Journal of Engineering Mechanics

The conventional finite‐element method shows its weakness in determining the stress distributions along free‐ and interboundaries for plate (facet shell) analysis. This is because the chosen element displacement and rotation functions do not implicitly satisfy the conditions that prevail at the boundaries. A procedure has been proposed to modify the conventional finite‐element method so as to allow the elastic stresses along the free‐ and interboundaries of plates to be determined with improved accuracy. The results obtained by this modified method are compared with both an experimental and a traditional finite‐element solution. The comparison shows that the modified solution is in better agreement with the experimental test data as compared with the traditional solution. The computation time required to perform the additional calculations for determining free‐ and interboundary stresses with improved accuracy is only a small fraction of that required for the complete finite‐element analysis.

Bicycle wheels achieve their structural efficiency by making use of prestressing in three ways. Tests show that the bottom spokes carry virtually all the load by compressive forces, which reduce the tensile prestress set up in the spokes when the wheel was made. The test results are compared with an analysis that considers the spokes as a disk that can carry force in one direction only. This is shown to give good agreement, as does an analysis that considers the rim as a straight beam on an elastic foundation. The behavior of the wheel with an inflated tire is also considered, and it is shown that good comparisons with theory are obtained if the reaction from the road is assumed to be distributed over a specific length of the rim. Prestressing is shown to be important also in the mechanism by which the various forces are transmitted through the tire from the road to the rim.

Mobile or articulated structures have kinematic connections that permit large relative displacements between components that undergo small elastic deformations. Deployable structures are one example. They can be stored in a compact, folded configuration and can be deployed into a load‐bearing, open form by simple articulation. The deployable structures investigated in this paper are assemblages of basic units consisting of two straight bars connected to each other by a pivot that are called scissor‐like elements. These structures are stress free and stable in both their folded and deployed configurations, but exhibit a geometrically nonlinear behavior during deployment and dismantling. This behavior is influenced significantly by friction between the bars of each scissor‐like element as they experience a relative rotation about the pivotal connection. Because of the highly nonlinear nature of the structural response, modeling of the problem with contact‐type finite elements is not only very expensive, but also of doubtful convergence. Therefore, a simple model is proposed, based on simulating the effect of friction by adding nonlinear rotational springs at the pivotal connections. Numerical results obtained from this model were found to be in very good agreement with experimental measurements.

Buckling behavior of sandwich beams with a soft core is presented. The buckling analysis consists of formulation of linear and nonlinear behavior equations, boundary conditions, and continuity conditions. The beam construction is general and consists of two skins (not necessarily identical), metallic or composite laminated symmetric, and a soft core made of foam or a low‐strength honeycomb that is flexible in the vertical direction. The analysis uses a high‐order theory that permits nonlinear distortion of the plane of section of the core as well as changes in its height. Closed‐form solutions are presented for simply supported beams with identical skins and only numerical results for other cases. The analysis determines overall and local buckling behaviors as well as deformations, internal resultants, and stresses in the interface layers between core and skins due to imperfections. Numerical studies reveal that under some structural configurations, local buckling is critical, rather than global buckling. The imperfection analysis study explains the sensitivity of such structures to premature failure due to disbonding of one of the skins from the core.

A three‐dimensional boundary element technique for the earthquake analysis of arch dams is presented. The dam and the foundation rock are assumed to be viscoelastic domains, the latter being boundless. Under the assumption of linear behavior, the dam‐foundation rock interaction and the traveling‐wave effect are represented in a direct and rigorous way (existing finite element representations include the former effect in a very approximate way and do not consider the latter). The linear response of an arch dam (the Morrow Point dam) to harmonic P‐ or S‐waves propagating vertically is presented for empty reservoir conditions. The importance of the dam‐foundation rock interaction and the traveling‐wave effect are clearly shown. The results are in contrast with some obtained using the finite‐element method. The water domain and the combined dam‐water‐foundation rock interaction effects are included in the model in a companion paper, in which results for the same arch dam with the reservoir full of water are presented.

The three‐dimensional boundary element (BE) technique presented in a companion paper by Maeso and Domínguez is extended to include the fluid domain in addition to the dam and the compliant foundation. Linear viscoelastic behavior is assumed for the solid media and the water is assumed to be compressible. The three domains are discretized into BE in a single model that includes a rigorous representation of the dam‐water interaction, the dam‐foundation rock interaction, the water‐foundation rock interaction, and traveling‐wave effects. The response of an arch dam (the Marrow Point dam) to harmonic P‐ or S‐waves propagating vertically is studied for full‐reservoir conditions. The importance of these interactions and traveling‐wave effects is clearly shown by the computed results. These results are in contrast with some obtained by other authors using a finite element model. The importance of having a realistic representation of the actual reservoir geometry is also shown.

