Journal of Engineering Mechanics

The integral description of the back stress evolution model is extended to describe the behavior of structural steels with a yield plateau. For this purpose a new concept of the yield plateau region is introduced. The memory of maximal prestress, loading amplitude sensitivity, and hysteresis shape evolution are incorporated into the model. The proposed material description is applied to simulate the deformation response of structural steel st52 for a variety of uniaxial loading programs. Predicted results are compared with experimental observations.

The linear analysis of a uniform pantographic deployable column shows that, in bending, its behavior is very similar to that of an equivalent solid column, whereas under axial loading the two columns display distinct differences in their force and deformation distributions. The total change in the height of a particular pantographic unit in the deployable structure consists of two parts, one due to relative rotation of bars in the unit, the other to their bending. To account for configuration changes, the internal forces must satisfy the equilibrium of each unit “after rotation.” The additional pantographic unit deformation due to bending of bars is found to be based on these forces. The set of equilibrium and nonlinear deformation equations is solved iteratively. The “deformation-controlled” approach for solving this system of equations shows the load maximum in the equilibrium paths that corresponds to the snap-through buckling of the top pantographic unit. It is found that the change in the number of units in the column introduces only minor differences in the equilibrium paths as long as the column height and degree of deployment are kept constant. The axial stiffness of the pantographic column is greatly increased and the snap-through buckling considerably postponed if just one additional constraint is introduced, namely the horizontal link between the two nodes at a particular unit interface. The optimal location of the link is found.

This paper presents a new analytic solution for the stresses within an elastic solid finite cylinder subjected to the axial point load strength test (PLST). The “displacement potential approach” is used to uncouple the equations of equilibrium; then the contact stresses on the end surfaces induced by the point load indentors are expanded in terms of a Fourier-Bessel expansion to yield the unknown constants of the appropriate form of the displacement potential. Our solution shows that a zone of higher tensile stress is developed in the vicinity of the applied point loads, compared with the roughly uniform tensile stress in the central portion of the line between the two point loads. This peak tensile stress within the cylinder decreases with increasing Poisson's ratio and the size of the loading area, and it increases with increasing Young's modulus. The tensile stress distributions along the axis of symmetry in a cylinder under the axial PLST are remarkably similar to that observed in a sphere under the diametral PLST. Our solution also demonstrates both size and shape effects on the point load strength index (PLSI) that we observed in our experiments. In particular, for a fixed length-to-diameter ratio, the larger the specimen, the smaller the PLSI, whereas for a fixed diameter, the longer the specimen the smaller the PLSI.

For a framed structure that is subjected to bifurcation buckling, it may be useful to trace its secondary equilibrium path to gauge its sensitivity to geometric imperfections or to study the nature of load shedding from the buckled structure. For this purpose, a substantial number of branch-switching algorithms for tracing the secondary equilibrium paths of elastic structures have been proposed in the literature. However, virtually all of the published algorithms have heavy mathematical overtones that are not readily appreciated by practicing structural engineers. This paper presents a simple and efficient branch-switching algorithm that is explained in more easily understood terms. The proposed algorithm is demonstrated through numerical examples to be effective in tracing the secondary equilibrium paths of various framed structures with different types of postbuckling behaviors.

A 3D method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight-line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components u_;gf, u_z, and u_;gu in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ϕ and z directions. Potential (strain) and kinetic energies of the entire body are formulated, and upper-bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations and completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.

In this work, classical modal analysis has been extended to treat lumped parameter asymmetric linear dynamic systems. In the presence of general nonconservative forces, the damping matrix is not simultaneously diagonalizable with the mass and stiffness matrices. The proposed method utilizes left and right eigenvectors of the second-order system and does not require conversion of the equations of motion into the first-order form. Left and right eigenvectors of the nonconservative system are derived in terms of the left and right eigenvectors of the corresponding conservative system using a Galerkin error minimization approach in conjunction with a Neumann expansion method. Transfer functions for the asymmetric nonconservative system are derived in terms of the left and right eigenvectors of the nonconservative system. Suitable numerical examples are given to illustrate the proposed method.

