Journal of Engineering Mechanics

In this paper, the finite deformations of laminated rubber bearings are analyzed by employing a one-dimensional model consistent with the framework of three-dimensional finite elasticity. In such a context, the equilibrium deformations are governed by a nonlinear system of differential equations involving unknown scalar functions of the axial coordinate. It is shown how to obtain the pure bending and the simple extension of the bearing as exact solutions of the equilibrium problem. Moreover, for each of these two cases, the corresponding relation between the significant kinematical parameter and the load sustaining the deformation is established. Small deformations of the bearing superimposed on a finite compression are also considered. In particular, stability of the finitely stressed state and structural response for superimposed small shear and bending are investigated.

General discussions are presented on an instantaneous optimal prediction control, which includes a series of identification, prediction, and control on a single degree of freedom (SDOF) system. First, a method for the identification of the dynamic properties of the system, which is modeled by a multivariate autoregressive moving average (ARMA) model, is investigated with the responses of the system excited by an active control device. Then general modes of an instantaneous optimal prediction control rule are formulated in terms of the identified components of the coefficient matrix of the ARMA model and the weights included in the control objective function. The prediction control rule is interpreted as an equivalent neural-network model whose links have physically meaningful weights.

In this study, a method of statistical cubicization is proposed to predict stochastic response of offshore platform to a Morison-type nonlinear random wave loading. The nonlinearity is replaced by an equivalent polynomial expansion up to cubic order. The Volterra series method is used to solve the resulting nonlinear equivalent system in the frequency domain. Complete expressions to evaluate response central moments up to the fourth order are obtained for a three-term Volterra system driven by a stationary Gaussian input. To make the developed method efficient and practical, an efficient solution scheme is proposed to implement the Volterra series method. Results (i.e., response mean, variance, skewness, and kurtosis) are presented for the cases of fixed offshore structures and compared with those obtained by simulation, equivalent linearization, and quadratization methods. The statistical cubicization method is superior to both the statistical linearization and quadratization method.

Conduit cross sections of nonelementary shape are the rule in biological fluid systems. Because of mathematical and experimental difficulties, however, relatively little is known about the dynamics of flow in these vessels, particularly under time-varying conditions, although knowledge of the fluid motion therein in terms of properties such as driving head, velocity, and wall shear stress is clearly essential for proper diagnosis of a flow problem. This paper presents an analytical method for solving problems of unsteady laminar flow in long ducts of arbitrary cross section. The implied assumption of parallel flow renders the mathematical situation linear, but the proposed method is far from conventional because it allows consideration of almost any cross-sectional configuration conceivable. This novel approach is made possible by joining a steady-state superposition method for creating new conduits from known basic shapes with a regular perturbation scheme found suitable for dealing with fluid transients in circular pipes. The method is developed step by step, and the results are applied to an example with biomedical implications.

The tapered-plate energy absorber (TPEA) has been accepted as an effective energy dissipator to absorb earthquake-induced energy and improve seismic resistance of a structure. Previous analytical studies associated with the TPEA device were primarily based on simple methods to predict its behavior. In this study, a more complex model, based on plasticity theory, and a finite-element formulation for the TPEA device are developed. The proposed model predicts effectively the device behavior under wind and earthquake loadings. Analytical results obtained by the proposed model are in good agreement with the experimental observations from the tests of the TPEA devices. Furthermore, numerical simulations of a 10-story building equipped with TPEA devices and subjected to earthquake ground motions show that the energy-dissipation capacity of the structure increases, and that its responses to earthquake loadings are significantly reduced when the TPEA devices are employed.

An innovative vibration-control system is proposed to reduce the dynamic response of tall buildings to wind and seismic loads. This system takes advantage of the so-called megasubstructure configuration, which is especially popular in tall buildings. Substructures contained in the megastructure serve as energy absorbers so that no additional mass is required for the intended vibration control as seen in the conventional mass damper systems. The proposed system naturally resolves the difficulties in augmenting damping capacities of tall buildings associated with the high rigidity and deformation in the dominant bending mode. Dynamic characteristics of the proposed control system including the frequency response and the energy flow are investigated. Optimal values of structural parameters such as the damping ratio and stiffness of the substructure are determined. The feasibility and effectiveness of this unique control system in improving human comfort and protecting structures under both wind and earthquake loads are demonstrated through analytical and numerical analysis.

