Journal of Engineering Mechanics

The dynamic stability of electrically conducting beam-plates in transverse magnetic fields is considered in this paper. A concise theory of flexural vibration of magnetoelastic plates immersed in transverse magnetic fields is presented first. The dynamic stability of a beam-plate is then examined without making a priori assumptions about its magnetic property. In contrast to the writer's earlier work, where a beam plate is subjected to an external axial load in the presence of a longitudinal magnetic field, an axial force arises naturally from the magnetoelastic interaction in the form of surface traction. The magnetic damping due to the induced eddy current is also included in the analysis. Two nondimensional parameters are introduced and the stability of a simply supported beam-plate is examined as a function of these parameters. It is shown that three stability regions exist. Critical fields are obtained explicitly and discussed in some detail.

This paper presents a computationally efficient and highly accurate numerical method for analyzing the elastic buckling of columns and plates. The proposed generalized differential quadrature method (GDQM) proposes a simple numerical approach to determine the weighting coefficients for derivative approximations without any restriction on the choice of grid points. It will be shown here that the GDQM is very easy to use and implement numerically. During the solution procedure, different boundary conditions can be easily incorporated. Applications of the GDQM to the buckling analysis of columns and plates have shown that accurate critical buckling loads can be achieved using considerably fewer grid points; thus, less storage and computing time are required during computation. The numerical results obtained, wherever possible, are compared with those from existing literature in order to verify their accuracy.

A general formulation is presented based on the maximum likelihood method to identify the best estimator of a stochastic Gaussian field when the observation is made at discrete spatial points. The uncertainty of the estimator in terms of the uncertainty of the stochastic field and in the observation noise are discussed, and the updating of the estimator's mechanism by observation is clarified. Two methodologies, that is, a simple kriging method and an extended Kalman filtering procedure are derived as special solutions of the general formulation. The method developed here may be applied to updating a general stochastic finite-element method (FEM) system by observation, where the system consists of a stochastic field of elastic moduli or loading forces or both, and the observation may be for elastic moduli and/or displacements at finite spatial points. A numerical example is carried out with a beam on a continuous elastic foundation, and the efficiency and practical applicability of the method are demonstrated.

A difference scheme for the mild-slope wave equation that governs the combined diffraction and refraction of nearshore waves is derived based on the finite analytic method. The nine-point scheme expresses the value of the dependent variable at the central point of a rectangular grid element as a linear combination of its values at the surrounding nodes. The coefficients of the linear combination depend on the local wave number as well as the width-to-length ratio of the grid element and are approximated, by Taylor expansion, as the polynomials of the relative mesh size with coefficients being functions of the width-to-length ratio of the grid element. Performance of the scheme is studied by comparing the numerical results with the exact solution for a Dirichlet problem and with the solution by separation of variables for the forced oscillation in a square basin. The scheme is also applied to the computation of wave diffraction by the spherical shoal in a wave channel, on which carefully measured data in laboratory are available for comparison.

A procedure for time-domain seismic analyses of concrete dams is presented. This procedure employs substructure technique, the finite-element method, and a general transmitting boundary proposed by the writers. This transmitting boundary yields accurate hydrodynamic pressures acting on the dams, with low computational cost. The procedure can be adopted for both linear and nonlinear time-domain analyses of dam-reservoir systems. Modal analysis can be incorporated in the linear analysis to further reduce the computational effort. Several numerical examples under various ground motion inputs are also presented to demonstrate the accuracy and efficiency of the proposed procedure.

The weighted residual method was applied to the problem of scattering and diffraction of plane SH-waves by an underground inclusion of a different elastic medium and of arbitrary shape in a two-dimensional half-space. Results from the application of the weighted residual approach to the case of an underground circular inclusion closely approximate those obtained using the closed-form solution for underground inclusions. To demonstrate the versatility of the method, it was applied to inclusions of elliptical and square shape. It was shown that significant ground-motion amplification, with respect to the amplitude of the incident waves, occurred due to the presence of an inclusion or cavity. Amplifications were dependent on the size, shape, and depth of the inclusion as well as the frequency and angle of incidence of the incident waves. Amplification profiles for the lower-frequency incident waves were simple with peak values that did not differ significantly from 2, the value expected on the surface of a uniform half-space. As the frequency is increased, amplification profiles become more complicated with worst-case values exceeding 7 for elliptical-shaped inclusions.

The behavior of Voronoi-Delaunay parallel-brittle networks of truss elements as models for material behavior is studied. Means and variances of both the number of elements in a network and their length are given. The uniaxial stiffness of the networks is found equal to the element axial stiffness. The expected value of the networks' uniaxial-tensile strength is proportional to the square root of the expected number of elements and to the expected value of the strength of the elements. The toughness of the networks is proportional to the square of the expected value of element strength and to the square root of the expected number of elements. An application to pullout of an anchor is presented. Daniels systems and chain-of-bundles systems are also analyzed to provide perspective. Statistical size effects for parallel-brittle networks are quite different from those associated with weak-link systems.

