Journal of Engineering Mechanics

Previously reported orthotopic sheet theory is used for obtaining estimates of interwire/interlayer contact stresses throughout realistic pretensioned multilayered structural strands. These data are used in conjunction with axial fatigue data on single wires to develop a theoretical model that predicts axial fatigue life of strands (under constant amplitude cyclic loading) from first principles. The theoretical interlayer slippage over the individual points of contact between cross‐laid layers is addressed, which takes interwire friction into account. The match between the theoretical predictions and experimental fatigue data is very encouraging. Numerical examples suggest that cable axial fatigue life depends on the type of strand construction. The level of mean axial load appears to have a modest effect on the cable stress range versus fatigue life (S‐N) curves. For a given wire material, the endurance limit is found to increase with increasing level of mean axial load, becoming practically constant for mean axial loads greater than 40% of the cable maximum breaking load. Different types of cable construction are found to possess significantly different levels of endurance limit.

A method for computing the critical (worst) initial imperfection of elastic truss structures is presented, on the basis of a previous work of the writers. This method can deal with initial imperfections of various properties, including loading pattern vectors, nodal initial position vectors, initial member length, and the product of Young's modulus and cross‐sectional area. Imperfection sensitivity matrices, which express the effects of initial imperfections, are computed compatibly with the method of finite element analysis of truss structures. Critical initial imperfections of a reticulated elastic truss dome structure are investigated in detail as a numerical example. The effects of various kinds of initial imperfections are compared quantitatively. It is shown that the load‐bearing capacity computed for the critical initial imperfection gives the lower bound on the capacity for the imperfections chosen at random. The present method is less costly and more accurate than the method of random imperfections.

A general and efficient method for reliability and sensitivity analysis is presented. The methods are for the analysis of components and systems in design situations where uncertainties are represented by a vector of random variables and a stationary Gaussian vector process. A formulation as a first‐passage problem for a vector process outcrossing a safe set is first applied for a fixed value of the random variable vector. This gives a conditional failure probability, and a fast integration technique based on a first‐ or second‐order reliability method is then applied to compute the unconditional failure probability. Extensive use of analytical gradient information is made in the iteration algorithms and in the calculation of sensitivity factors. A nested first‐order reliability method is proposed together with a method based on an integrated optimization for the two first‐order reliability analyses. For a preliminary analysis, a “crude” first‐order reliability method is described. The computation time is only a few times the computation time for a first‐order reliability analysis of a similar time‐independent problem. Software developed from existing special software for first‐order reliability analysis or existing general optimization software can be applied.

The pullout of a single fiber from a brittle matrix is widely recognized as one of the basic tests to be performed to provide information about the expected behavior of a given fiber‐reinforced brittle matrix composite material. Thus, it is of great importance that the pullout test be interpreted in a way that yields the true material parameters. Two approaches to the fiber/matrix debonding problem can be made: (1) The stress approach where the criterion for growth of the debonded fiber/matrix interface is expressed in terms of the interfacial stress; and (2) the fracture mechanical approach where the criterion for interfacial debonding is expressed in terms of energy equilibrium. This paper investigates these two approaches by applying both to the same model, which includes frictional stresses on the debonded interface. The debonding load‐versus‐crack length relationships predicted by the two approaches are compared and differences in the parametric dependency are discussed. The results predicted by the fracture mechanical approach are compared with available experimental results.

The nonlinear behavior of dam‐reservoir interactions is not well understood, especially when the system is formulated as a three‐dimensional problem. One of the major difficulties is a lack of time‐domain transmitting boundary for the far field (extending to infinity in the fluid domain). An efficient time‐domain analysis procedure for a three‐dimensional fluid‐structure system based on a semianalytical method is developed, which takes into consideration the radiated waves in the far field. The cross section of the far field, which may have an arbitrary shape, is assumed to extend uniformly to infinity in the upstream direction. The irregular near field with arbitrary geometrical shape and boundary conditions is modeled using the conventional finite element method. Accuracy of the proposed method is established by comparing the numerical results with piecewise exact form of analytical solutions for a vertical rigid dam with vertical valleys subjected to actual earthquake and ramp loadings. In the proposed method, all of the procedures are processed directly in the time domain, which is efficient for nonlinear analyses of dams with infinite reservoirs formulated as a three‐dimensional problem.