A study on the dynamic response of upright circular cylindrical liquid‐storage tanks containing two different liquids under a horizontal base motion with an arbitrary temporal variation is presented. Only rigid tanks were studied. The response functions examined include the base shear, base moments, and hydrodynamic pressure on the tank wall and base. Unlike the cases of tanks containing one liquid, in which the response is controlled by one parameter, height‐to‐radius ratio, the responses of tanks that contain two different liquids are controlled by three parameters: height‐to‐radius ratio, mass density ratio, and height ratio of the two liquids. The response functions are evaluated for a wide range of values for each parameter; the results are presented in graphic forms. The study shows that the dynamic response of a tank filled with two liquids is quite different from that of an identical tank filled with only one liquid; the maximum sloshing wave height may increase significantly, and the fundamental period of the sloshing motion is longer in a tank containing two liquids.

In this paper, a new general procedure is presented for modeling the effects of large displacements on the response of space frames subjected to conservative loading. An incremental definition of rotations is adopted based on an improved rotational transformation matrix, and a convected (Eulerian) system is employed for establishing the contribution of individual elements to the strain energy ($U$). The Eulerian displacements are obtained by means of element‐based local vectors in which the vectors representing the principal axes of bending follow the deformed configuration of the element and are continuously updated to a position normal to the element chord. The nonlinear solution procedure is formalized in terms of transformations between the Eulerian and the global systems, and expressions for geometric stiffness and transformation matrices are explicitly derived. Verification examples utilizing an elastic quartic formulation and employing the nonlinear analysis program ADAPTIC are presented to demonstrate the accuracy and versatility of this method in the large‐displacement analysis of space frames.

The paper addresses instabilities that can affect long panels with arch cross sections. It is demonstrated that in addition to the classical limit load and bifurcation buckling instabilities, such panels can also develop instabilities that propagate. Such instabilities can be initiated from local imperfections or as a result of localization of deformation that follows buckling into one of the classical modes. The lowest pressure required to sustain such a buckle in propagation can be evaluated from a simple but exact energy balance argument. For arches with reasonable rise this pressure is significantly lower than that required to initiate an instability in a geometrically intact structure.

In the currect paper, we consider the stress distribution in adhesive‐bonded cylindrical lap joints for which the two adherends, subjected to axial loads, may have arbitrary thicknesses and consist of different materials and the adhesive layer may be flexible or inflexible. Because of the difficulties in the analysis, no theoretical studies of the present problem are available in the literature. The current paper intends to seek approximate solutions by means of the principle of minimum complementary energy. All boundary stress conditions and conditions of continuity of stresses across the dividing surfaces of adhesive and adherends are strictly satisfied. Since high‐stress intensities occur in the end zones of the joint, the stress‐free end conditions of the joint need to be satisfied. By means of the present approach, closed‐form solutions are obtained. Numerical examples are provided to illustrate the effects of various parameters on the distributions and intensities of stresses in the joint.

The discrete wave‐number boundary element method is extended to apply to three‐dimensional elastodynamic problems. The method—which was first introduced and applied to two‐dimensional problems—combines the direct boundary‐element method with the discrete wave‐number Green's function. The advantage of this method is its accuracy and flexibility for boundary configurations. As a demonstration of the applicability of the method, the responses of a hemispherical canyon for incident SH, SV, and P waves in a three‐dimensional half‐space are presented in time domain as well as in frequency domain. Time histories of seismic motion along the surface in and around the canyon are studied for incident SH, SV, and P waves with the shape of a Ricker wavelet. Many of the physical phenomena—such as diffracted waves (called creeping waves) propagating inside the canyon and Rayleigh waves generated at the edges of the canyon and propagating outward, away from it—which have been observed in the response of the two‐dimensional model (i.e., semicircular canyon in an elastic half‐space), are also observed in the response of the three‐dimensional model (i.e., hemispherical canyon in an elastic half‐space). The mathematical formulation presented is general. Nevertheless, the axisymmetric geometry of the hemispherical canyon is exploited to develop a very efficient computational algorithm to solve the problem. Since a nonaxisymmetric scatterer may always be assumed to be embedded in a region that is defined by an axisymmetric imaginary boundary (such as a hemisphere), application of this algorithm can be extended to nonaxisymmetric scatterers.