The role that plastic-frictional energy dissipation in the fracture process zone plays in the work-of-fracture method for measuring the fracture energy of concrete or other quasibrittle materials is analyzed, and a possible improvement of this method is proposed. It is shown that by measuring the unloading compliance at a sufficient number of states on the post-peak descending load-deflection curve, it is possible to calculate the pure fracture energy, representing the energy dissipated by the fracture process alone. However, this value of fracture energy is pertinent only if the material model (constitutive law and fracture law) used in structural analysis takes into account separately the fracture-damage deformations and the plastic-frictional deformations. Otherwise, one must use the conventional fracture energy, which includes plastic-frictional energy dissipation. Either type of fracture energy should properly be determined by extrapolation to infinite specimen size. Further, it is shown that the unloading compliancies to be used in the calculation of the pure fracture energy can be corrected to approximately eliminate the time-dependent effects (material viscoelasticity) and reverse plasticity. Finally, it is proposed to improve the work-of-fracture method by averaging the work done by fracture over only a central portion of the ligament. However, experiments are needed to check whether the specimen size required for this improved method would not be impracticably large.

Spherical-nose copper and tantalum rods with aspect ratios between 4.0 and 14.6 were gun launched against 91-cm-diameter and 91-cm-long concrete and simulant reinforced-concrete targets with velocities ranging from 0.15 cm/μs to 0.19 cm/μs. Targets were instrumented with a sequence of break gauges that provided valuable data for characterizing the penetration process. Target-hole profiles and projectile residual masses were measured and reported. Analysis of the penetration performance of projectiles was performed within the framework of the modified hydrodynamic theory of penetration. Based on the results of these calculations, the penetration efficiencies of the copper and the tantalum projectiles were compared as functions of impact velocities. Analysis of the penetration resistance of the simulant reinforced-concrete targets was based on treating the targets as “composites,” comprised of layers of concrete proper and reinforcing steel; the results of these calculations were compared with the experimental data. Using this theory, the penetration resistance of a concrete/steel/concrete “composite” was investigated as a function of the following parameters: thickness of the surface layer of the concrete, thickness of the steel reinforcement, and impact velocity.

A hybrid numerical method for the prediction of free surface flows including both nonlinear wave and viscous effects is presented. In this method, a zonal approach that combines a potential flow method for fully nonlinear free surface waves and a Reynolds-averaged Navier-Stokes (RANS) method for turbulent incompressible flow is used. The potential flow equation is solved in the far field to provide the nonlinear waves generated by the body motion. The RANS method is used in the near field to resolve the turbulent boundary layer and wake flows around the body. Extensive results are presented for a submerged hydrofoil with and without the presence of free surface waves. The coupled RANS and potential flow method successfully resolves the body boundary layer, the viscous wake, and the nonlinear free surface waves. The results clearly demonstrate the feasibility of the coupling approach and therefore enables the use of a rather small RANS solution domain for efficient and accurate resolution of free surface flows including both the viscous and nonlinear wave effects.

The problem of a block of nearly incompressible elastic material, bonded on its top and bottom parallel faces to rigid end plates, against which any slip is prevented, and subjected to direct compression, is examined. Approximate solutions are obtained using the minimum potential energy and Hellinger-Reissner variational principles. Bulk compressibility is naturally included in these solutions. The necessity of avoiding a severe overestimation of the effective compressive stiffness of thin blocks is demonstrated. For such blocks, the results confirm solutions, extensively used in engineering design, which are based on the assumption of a pressure distribution within the block.

The statistical distribution of the time series generated by three simulation algorithms of Gaussian stochastic processes are derived and compared. In all three methods, the time histories are modeled as weighted linear combinations of terms of the form cos(ω_kt +φ_k) where the phases φ_k are independent random variables uniformly distributed in [0, 2π]. The frequencies ω_k, however, are either deterministic parameters (the spectral representation algorithm), or independent random variables either uniformly distributed in a very small interval (the randomized spectral representation scheme) or distributed according to the specified power spectral density (the random frequencies algorithm). The results of the present investigation show that, from the standpoint of normality of the generated time series and irrespectively of computational aspects, the random frequencies algorithm performs always (considering first-order distributions) and generally (considering second-order distributions) better than or as well as the spectral representation technique and its randomized version, which yield almost identical probability density functions. Finally, if the spectral representation algorithm or its randomized version is used, it is recommended that the frequencies ω_k be selected so that the energy associated with each term cos(ω_kt +φ_k) be the same.