A solution is found for a cracked half‐plane loaded by a wedge‐shaped rigid punch with friction. It is assumed that Coulomb's friction law is applied between the punch and the matrix and that the contact region is straight. Since the punch ends are sharp corners, stresses become singular and a crack begins from the punch end. An analytical solution is obtained by means of a rational mapping function and complex stress functions. Stress distributions, stress‐intensity factors, and resultant moments are shown for various angles of the wedge‐shaped punch. The conditions for crack initiation are also investigated for the various combinations of coefficient of friction, loading, and angle. When a flat‐ended punch is subjected to rotation, the stress‐intensity factor of the opening mode vanishes for a certain frictional coefficient ${\mu }_B\text{.}$ If a coefficient of friction is larger than ${\mu }_B$ and the stress‐intensity factor is larger than the fracture‐toughness value, then a crack begins. When it is smaller than ${\mu }_B\text{,}$ the initiation of the crack depends on load, angle, and coefficient of friction.

A three‐dimensional stress analysis for a short cantilevered cylinder subjected to a partial shear load on one end is presented based on the theory of elasticity. A solution to three‐dimensional elasticity problems proposed by the writer is used for the analysis. Boundary conditions on the fixed end are rigorously prescribed by three components of displacement. Basic and additional solutions are determined to satisfy boundary conditions. Numerical results for stresses and displacements in the short cantilevered cylinder, with a length‐to‐radius ratio of 2.0, are illustrated and are compared to those obtained by Saint‐Venant's method. A criterion of applicability of Saint‐Venant's method to this problem is proposed. The values of three components of stress at the loaded end become infinite at the boundary of the loaded area. The values of four components of stress at the fixed end show a tendency for stress concentration at the circumference of the end.

A buckling analysis of anisotropic composite layered plates is presented. The analysis employs finite strips in conjunction with a perturbation technique and is applicable to rectangular plates with one pair of opposite edges simply supported. The perturbation technique plays the vital role of decoupling the harmonics characterizing the solution. The perturbation parameter is θ, the ply angle, which gives the orientation of the plies with reference to the plate axis. The technique is seen to be a powerful one, producing rapidly converging solutions over a considerable range of θ. The results obtained using this technique are compared with currently available analytical and experimental results.

An analytical solution is presented for the postbuckling behavior of composite laminated stiffened curved panels, whether curved in a longitudinal or lateral direction (not both). The nonlinear equations for the model are based on the Von Karman kinematic approach and consist of equilibrium equations for curved plate, continuity requirements, and boundary conditions. These equations are expressed in terms of the out‐of‐plane displacement and Airy stress functions. The characteristic behavior in the pre‐ and postlimit positions is exploited by using an eigenfunction series in the longitudinal direction (direction of the stiffeners) and a finite difference scheme in the other direction. A modified Galerkin procedure is used to minimize errors involved in the truncated series and the nonfulfillment of the boundary conditions. The solution obtained through this procedure proved to be very efficient compared to general purpose finite element codes, especially when mode interactions and parametric studies are involved.

In this paper a hybrid boundary element formulation (method I) is presented to evaluate the impedance and compliance functions of piles and inclined pile groups embedded in a homogeneous soil media. The piles are represented by compressible beam‐column elements and the soil as a hysteretic viscoelastic half‐space. A new Green function for semi‐infinite solids is used in the numerical formulation. A realistic lateral load calculation procedure for piles of circular and noncircular cross sections is proposed. Particular attention is given to incorporate accurately the inertia effects. Ah alternate axisymmetric rigorous boundary element formulation (method II) is used to analyze the same problem, where the boundary tractions and displacements are expressed in terms of Fourier series expansion. Extensive comparisons through a unified presentation of existing solutions are made. Finally, some representative results for inclined pile groups are presented.

