Journal of Engineering Mechanics

Load‐transfer mechanisms in wind‐loaded cylindrical shells are described and interpreted using a simple analytical model. This model generalizes to the higher load harmonics $\left(n>1\right)$ the well‐known beam‐on‐elastic‐foundation analogy, which is so useful for axisymmetric pressure loadings. It provides an easily visualized physical model of Vlasov's semimembrane theory; it accurately replicates the most important bending effects in closed thin‐walled cylinders, and it explains in an intuitively appealing way the phenomenon of very long decay lenglhs of edge loadings, which is most pronounced in ovaling modes of deformation. The slowly decaying bending solution of this model can be considered as an improved membrane theory, which automatically transitions to ring bending when the height‐to‐diameter ratio or the load harmonic number is large. This transition from membrane action to ring‐bending behavior is primarily responsible for the moderating influence of shell bending on the membrane stresses in wind‐loaded cylinders. A single shell parameter $L/a\sqrt{h/a}\text{,}$ which can be regarded as the length of the shell relative to an effective decay length of edge disturbances, fully describes the behavior of wind‐loaded cylinders, according to this simple theory. For the ASCE wind‐load distribution, a fixed‐free cylinder responds essentially as a membrane for $L/a\sqrt{h/a}\text{,}$ less than about 0.1, and for $L/a\sqrt{h/a}\text{,}$ about 1.0 the membrane theory overestimates the axial membrane stress at the base by a factor of about 3.

In resisting lateral forces, X‐bracings are considered very effective for high‐rise frames. As an extension of earlier work of vibration of X‐braced portal frames, in‐plane vibrations of N‐story X‐braced frames are investigated. The elements of such a frame are made of elastic continuum undergoing transverse as well as axial vibrations. Comparing this approach with other numerical methods such as the finite element method, for dynamic analysis of elastic frames, the present method is simpler in formulations and better in results since the solutions obtained are exact in the framework of small‐vibration theory. The characteristics of X‐braced frames are investigated by six sets of numerical examples including free and forced vibrations, and dynamic responses of ground motion. The effectiveness of X‐bracings is also examined by comparing an X‐braced frame with an unbraced rectangular frame.

A concise review of the fheory of adaptive modeling, identification, and control of dynamic structural systems based on discrete‐time recordings is presented. Adaptive methods have four major advantages over the classical methods: (1) Removal of the noise from the signal is done over the whole frequency band; (2) time‐varying characteristics of systems can be tracked; (3) systems with unknown characteristics can be controlled; and (4) a small segment of the data is needed during the computations. Included in the paper are the discrete‐time representation of single‐input single‐output (SISO) systems, models for SISO systems with noise, the concept of stochastic approximation, recursive prediction error method (RPEM) for system identification, and the adaptive control. Guidelines for model selection and model validation and the computational aspects of the method are also discussed in the paper. The present paper is the first of two companion papers. The theory given in the paper is limited to that which is necessary to follow the examples for applications in structural dynamics presented in the second paper.

Recently developed adaptive methods for modeling, identification, and control are now being successfully used in various branches of science and engineering. These methods present significant advantages over the classical methods, e.g., they can remove the noise from the signal over the whole frequency band, they can track time‐varying characteristics of systems, and they make it possible to control unknown systems. In this paper, five examples for the application of adaptive modeling, identification, and control techniques in structural dynamics are presented. The examples are as follows: (1) Identification of a time‐varying simulated system; (2) identification of a building with soil‐structure interaction by using earthquake vibration recordings; (3) identification of a building with nonlinear vibrations by using earthquake vibration recordings; (4) adaptive control of a simulated system; and (5) adaptive control of ambient vibrations of a building. Prior to examples, methods for preprocessing the data are outlined. The paper is the second of two companion papers. The theory pertinent to examples is given in the first paper.

A general three‐dimensional analytical solution, exact within elastostatics, is presented to the problem of an infinite transversely isotropic elastic medium containing a spheroidal cavity with zero body forces, prescribed asymmetric displacements on the surface of the cavity, and vanishing stresses and displacement at infinity. The approach is applied to obtain the solution to the problem of a transversely isotropic medium containing a perfectly rigid spheroidal inclusion, where the medium is subject at infinity to uniform tension in the direction perpendicular to the axis of elastic symmetry of the material. Numerical results and the effect of anisotropy on the interfacial normal stress are discussed.

The research in this paper consists of an analytical study of the computation of large deflections of uniform and variable stiffness members by using pseudolinear or nonlinear equivalent systems of constant stiffhess. By using the second‐order nonlinear differential equation of the elastic curve, a mathematical proof was first obtained, in order to establish the existence of exact pseudolinear or nonlinear equivalent systems of constant stiffness EI that can replace the initial nonlinear system whose moment of inertia I, or stiffness EI, is either uniform or variable. Once the equivalent system of constant stiffness is obtained, linear or nonlinear analysis can be applied to this equivalent system in order to determine displacement requirements of the initial nonlinear system. The equivalent system will always be of constant stiffness, and its deflection curve will be identical to that of the initial nonlinear system. The use of equivalent pseudolinear or nonlinear systems simplifies a great deal the mathematical complexity of the nonlinear problem, particularly when the initial problem has continuously varying stiffness EI along its length. For convenience, a very accurate approximate method is also introduced.

