Journal of Engineering Mechanics

The edge-based smoothed finite element method (ES-FEM) was proposed recently to improve the accuracy of the standard finite element method for solid mechanics. In the present paper, the ES-FEM is incorporated with the three-node Mindlin plate element (MIN3) to give a novel edge-based smoothed MIN3 (ES-MIN3) for plate analysis. The system stiffness matrix is computed by employing the edge-based strain smoothing technique over the edge-based smoothing domain. For the purpose of avoiding the transverse shear-locking, the MIN3 element is performed to calculate the strains in each element. From a series of selected numerical examples, it is found that the present ES-MIN3 possesses highly accurate solutions, and can be competitive with many existing plate elements.

In most finite-element codes, a Newton-Raphson procedure is used for solving the global equilibrium problem. To preserve quadratic convergence of the aforementioned iterative scheme, this paper presents an analytical full linearization of the principal of virtual work in an updated Lagrangian framework and develops tangent operators consistent with the integration algorithms. Four implementations of the most-used objective rates are described and are shown to be consistent, stable, and objective. The rigid body rotation tensor is obtained by a new computational implementation of polar decomposition scheme in two-dimensional problems. An automatic substepping algorithm is used for integrating elastoplastic constitutive laws in large deformation problems. Numerical examples are presented to test the algorithms, validate the proposed schemes, and compare their performance with other integration algorithms.

An ultrasonic technique for measuring reflection of horizontally polarized shear (SH) waves at different angles of incidence from early-age hydrating mortar and cement paste is described. Measurements from mortar with varying sand content are presented. A poroelastic formulation for predicting wave reflection from hydrating mortar, which considers mortar as a two-phase, water-filled solid skeleton, is developed. In this representation, the solid phase in early-age hydrating mortar consists of sand, products of hydration and unhydrated cement. Reflection at the mortar interface is predicted using the poroelastic theory. Changes in the reflected amplitude of SH waves are used to obtain changes in the water-filled pore space and the shear modulus of the porous skeleton within the two-phase poroelastic idealization. The water-filled pore space in mortar is identified with the porosity in the two-phase poroelastic material. The porosity of mortar obtained from the poroelastic idealization when referring to the volume of cement paste within the mortar is comparable to the results obtained by directly applying the two-phase idealization to cement paste with identical water-to-cement ratio. The reflection of SH waves is strongly influenced by the absolute porosity of the material at any given time. A methodology for real-time, nondestructive monitoring of evolution of porosity in hydrating cement paste and mortar is established.

A three-dimensional (3D) Ritz method of analysis is presented for determining the free vibration frequencies of completely free, toroidal shells of revolution with hollow circular cross-section having variable thickness. Displacement components $u_r$, $u_{\theta }$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in $\theta$, and ordinary algebraic polynomials in the $r$ and $z$ directions. Strain and kinetic energies of the torus are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the torus. Comparisons are made between the frequencies from the present 3D Ritz method, a 3D finite-element method, experimental methods, and thin and thick ring theories.

This paper presents an enhanced-strain beam formulation for the analysis of frame structures with material and geometric nonlinearities. The focus is on slender members, for which the Euler–Bernoulli beam theory can be adopted. The generalized strain enhancement vector, which only includes an axial strain component, is introduced in an element for which the sectional response is evaluated at the two end points. When combined with a modified integration rule, the enhanced-strain formulation resolves inherent problems of displacement-based elements caused by the weak satisfaction of equilibrium, while ensuring a simpler and more robust element state determination algorithm compared to those of mixed and force-based elements. The accuracy of the proposed formulation is validated through a series of analyses.

This study assesses the implementation of locally resonant metamaterials in seismic isolation applications by investigating their potential feasibility in the [0.5, 5.0] Hz frequency band. To this end, via adoption of both Bloch’s theory and classical vibration analysis, the one-dimensional mass-in-mass lattice is analyzed in three overlapping subbands and corresponding relations for the structural parameters are derived. Accordingly, a basic unit cell is proposed that incorporates a core of dense material that is suspended in a thin shell composed of a lightweight material using distributed elastomeric tendons. Initial numerical simulations on finite-dimensional lattices reveal significant potential in the proposed solution and encourage further investigation, particularly to the two-dimensional case.

