Journal of Engineering Mechanics

Nonlinear analyses of structural components are normally carried out by finite element codes making Use of constitutive theories in which the material response is separated into the two important groups of phenomena known as rate‐dependent “creep” and rate‐independent “plasticity.” A number of viscoplastic constitutive theories in which creep and plasticity effects are combined into a unified plastic strain model have recently been proposed and are still undergoing active development. In this paper, the constitutive equations of the Bodner‐Partom model are used to present the time dependent, inelastic properties of Inconel 718 at 650 °C. This representation covers a wide range of loading conditions. The developed numerical technique to establish the Bodner parameters is based on simulation with fourth‐order Runge‐Kutta integration coupled to a least square measure for good curve fitting to a series of tests. To determine the eight Bodner parameters, an error function consisting of the square of the difference between experimental and model strains was minimized in the time domain by a direct search method. The specific material parameters for the Bodner model were determined to best fit sets of tensile and creep data. The parameters so obtained are in good agreement with those obtained by other investigators. The present parameters generate better response curves than those from graphical methods used in earlier investigations.

The torsional response of a one‐story, 1/11 scale model to ambient and steady‐state incident wave motion is measured at various depths of foundation embedment. Two modes of response are found. Modal frequencies and displacement ratios exhibit a qualitative dependence on embedment that is consistent with the additional restraint of the foundation. Lumped parameter analysis, using a two degree of freedom system that includes soil‐foundation interaction effects, is used to predict the lower mode response.

In the current practice of seismic design of secondary systems, the interaction between the supporting structure and the secondary systems is often ignored, the interaction between any two secondary systems through their supporting structure is rarely considered. This paper examines the latter type of interaction between simple pieces of equipment. This is done by evaluating the effect on the floor response spectra, representing the response of an oscillator with varying frequency due to an addition of a second oscillator. To include the interaction effect, the modal properties of a composite system consisting of the primary structure and two oscillators are obtained and used in calculating the floor spectra. The frequencies are calculated by solving a characteristic equation, the expression of which is defined in terms of the parameters of the oscillators and the eigenproperties of the supporting structure. A method is presented to solve this characteristic equation by a simple Newton‐Raphson scheme. The mode shape for a calculated frequency is defined by a closed‐form expression. A parametric study is conducted to ascertain the interaction effect. This interaction between the two pieces of equipment can be significant if the second piece of equipment is tuned to a dominant mode of the supporting structure. The effect also depends upon the mass of the second piece of equipment as well as its location with respect to the first piece of equipment.

An analytical model is presented for the transverse vibration of a semi‐infinite beam due to forced longitudenal harmonic motion at the end. The model is applied to the “snaking” behavior of a floating hose‐string attached to an SPM buoy: the surge response of the buoy to incident sea waves results in the hose‐string bending in the plane of the water surface. The dependence of the snaking characteristics—frequency, amplitude, and wavelength—on the buoy's surge frequency and amplitude and on the damping present is established. Predictions from the model are compared with model test measurements of snaking.

Giving specific consideration to the Eulerian mean flow structure between the crest and the trough, the wave‐averaged and depth‐integrated conservation equations for mass and momentum are established. These equations are closely analogous to the long wave equations and include some features that have escaped detailed attention. Qualitative details of the vertical structure implicit in these equations are revealed from predictions from steady wave theory together with experimental observations through the surf zone.

In this paper, a virtual force method for solving shakedown limit ${\lambda }_s$ is introduced. The elastic deformations of a structure are taken as the virtual displacements of the residual moment in the structure so that the virtual work equations of the residual moment can be expressed and solved by a mathematical programming method. It is mentioned that comprehensive combinations of failure mechanisms are not necessary for the solution and thus it is most suitable for computational analysis.

A finite element formulation for multilayered and thick plates, based on a multilayered theory, which was previously applied to a static analysis is extended to include vibration and stability analyses. First, a mass matrix formulation is presented which is consistent with the stiffness coefficient derivation, namely a virtual work expression is obtained which is then evaluated through numerical differentiation. This is followed by a more general discussion of a geometric stiffness derivation which is seen within the concept of linear elastic stability. The geometric stiffness itself, in this context is the difference between the linear stiffness and the tangent stiffness where the tangent stiffness is evaluated, within the general nonlinear theory, usually at a unit load stress state. In both cases vibration and stability analysis, the usual generalized eigenvalue problem follows. In some applications for layered beams and plates the vibration and stability analysis presented is compared with exact solutions.