On‐line identification becomes an important issue when structures undergo nonlinear and time‐dependent degrading behavior under large loads. In this paper, a real‐time, time‐domain system‐identification technique is developed to identify time‐varying system parameters for a multidegree‐of‐freedom degrading structure subjected to general dynamic loads, such as earthquakes. A system of second‐order, linear, ordinary differential equations with time‐varying system parameters is solved to generate the system response using the Newmark time‐integration method. Gaussian white noise is added to the response, and the results are used to simulate the measurements. Then, a least‐squares method is employed to estimate the system parameters in real time based on input data and corresponding response measurements with or without noise. Two numerical examples, a single‐degree‐of‐freedom and a three‐degree‐of‐freedom structure subjected to a simulated El Centro earthquake, are considered. The changes in structural stiffnesses for the example problems are identified. Encouraging results are obtained for both cases.

To determine the dynamic response of submerged structures with complex internal structures to shock loading, it is often necessary to uncouple the equations of motion of the infinite surrounding fluid from those of the structure by means of acoustic approximations. The addition of external appendages to a submerged convex structure can create local concavities in the structure's surface. When subjected to pressure waves traveling through the surrounding fluid, these concavities permit multiple reflections, which cannot be tracked using the acoustic approximations on the wet surface of the structure. By applying an acoustic approximation to a convex fluid surface circumscribing the structure, a method is developed that can be used to compute the motion of the structure. It is found that the multiple reflections caused by concavities significantly affect the structural response when the size of the appendages approaches or exceeds the characteristic dimensions of the convex structure.

Iterative reanalysis methods are formulated for use with the boundary‐element analysis (BEA) method. They find application, most commonly, in procedures for the optimum design of structural shapes. Reanalysis strategies that use analysis information from the original (unmodified) BEA model are first established. A scaling technique is then presented to accelerate the rate of convergence and extend the relative amount of modification a model can experience in a convergent iterative reanalysis. Numerous test cases are discussed to demonstrate the effectiveness of these strategies. Timing, storage, and accuracy results are included in these studies. It is shown that the formulated iterative techniques produce displacement and stress results that are as accurate as those produced in a completely new analysis, with less use of computer resources. For the technically important class of continuum problems involving large stress gradients and stress concentration, the iterative techniques are shown to converge for shape modifications beyond the range of those expected to occur in the course of a shape optimization search sequence.

The micro‐ and the macro‐mechanical measures of heterogeneous granular solids are investigated using two methods, namely a computer simulation method, and a micro‐structural continuum method. The micro‐structural continuum method used in this study is based on a uniform strain assumption. The applicability of the uniform strain assumption is evaluated by comparing the results from the micro‐structural continuum method to those from the computer simulation method. Two types of granular solids, viz. with linear bonded contacts and with nonlinear frictional contacts, are studied to investigate the influence of contact behavior on the heterogeneity of the strain field. It is observed that packings with bonded contacts have a reasonably homogeneous strain field, implying that the uniform strain assumption is applicable for this condition. Packings with frictional contacts have a heterogeneous strain field, except at low levels of deviatoric stress. The natures of inhomogeneity for the particle rotation, stress, and contact force fields in granular solids are also discussed.

Vibration frequency measurements are sometimes used to nondestructively predict buckling loads. Various powers of the fundamental frequency may be plotted as a function of the load. A curve-fitting procedure may be applied to obtain estimates of the buckling load, which occurs when the fundamental frequency decreases to zero. Often such predictions lead to a value that is higher than the actual buckling load. It would be useful if both lower and upper bounds on the buckling load could be obtained from the vibration data. In this technical note, the convexity properties of the curves of load versus a power of the frequency are utilized to predict such bounds. These ideas are demonstrated on typical curves associated with buckling at a limit point and a bifurcation point. The curves are derived from an example of a shallow elastic arch with pinned ends and a sinusoidal initial shape, which is subjected to a sinusoidal distributed load.