This paper reports on wind tunnel experiments with an elastically suspended circular cylinder vibrating under the excitation of natural wind of high turbulence degree. The natural wind turbulence was simulated by superposing the low frequency part of the natural wind turbulence on the background high frequency turbulence of the wind tunnel flow. This was done by controlling the propeller rotation speed according to an artificially generated low frequency speed sample function drawn from a suitable random process model. The experiment provided statistical data on the intermittent random occurrence and size of strong lock-in vibrations in resonance with the vortex shedding excitation. The purpose of the experiment was to obtain data to support the formulation of a sufficiently detailed stochastic model to allow computer simulation of reasonably realistic fatigue damage accumulation at “hot spots” of tubular structural elements subject to the natural wind. The engineering relevance of the investigation is supported by comparing it with the unrealistic highly conservative rules of wind-induced fatigue commonly given in codes of practice. The stochastic lock-in model as well as the related fatigue calculation procedure is reported in the paper.

Numerous micromechanical models have been developed based on assemblies of spherical particles with certain fabric distributions. Most of these distributions are hypothetical, and only very few of them can be determined experimentally. This paper presents a study to provide some useful fabric information for granular material. The discrete element method is used to study the microscopic information for granular materials after compaction. Specimens with 520 identical ellipsoidal elements are generated and compressed under different conditions. Up to six different aspect ratios are used to study their effect on the compression process. Two different compression methods and five different microfrictions between particles are used. The fabric of the specimens after compaction, including the total number of contacts, the distribution of particle orientations, the distribution of branch vectors, the distribution of the length of branch vectors, and the spatial distribution of a similar length of branch vector, is presented. The relations between these fabrics and particle shape, microfriction, and the compression process are also developed.

A method is developed for generating samples of the state X of a linear filter driven by Gaussian white noise. The method can also be applied to developed formulas giving the second moment properties of X. The proposed solution is based on two facts. First, the integrals defining the forcing component of X are continuous martingales because their integrands are continuous deterministic functions and their integrators are Brownian motions. Second, a continuous martingale satisfying some additional properties can be time changed to a standard Brownian motion. The proposed Monte Carlo algorithm for generating samples of X calculates samples of this process from samples of a standard Brownian motion defined in a new clock by mapping these samples to the original clock. The algorithm does not use recurrence formulas for generating samples of X and does not approximate the probability law of this process. Examples are presented to illustrate the application of the proposed method. The examples include the Ornstein-Uhlenbeck process and the response of a simple oscillator and multi-degree-of-freedom system to Gaussian white noise.

A constitutive law to model the strain-rate-dependent compression behavior of concrete is proposed. It is derived from a mechanical model, where inertia effects influence damage formation. To verify this model an experimental method based on the split Hopkinson bar (SHB) technique is described, one that considers the special properties of concrete specimens. Compressive stress waves with varying peak values and durations were realized using an extended SHB device. Dynamic stress-strain relations—which differ considerably from the corresponding static relations—are derived for the investigated load histories and are modeled with the proposed dynamic constitutive law. While a number of compression load histories are sustained by the specimens, others result in failure. So a dynamic failure criterion is established, connecting failure occurrence, peak stress, and the time to reach the peak stress.

Concrete strength is highly sensitive to loading procedure, especially in the range of high strain rates. On the basis of experimental results, it is demonstrated that the full loading history must be included in a dynamic constitutive model, not just consideration of the current strain rate. The rate effect is mainly attributed to internal inertia forces during microdamage evolution. A strain-history-dependent constitutive model is proposed based on this retarded activation of microdamage. A simplified version allows identification of material parameters for practical application. It is shown how this dynamic approach fits into the general framework of continuum damage mechanics.