Buckling of pressure loaded cylindrical panels is investigated using a fully nonlinear Ritz solution procedure and a classical bifurcation analysis of an idealized model. The dialectic between these two contrasting approaches is shown to produce greater understanding than if either one of them were to be used alone. Apart from illuminating the specific buckling behavior of the pressure loaded panel and demonstrating the lower boundedness of the reduced stiffness analytical procedure, the paper suggests that a similar interplay between classical and numerical analysis could be useful in elucidating behavior and providing design analysis procedures for many other shell buckling problems.

This paper presents a review of the different models for concrete based on continuum damage theory, formulated at the Laboratoire de Mécanique et Technologie (Cachan, France). Derived in the framework of the thermodynamics of irreversible processes, each formulation is based on physical observation. Induced anisotropy, ductile behavior, and directional effects such as the closure of cracks are discussed and adequate damage models are proposed. Finally, the numerical implementations performed give a good description of the failure process as well as an accurate prediction of the behavior of concrete and reinforced concrete structures.

Many have attempted to quantify the fracture toughness of concrete using linear elastic fracture mechanics (LEFM). It has been observed that critical mode I stress intensity factor, $K_{\mathrm{Ic}}\text{,}$ calculated by substitution of measured peak load and initial notch length in the LEFM formulas, is size‐ and geometry‐dependent. In this paper, the mode I fracture of concrete is studied using center‐cracked plate specimens with a point load applied at the center of the crack. A special clip gage was developed to measure the crack opening displacement (COD). The results were analyzed using the measured load‐COD response of the specimen. This investigation confirms that conventional LEFM is not applicable to concrete and that the use of an effective crack length approach based on compliance calibration may be more appropriate for analyzing the nonlinear response of concrete.

A modified stochastic averaging technique is employed to calculate stability boundaries for the second‐order statistical moments for bridges under turbulent wind excitations. Assuming that the structural motion is dominated by a coupled critical mode, contributions from other more stable coupled modes are accounted for approximately in the averaging. When the dimension of the state space for the combined structure‐fluid system is large this mathematically approximate procedure is numerically much more efficient than the exact procedure used in Part I. The accuracy of this procedure is first tested in the case of 2‐DOF structural models, capable of vertical and torsional displacements, for which the exact results are known. New results are then obtained from structural models with an additional degree of freedom in the sway motion. Turbulence is shown to play two opposite roles in the process. It destabilizes the critical mode if the critical mode were to act alone, however, it also promotes the participation of other more stable modes that transfer the vibrational energy away from the critical mode. Thus, turbulence can be beneficial when the second effect is greater.

This paper describes the parametric analysis of the distribution of stresses in uniformly loaded beams, aimed at being of use to the designer. The range of parameters covers the field, from very tall beams (columns resting on two supports) to thin beams that can be analyzed using the common bending theory. The study includes the influence of the horizontal reaction which may be associated with the supports. Results of the analysis, obtained primarily by using photoelasticity, are given by curves corresponding to five ratios β between the width W of the beam and its height H. Interpolation for any other β should be easy. The unexpected appearance of a large tensile stress concentration at the bottom boundary off the axis of symmetry and off the neighborhood of the supports, for some ratios of span to height, should be emphasized, as it is the highest tensile stress in the structure.

The U‐transform method has been applied successfully to the vibration analysis of infinite periodic continuous beams and has been proven to be a very useful exact analytical method for analyzing periodic structures. In this paper it is established that this method can be applied to the rigorous analysis of some finite periodic structures under all types of static loading conditions as well. In order to demonstrate this fact, a continuous beam and a continuous plate with finite or infinite number of spans under uniformly distributed or concentrated static loading conditions are analyzed and presented as examples. The solutions obtained are rigorous analytical solutions without any restriction on the condition of loading.

There are many methods available in the literature to study the static behavior of plates with different boundary conditions. Except for a few simple cases, exact solutions for plate problems are rather difficult to obtain. In many cases, one may have to resort to various approximate and numerical methods. Each method has its own merits and demerits. In this note, a new method of solving plate bending problems known as charge simulation method is introduced. This method is somewhat similar to the boundary element method, but differs from it in that the source is placed outside the domain. The method is applied to a circular plate fixed at a number of points along its edge. Experiments have been carried out to check the results presented.