lognormal distribution function is used with IGA to perform Monte Carlo simulations. The number of realizations in the Monte Carlo simulation accounts for the effect of stochastic soil parameters in unsaturated soil analysis. The application of the proposed RIGA is illustrated by simulating unsaturated seepage in two example problems, a one-dimensional flow in a rectangular domain and a two-dimensional infiltration problem in a semicircular furrow. The results of these problems depict the statistical outputs relating to seepage quantities and negative pore water pressure with respect to standard deviation and correlation between SWRC and HCF model parameters. In all cases, the results are compared with those obtained from an alternative deterministic analysis and it is shown that negative pore water pressure, flow rate, and other quantities of interest change considerably with respect to standard deviation and correlation of the model parameters.

Bolted joints are critical in bracing elements subjected to seismic loads. When fabricated out of glass fiber reinforced polymers (GFRP), joint capacity is limited by the shear strength of the GFRP. We hypothesize that adding multiwalled carbon nanotubes (MWCNTs) to the epoxy resin prior to fabricating GFRP elements can improve the seismic resistance of GFRP bolted joints. Linear elastic structural analysis of a structure with GFRP bracing subjected to the 1940 El Centro earthquake was conducted. GFRP joints were fabricated using neat epoxy and epoxy nanocomposite incorporating 0.5% by weight MWCNTs. Bolted GFRP joints were tested under a seismic displacement time history identified using the finite-element (FE) model. Static tension test to failure was then used to determine the joint postseismic capacity. It is shown that the seismic resistance of GFRP bolted joints incorporating MWCNTs increased by 44% compared with neat GFRP joints. Furthermore, GFRP joints incorporating MWCNTs showed a postseismic static resistance that is 250% higher than neat GFRP joints and demonstrated a tension-stiffening behavior not observed in neat GFRP joints.