Journal of Engineering Mechanics

In this study the failure mechanism of cylinders with an $R/t$ ratio equal to 250 is numerically investigated under transverse shear. The effects of geometric imperfections and initial stresses due to manufacturing procedures (cold bending and welding) are considered. Seven models, consisting of combinations of different degrees and patterns of imperfection and residual stresses, are analyzed. All the models lose their stability by buckling in a shear mode. The influence of imperfection on the magnitude of critical load is moderate. By contrast, the locked‐in stress induced in the shell by the manufacturing procedures proves to have a large influence on the magnitude of the critical load. In the postbuckling range, a stable equilibrium path is reached by all models at a lower load level than the initial load. The carrying mechanism at this level resembles a truss with tension diagonals and inclined compressive struts.

Rectangular specially orthotropic plates subjected to uniform lateral pressure are analyzed into the large deflection regime, using the computer program ELDAROP. All four edges are supported against out‐of‐plane movement, with either simple support, or clamping, all round. With regard to the in‐plane boundary conditions, all four edges are either free to pull in straight, or completely restrained from normal movement. Some plates analyzed are initially flat. The others have a geometrical imperfection shaped as the first term in the series used to represent the lateral displacement. A positive imperfection means that the pressure is applied to the concave surface. Particular attention is given to the effect on plate behavior of the modular ratio $E_x/E_y\text{,}$ the aspect ratio $a/b\text{,}$ the geometrical imperfection amplitude ${\Delta }_0/t\text{,}$ and various combinations of boundary conditions. Negative as well as positive imperfections are considered; certain negative ${\Delta }_0/t$ cases exhibit snap‐through behavior when the edges are fixed in‐plane. Of the design parameters that control plate behavior, the normalized aspect ratio $(a/b)(E_y/E_x{)}^{1/4}$ is shown to have the dominant effect for the cases analyzed.

This paper deals with the nonlinear axisymmetric static buckling analysis of cylindrically orthotropic full and annular shallow spherical shells continuously supported on elastic subgrades. Considering Winkler and Pasternak models for the elastic subgrade interaction, the buckling loads have been estimated using three criteria: (1) Sudden jump; (2) convergence failure; and (3) point of inflection. The effect of Winkler and Pastemak foundation‐stiffness parameters, shell material orthotropy, and annular ratio on the static buckling loads has been determined for several values of shell geometric parameter. The results reveal that these parameters have a significant influence on the buckling loads of the spherical shells. Both the clamped and simply supported boundary conditions are considered. In case of the hole, free edge conditions are assumed.

In this study, two‐dimensional irrotational gravity flows over a spill‐way with a free surface are investigated numerically and compared to available experimental measurements. The difficulty of the present problem lies in that both the free surface elevation and flow rate are unknowns, even when the reservoir and spillway crest heights are given. In order to solve the problem, the boundary‐fitted coordinate system is adopted to map the complex domain into a rectangular domain with uniform meshes. The finite analytic method is used to obtain the numerical solution. In the finite analytic method, the local analytic solution of the governing equation in an element is obtained and used to formulate the algebraic representation of the governing equation. The discharge coefficient is deduced by a scan method according to the variational principle for variable domains. The prediction is made for the Waterways Experimental Station spillway, where extensive data are available for comparison. The numerical results agree well with experimental data on discharge coefficients and free surface elevation.

A constitutive law for dilatant frictional behavior is reviewed. It is developed by distinguishing between the macrostructural and raicrostructural features of a material discontinuity. Macrostructural considerations provide the general form of the constitutive equations, while microstructural considerations ailow the inclusion of an appropriate surface idealization. The result is an incremental relation between contact stresses (traction) and relative surface deformation that accounts for phenomena such as surface damage due to wear and arbitrary cyclic sliding. A quadratic‐displacement‐isoparametric finite element is derived that permits modeling of curved‐contact surfaces and crack surfaces terminating at a tip with a surrounding medium that is modeled with quarter‐point quadratic elements. Emphasis is on the use of established finite‐element‐solution methodologies and program architecture for material‐nonlinear problems. Several examples are considered. The resulting methodology is useful for modeling geologic discontinuities, crack‐shear transfer in concrete, and dilatancy‐induced mixed‐mode fracture mechanics.s

Two‐dimensional continuous models have been used to investigate the effects of the propagation of seismic waves into buildings with shear walls at the ends and with a central core. Neglecting the soil‐structure interaction, analytical solutions have been obtained for the displacement response to monochromatic SH‐waves, propagating with finite phase velocities on the surface of the homogeneous half‐space. Two‐dimensional models were found to be more representative than the equivalent one‐dimensional models of the response characteristics of such buildings. It will be shown that shear walls at the ends reduce the horizontal whip‐ping of the building, that the central core does not reduce the torsional displacements, and that the core may allow too much horizontal whipping of the free ends of the building. It is suggested that the shear‐resisting elements are more efficient if placed symmetrically and closer to the ends of long buildings.

