Journal of Engineering Mechanics

An analogy between the bending of simply supported plates loaded by uniformly distributed edge moments and the torsion of prismatic bars is derived. The analogy is drawn for both straight‐sided and circularly curved boundaries. The method is extended to the case of hollow shafts. The analogy is demonstrated using analytical and the finite element methods for the rectangular, triangular, circular, hexagonal, semicircular, and hollow circular section. The method shows that excellent results can be obtained using the finite element plate analogy. The deviation between the plate analogy and classical solutions is less than 10% for the maximum shear stress evaluation and less than 13% for twist evaluations. The very wide‐spread availability of plate bending finite elements makes the plate analogy a pragmatic engineering solution technique, by which one operation can solve two different problems. The analogy offers a method of problem solution without the development, acquisition, and maintenance of additional software.

The structural optimization problem of minimizing the weight of beams and orthotropic plates on elastic foundation for a given critical buckling load is formulated and solved. The cross‐sectional area and thickness variations are sought for the beam and plate problems, respectively. Optimality conditions are first derived via variational calculus, and the semianalytical truncated Fourier series approach is used to obtain optimal designs that indicate up to 50% increase in buckling load for the beam and about 112% increase in buckling load for the plate.

Rocking or toppling of a cylindrical structure or object on a shaking foundation is a common occurrence of engineering interest. The behavior is analyzed with a simple three‐dimensional model which has an upright rigid cylinder standing on a rigid foundation. Given an initial side impulse, the cylinder will rock and rotate on the base under the influence of gravity alone. The constraint for the model is that no slipping occurs at the point of contact between the cylinder and the foundation. Otherwise, rolling, rocking, and toppling are not restricted. The governing equations are derived, and the response of the cylinder under free rocking is calculated for various initial conditions. Three types of response are observed: rocking, nutation, and toppling. Rocking is the side‐to‐side motion, while nutation is the wavy precession about the vertical. In addition, rocking and nutation both exhibit a stiff type and a smooth type. The regions for each type of response are mapped out in the domain formed by the initial conditions. From the plots of these regions, one can predict the type of response for a given set of initial conditions.

The fictitious crack model is extended so that it includes the effect of crack shearing. By the introduction of the so‐called equivalent length, it is possible to establish a smeared version of the fictitious crack model. The equivalent length is a purely geometrical quantity that depends entirely on the size and form of the element and on the crack direction. A realistic modeling of crack shearing is obtained, and the smeared constitutive relations are objective with respect to both loading normal to the crack plane and loading tangential to the crack plane. The existence of multiple cracks is considered, and a consistent theory for unloading and possible closure of the cracks is presented. FE calculations of a concrete specimen using four different element types demonstrate the objectivity of the theory even when distorted meshes are used.

The equation of motion of a fulid‐conveying pipe that includes the effect of damping is derived on the basis of Hamilton's principle. Depending upon the constraint conditions on the ends of the pipe, the induced or applied end forces may be classified as being either conservative or nonconservative. It is shown that when internal damping is taken into consideration, the conservative system could be subjected to a flutter type of instability. In certain cases, the capacity of the curved pipe to sustain flow is greatly affected by the internal damping factor. Under increasing fluid velocity, the pipes with an angle of bend less than 90° yield natural frquencies that do not follow the pattern of the pipe bends with angles of bend greater than 90°. Numerical results are presented for a wide range of parameters, including fluid velocity, damping parameter, and angle of the pipe bend.

The flexural behavior of reinforced concrete slab‐beam sections is investigated for the case where the slab is in tension. To describe the behavior of the cross section, the traditional kinematic assumption that plane sections remain plane is relaxed and higher order strain profiles in the transverse direction are adopted. A variational formulation leads to a load‐dependent strain profile in the participating slab. The method is based on the minimization of the unbalanced loads associated with a selected kinematic pattern that satisfies the boundary conditions and compatibility requirements. An iterative algorithm is adopted to solve for the values of parameters describing the kinematics. The paper also includes comparison with experimental results.

This study presents an analytical method for calculating the fourth‐moment properties of the response of linear systems to a Morison‐type nonlinear random wave loading. The method is applicable to general cases with no restriction that the structure behaves in a quasi‐static way or that the response is completely dominated by resonance. The developed method is efficient and practical. According to a comparison with the results obtained from repeated simulations, it is found that the proposed method is superior to the other two existing methods, i.e., the Δ‐correlated method and the separable method.

A frequency‐domain investigation into the effects of nonuniform earthquake excitation on the response of a three‐dimensional arch dam‐water‐foundation system is performed. The analysis consists of two parts. First, the free‐field motions of the canyon walls are obtained by the boundary element method after making some simplifying assumptions about the canyon geometry and the earthquake mechanism. In the second part of the analysis, the frequency‐domain response of the dam‐water‐foundation system is computed by the finite element method using the previously determined free‐field excitations. To more concisely quantify the effect of nonuniform seismic input, the frequency‐domain responses are converted into the time domain in the form of standard deviations of the response to a random input with an earthquake‐like frequency content. As shown by an analysis of Pacoima Dam, inclusion of nonuniformity in the stream component of the excitation reduces the dam response, and the effect of nonuniformity in the cross‐stream and vertical components varies, with the potential for a significant increase.