Studies on open channel flows generally focus on the flow profiles in the longitudinal direction. When generating the analytical solutions, the simplified governing equations are usually employed by neglecting the vertical velocity component, which is much less in quantity than the horizontal one. However, the vertical velocity is actually not negligible, especially at the permeable bottom, as well as the horizontal velocity. In this study, the authors investigate a two-dimensional flow field composed of a fluid (upper) layer and a homogeneous porous medium (lower) layer with downward suction. In the upper layer, Navier-Stokes equations are employed to describe the flow, whereas the porous medium flow theory is addressed in the lower layer. Setting the stream function for the velocity components associated with corresponding boundary conditions, the authors successfully obtain the analytical solutions by the six-order power series method (PSM) and the differential transform method (DTM) respectively, and then acquire the velocity profiles in both layers. Comparing these solutions with previous research, the authors find that the present approach can simplify the algorithm process and the results are in very good agreement.

This paper presents a probabilistic framework for estimating seismic-induced damage in partially instrumented buildings. The proposed framework uses acceleration measurements at a limited number of stories and Bayesian filtering to estimate the response at all stories. The paper compares four Bayesian filters: the extended, unscented, and ensemble Kalman filters, and the particle filter. The estimated response throughout the building serves as input to a damage model that yields an estimate of structural damage and its uncertainty at all stories. The methodology is numerically verified in an elastoplastic 5-story shear building and in a 10-story inelastic moment-resisting frame under various types of model errors and minimal instrumentation. It was found that under ideal and mild modeling error conditions, the proposed methodology provides consistent estimates of damage and its uncertainty.

A generalized statistical linearization technique is developed for determining approximately the stochastic response of nonlinear dynamic systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Specifically, relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, a family of optimal and response-dependent equivalent linear matrices is derived. This set of equations in conjunction with a generalized excitation-response relationship for linear systems leads to an iterative determination of the system response mean vector and covariance matrix. Further, it is proved that setting the arbitrary element in the M-P solution for the equivalent linear matrices equal to zero yields a mean square error at least as low as the error corresponding to any nonzero value of the arbitrary element. This proof greatly facilitates the practical implementation of the technique because it promotes the utilization of the intuitively simplest solution among a family of possible solutions. A pertinent numerical example demonstrates the validity of the generalized technique.

The interpretation of low-strain integrity testing performed on piles is commonly based on methods developed from the one-dimensional wave propagation theory. However, stress waves generated from the impact of the hammer on the head of a pipe pile propagate not only along the vertical, but also the circumferential and radial directions. One-dimensional methods that ignore these waves may underestimate the amplitude of the incident wave, and fail to predict the development of high-frequency interferences that may compromise the assessment of the integrity, particularly of large-diameter pipe piles. To account for these three-dimensional effects, the authors formulate a solution for determining the vertical vibration response along the cross-section of the pipe pile head to an impact load, which robustly accounts for coupling of pipe pile and viscoelastic soil vibrations. Presentation of the method is followed by a discussion on identifying the mechanisms that underlie body and surface stress-wave propagation along the section of the pipe pile head, and the conditions under which these may undermine the interpretation of pile integrity tests with conventional one-dimensional methods. A detailed parametric investigation revealed that there is an optimal position of the receiver, relative to the hammer impact, where the amplitude of the high-frequency interferences is minimized and the arrival of the reflected wave is clearly identified in the waveforms.

As is well known in the boundary element method (BEM), thermal effect reveals itself as an additional volume integral in the associated boundary integral equation. Any attempt to directly integrate it shall require domain discretization that will destroy the BEM’s most distinctive notion of boundary discretization. For anisotropic elastostatics, this additional volume integral can be exactly transformed onto the boundary; however, additional line integrals intersecting the domain are invoked in such a transformation. For simply connected domains, evaluation of the extra line integrals can be avoided by simply employing branch-cut redefinitions; however, the evaluation is inevitable for multiply connected domains. This paper presents a new approach to validate the exact transformation yet without invoking extra line integrals. For the two-dimensional thermoelastic analysis of anisotropic bodies, the present approach has completely restored the BEM’s feature of boundary discretization without extra line integrals involved. In the end, a few typical examples are presented to illustrate the veracity of the formulation and its applicability to engineering practice.

In this paper, a statistical linearization method based on Rayleigh distribution is proposed for hysteretic systems described by the Ramberg-Osgood model. The method is based on the assumption that a set of hysteresis loops can be determined either from an analytical model or by laboratory experiments for imposed harmonic motion with different amplitudes, viewed as deviates from a Rayleigh distribution. A set of equivalent linear stiffness and damping coefficients, dependent on the distribution parameter, are assessed as functions of imposed motion amplitudes. Both the dissipated energy and stored elastic energy per cycle are determined using an accurate and simple analytical approximation of secant modulus, developed in the paper. The proposed method is applied for statistical linearization of a single-degree-of-freedom system equipped by hysteretic bracing devices with restrained buckling. The method is validated through numerical simulation of the output of the hysteretic and equivalent linear systems excited by band-limited and filtered Gaussian white noise.