A two‐stage analytical procedure for determining the distribution of shear and normal stresses in a variety of adhesive joints, subjected to bending and axial forces, is described. The analytical procedure is based on previous assumptions that the adhesive layer is relatively flexible and can be idealized as a medium possessing only shear and normal stiffnesses, The solutions are validated by comparison with existing two‐dimensional finite element solutions for single and double lap joints. Solutions are also presented for a variety of adhesive joints subjected to axial forces and bending. The nonlinear interaction between eccentric axial forces and bending of adhesive joints is also discussed and quantified.

An approximate solution for the hydrodynamic force exerted on a moving rigid vertical plate in an incompressible inviscid fluid is derived when the plate is undergoing long‐period motion. The first‐order solution for the velocity distribution is used to solve the equation of conservation of momentum locally on the plate and to derive the second‐order term of the pressure distribution. The hydrodynamic force is derived after integrating the pressure distribution. The lowest order and the second order of the finite‐amplitude solution is shown to agree with the linear theory and with the nonlinear/dispersive theory, respectively. In certain cases, this theory allows the calculation of the force from the plate motion directly. The theory is useful in calculations of wave generation, and it may be useful in calculations of the hydrodynamic forces exerted on dams during earthquakes.

A direct time‐domain boundary element method (BEM) for determining the dynamic response of a rigid massless foundation resting on the surface of an elastic half‐space is introduced for the case of relaxed boundary conditions. For the first time, closed‐form expressions are obtained for the integrals involved in defining the influence coefficients associated with this method. These time‐dependent coefficients relate the traction on a source element and the displacement in a receiver element. The method is then applied to evaluate the response of a massless rigid square foundation resting on the surface of an elastic half‐space and subjected to impulsive loading, and the results are compared with the response estimates derived from an existing time‐domain BEM approach that uses a numerical solution when dealing with the integrals defining the influence coefficients. The present procedure provides greater accuracy and involves less computational effort than this numerical treatment. When applied to a rigid disc foundation, it also yields response results that are in good agreement with those derived from an existing “exact” solution. The analytical method presented can also be employed to analyze the dynamic response of a foundation of arbitrary shape.

Energy‐based continuum damage‐elastoplasticity theories at finite strains are proposed within the framework of damage mechanics. The proposed damage models are based on the effective stress concept, damage threshold loading/unloading conditions, and the multiplicative split of finite kinematics. The models are linked to the history of “damage energy release rate” within representative volumes. The elastoplastic damage constitutive theories feature a thermodynamic basis, characterization of damage, coupling of damage and plasticity, as well as an anisotropic microcrack opening/closing mechanism. Both spatial and material descriptions are discussed. A simple and efficient computational integration algorithm is also given. In particular, a three‐step operator split algorithm is developed within the present framework. A numerical experiment of a notched specimen involving damage coupled with plastic flow is presented to illustrate the capability of the proposed method.

This paper deals with the nonlinear interaction between overall buckling and local buckling of stiffened panels with symmetric cross sections. Significant consequences of local buckling are reductions in the compressive and flexural rigidities of the entire cross section. It is indeed the reduction of the flexural rigidity that is responsible for the adverse nonlinear interaction between overall and local buckling. It is argued that the restriction to a single local mode should be adequate whenever the reduction in flexural rigidity is comparable to the reduction in compressive stiffness. This argument does not apply to a symmetric cross section in which significant deflections in the primary local mode occur on both sides of the neutral axis. In such cases the analysis should be improved by taking into account a second local mode. In the present paper the interactions between overall and two local buckling modes (primary and secondary mode) are considered for both the perfect and imperfect panel. Application of the present analysis to a square tube gives some important results.

A methodology to analytically and numerically evaluate the spectral distribution‐free upper bounds of the response variability of stochastic systems is developed. The structural systems examined consist of linearly elastic, statically determinate and indeterminate beams subjected to static loads. The analytical evaluation of these bounds is achieved by introducing the variability response function of the stochastic system. This is a function with many similarities to the frequency response function used in random vibration analysis. At the same time, the numerical evaluation of the bounds is carried out by means of the fast Monte Carlo simulation technique, which requires an extremely small sample size. In essence, the fast Monte Carlo simulation technique is a method to estimate numerically the variability response function, whose analytical evaluation is particularly cumbersome even for very simple stochastic systems. of equal importance is that this work provides not only insight into the underlying mechanisms controlling the response variability of a stochastic system, but also an analytical basis on which the analysis can be extended to trusses, frames, and two‐dimensional structures and eventually to nonlinear and/or dynamic problems.

A new control scheme with an optimal observer is presented for optimal control of civil engineering structures. The purpose is to increase the reliability and robustness of the control system. In classical optimal control without observer, there is no relationship between the real and simulated vibrations of structures. Thus, if any discrepancy occurred between the two, vibration might be amplified rather than controlled. Due to regulator‐observer control in the proposed optimal feedback control scheme, stable control is achieved very quickly in an asymptotic manner. The following conclusions are obtained. It is preferable to use the optimal regulator control because of its simplicity. It can be shown numerically that the same degree of control can be achieved using optimal regulator control as is achieved using optimal m‐step control. Further, it is preferable to use the optimal observer because the structure can be controlled steadily even if there is a discrepancy between real and simulated vibrations. It can be shown numerically that controlled vibration of a structure with additional mass decreases steadily by using an optimal observer, even if the mass matrix of the structure is evaluated without introducing the effect of additional mass.