A uniform slender beam with nonnegligible weight is lifted symmetrically at two points along its length. The elastica theory is used to obtain the nonlinear large deformation equations that are governed by the nondimensional flexibility parameter $K\equiv L(\rho /\mathrm{EI}{)}^{1/3}\text{,}$ where L is the length, ρ is the weight per length, and EI is the flexural rigidity. The beam is rigid when K is zero and becomes progressively limp when K is increased. Solutions are obtained by both perturbations for smaller and numerical integrations for arbitrary K. Forces, moments, deflections, and configurations are determined. The perturbation results, expressed in polynomials of the arc length, are fairly accurate for $K⩽1\text{.}$ Two different sets of optimum lifting locations are considered. One set yields the least maximum moment and another set leads to the least maximum sag. The results are useful in the design of lifting slender materials such as beams, cables and pipelines.

An analytical and experimental investigation of the phenomenon of dynamic soil‐structure interaction of buried structures is conducted. A shock impulse environment simulated by low velocity impact (free‐drop impact system) is developed to generate a well‐characterized dynamic loading on the free surface. Small‐scale model of cylindrical buried structures are tested under this shock impulse system. The dynamic behavior of a typical elastic buried structure is studied by using plexiglas. Load relief at the center of the roof of the buried structure is observed. When a linear‐elastic dynamic analysis by the finite element method is conducted, the numerical results are found to have good correlation with the experimental observation of the peak displacement on the buried roof. However, the behavior after the peak response cannot be simulated using the current linear‐elastic formulation.

A finite element model to analyze the case of incipient flow for cohesionless material in silos is presented. The model is formulated on the incremental principle of virtual work, and is based on small displacement theory. An elastic perfectly plastic material model is used, and wall friction is included in the formulation by the use of a thin layer interface element. The effects of load history are simulated by layering the bulk material in stages during filling and incrementally releasing the outlet forces during flow. A model problem is analyzed and the results for both initial filling and incipient flow cases are compared with classical theories. In addition, design situations involving incipient flow and “locked‐in” stresses are discussed.

In Cartesian coordinates importance sampling has been remarkably effective in improving the efficiency of Monte Carlo simulation techniques for reliability calculations in structural engineering. The approach is extended in this paper to the (hyper‐) polar coordinate system, firstly using an importance sampling function that has its mean at the radial distance, from the mean vector, where the limit‐state functions are expected to lie. This approach is then refined by using interpolation to estimate the location of the crucial limit state along any radial direction and to censor sampling not in the failure domain. The third development is to approximate, in a radial direction, the “tail” of the original probability density function by an appropriate Gaussian probability density function, and then to apply the established theory for directional simulation. Example applications for a linear limit‐state function and for a circular limit‐state function are given.

The maximum possible magnitude of earthquakes that can be generated by slip on any given geologic fault is a function of many characteristics of the fault. Semi‐empirical formulas are available relating the maximum possible magnitude to the nature of fault slips, to potential rupture‐surface length, to its area, to the slip rate, and to the maximum paleoseismic slip. We can also obtain expert estimates of the maximum magnitude, based on observation of other parameters. Bayesian criteria are developed for combining the various estimates for any given fault and for incorporating data about the magnitudes of past earthquakes. These criteria are applied to Mexican subduction earthquakes, pointing out the weaknesses of the approach and the need for semiempirical formulas applicable to conditions such as those under the Valley of Mexico, where the interaction of approximately orthogonal systems of faults leads to the need of fresh‐rock breakage associated with every new moderate earthquake.

A viscoelastic finite element contact analysis that predicts the hysteretic friction between a sliding rubber block and equally spaced triangular asperities is briefly described. Comparison of analytical results with experimentally measured friction values shows that the finite element analysis can be successfully applied to contact problems. The analysis is used to study the influence of sliding speed, contact pressure, and asperity geometry on hysteresis friction. Results show that the pressure dependence of friction is influenced by the amount of contact of rubber with the asperity. The coefficient of hysteresis friction increases with increasing speed to a maximum value and then decreases with further increase in speed. The coefficient of friction very much depends on the geometry of the asperity. Finally, the application of this procedure to study the road/tire interaction problems is discussed.

The paper investigates the elastic buckling of heavy rotating columns under an axial load using the Rayleigh-Ritz energy approach. Accurate formulas to predict the buckling capacities of the columns are presented. Moreover, it is shown that this problem is similar to both the stability problem of continuously restrained columns and the free vibration problem of columns due to their similar form of the total energy functional. The formulas obtained can thus be used, with a minor modification, to furnish the solutions to these latter problems. The results for special cases of the formulas are checked and verified by known solutions.

A formula for fatigue damage under stationary, weakly non-Gaussian responses is presented. The derivation makes use of the joint probability density function of the stress and its time-derivative given as a Charlier serie in the cumulants. The probability distribution function of the stress amplitudes is estimated assuming a narrow-banded spectrum and taking the average of the peak and trough distribution. The derived result is compared to other existing formulas and two examples illustrate the significance of small non-linearities on the fatigue damage estimate.