In this paper, the physical phenomena associated with wave passage under long buildings have been studied. A two‐dimensional, continuous model has been used to represent the building vibration. Analytical, closed‐form solutions have been obtained for the response to incident monochromatic, plane SH‐waves. The soil‐structure interaction has been neglected. The response of this model abounds with physical phenomena that cannot be seen from the response of one‐dimensional building models. Some of these phenomena are important and must be considered in the design practice. For example, the propagating waves excite antisymmetric horizontal modes of vibration even in perfectly symmetrical long buildings. Thus, they contribute with forces and deformations that are not present in the one‐dimensional analysis. It is shown in this paper that buildings can vibrate with modes that are exponential functions in the vertical direction, and that the transfer of the wave energy from the ground into the building depends on the phase velocities of the ground waves.

A solution is presented for the free out‐of‐plane vibration of thin, isotropic annular sector plates with different edge conditions. The classical method of separation of variables is employed. The basic functions in the tangential direction are chosen as the eigenfunctions for vibrating beams. These functions are employed in the finite‐strip method. However, the advantage of this method lies in the analytical, instead of numerical, representation of the funtctions in the radial direction. Satisfaction of the governing differential equation of the plate is achieved by the selection of general time‐dependent functions and the derivation of appropriate analytical radial functions in terms of Bessel functions. Sector plates of different radii and outer‐radius‐to‐thickness ratios, and with various end conditions along the straight and circular edges have been analyzed. Wherever possible, results are compared to previously published ones.

A fundamental theory of evolutionary stochastic waves is developed based on Priestley's evolutionary power‐spectrum theory and a technique for digitally generating samples of such waves is introduced as a further extension of the spectral representation method. This is done primarily for the purpose of developing an analytical model for propagating seismic waves that can account for their stochastic characteristics in the time and space domain. From this model, the corresponding‐sample seismic waves can be digitally generated with great computational efficiency. The efficacy of this new technique is demonstrated with the aid of a numerical example in which a sample of a nondispersive Rayleigh wave is digitally generated. This wave is idealized as a nonstationary stochastic wave with two‐dimensional spatial nonhomogeneity consistent with Lotung, Taiwan densearray data. The proposed model is useful for the seismic‐response analysis of such large‐scale structures extending over a wide spatial area such as water‐transmission and gas‐distribution systems and long‐span bridges.

A crack initiating from a rhombic rigid inclusion in an infinite plane is analyzed as a mixed‐boundary‐value problem of plane elasticity. Complex‐variable method is used with the aid of the rational mapping function of a sum of fractional expressions. A rigorous closed‐form solution is obtained for the shape expressed by the mapping function. The uniform tension and uniform shear stress are considered as loading condition. Stress distributions and stress‐intensity factors are computed for various combinations of crack length and corner angles. The intensity of corner of rigid inclusion is also computed. Through these analyses, we investigate the possibility of cracking and debonding initiation at the corner top when the crack becomes longer.

Very thin rectangular plates (sheets) may buckle due to concentrated tensile forces acting upon two opposite edges. In such cases the buckling (wrinkling) mode shape has a more rapid change in the direction transverse to the loading. The plane elasticity problem is first solved to determine the internal stress field with reasonable accuracy. This is done by superimposing the exact solution for the point‐loaded circular disk upon a finite element solution for the rectangular sheet. The Ritz method is used to solve the buckling problem for all the edges simply supported. Convergence studies are made to determine the accuracies of the results. Critical buckling loads and mode shapes are determined for plates of aspect ratio 0.5, 1, and 2, loaded either at the center points or quarter points of two opposite edges by two tensile forces. The physical reality of the tension buckling phenomenon is further analyzed by calculations for the free vibration frequency spectrum of the plate. This is fhe first known theoretical study made for tension buckling of plates.

The present paper introduces and discusses a stochastic finite element method. It can be used for the analysis of structural and mechanical systems whose geometrical and material properties have spatial random variability. The method utilizes a polynomial expansion of the numerical nonlinear structural operator (for which actual analytical form is unknown). The expansion is made according to a response‐surface approximation in terms of spatial averages bf the design variables. The polynomial form is then modified by suitable error factors, one for each geometrical or mechanical property. Each error factor is due to the deviations, of the single property, from its spatial average in the different finite elements. The method demands an accurate design of the experiments to be conducted in order to identify the model parameters. A numerical example has been worked out. In this numerical example, the stresses and the strains in a light‐water reactor pressurized vessel are computed by a stochastic three‐dimensional finite element nonlinear analysis.

The paper summarizes recent results on the unexpectedly critical role played by damping in the class of problems where pulse loading may lead to anomalous final displacements, i.e., opposite to the direction of loading. Use is made of a single degree of freedom (SDOF) model to study these effects. The main result being emphasized here is that in the range of conditions where these anomalous results may occur, it is not possible to predict the sign of the final displacement of the damped structure from calculations made on the undamped structure. In general the response is calculable by standard numerical methods, although severe difficulties will be encountered at sufficiently small damping magnitudes. An example in the literature is cited where lack of awareness of the unusual effects of damping in this problem led to erroneous results and conclusions.