Parallel mathematical models are presented and analyzed as a basis for representing the mechanical behavior of inelastic materials. These models are developed within the framework of incremental elastoplasticity theory. The models are shown to simply represent strain hardening through the adjustment of internal stresses within internal elements of the model, to capture Bauschinger's effect during stress reversal, and to provide hysteretic loops in closed stress cycles. The models are shown to provide stable, nonassociated plastic flow for frictional materials such as geologic materials, i.e., to obey Drucker's stability postulate. A simple parallel model for rock is presented that gives the same response as a conventional elastoplastic material model when used to fit idealized uniaxial strain and triaxial compression test data. However, the two models give much different results in triaxial extension after initial hardening occurred on the compression side first. It is believed that this modeling concept holds significant promise for improving mathematical models of the inelastic mechanical behavior of a variety of engineering materials.

A generalized theory is presented here for the analysis of buckling of built-up columns with end stay plates. The theory is a modification over the method presented by Atle Gjelsvik. Buckling loads are found for columns with some typical boundary conditions. Models of built-up columns were tested under axial compressive loads for different boundary conditions. The buckling loads obtained from the experiments agree quite well with the theoretical solutions. The buckling loads obtained were higher than the classical Engesser solution, which led to the conclusion that the theory presented here is an improvement over the Engesser's theory.

A technique is presented for the identification of localized reductions in the stiffness of a structure using natural frequency measurements. The sensitivities of the eigenvalues to localized changes in the stiffness have been developed as a set of underdetermined equations. These equations have been used as the constraints in an optimization problem, which minimizes one of three criteria: (1) the changes in the element stiffnesses; (2) the norm of the changes to the global stiffness matrix; or (3) the residuals of the eigenvalue problem. An additional constraint, which forces the stiffness to always decrease due to damage, places the optimization problem in the realm of nonlinear programming. The overall formulation has provided a useful method to identify damage with a small number of measured natural frequencies. Ten to 90% localized reduction in stiffness was successfully identified in a 10-story, two-bay steel frame. The method was verified using test data from an aluminum, cantilever beam.

A solution methodology is presented for computing the dynamic stiffnesses in all vibration modes of viscoelastic-fluid dampers with mechanical properties that depend strongly on both frequency and temperature. The method of reduced variables is introduced to construct the master curves of the dynamic modulus of the fluid at some reference temperature from experimental data at different temperatures. Three generalized-derivative (fractional and complex order) constitutive models are proposed to approximate the dynamic modulus of the polybutane fluid over a wide frequency range. The complex parameters of the proposed models are obtained by finding the best fitting of the master curves. The solution of the problem is obtained by transforming the constitutive and balance equations in the Laplace domain, and developing a boundary-element formulation. The resulting method is applied in the prediction of the mechanical properties of a damper containing the polybutane viscoelastic fluid. Results using the three proposed generalized-derivative constitutive models are compared against experimental data.

Certain materials exhibit a capability to heal with time. Healing implies that microcracks and microvoids reduce in size, with a corresponding increase in stiffness and strength, features that are exactly the opposite of those normally associated with continuum damage mechanics. A continuum healing mechanics model is proposed within a framework that automatically meets the restrictions of thermodynamics. Rate-independent and rate-dependent formulations are both given. Specific evolution equations are given for a scalar isotropic assumption and comparisons with a limited amount of experimental data on crushed rock salt are given. Good correlations are shown for changes in time of Young's modulus and inelastic strain. The preliminary results provide a good foundation for other examples of healing such as the curing of concrete, the sintering of ceramics and the compaction of cohesive sands and clays.

A new boundary-element formulation is given in this paper to treat gravitational and centrifugal body forces in plane orthotropic media. In this method, two functions have been defined to satisfy the orthotropic potential equations. After recasting the elasticity equations of equilibrium for orthotropic media including body forces in the form of scalar orthotropic potential equations, for which a relatively simple fundamental solution exists, the inhomogeneous terms, i.e. the effects of the body forces in the partial differential equations can be incorporated into the boundary values. Thus only boundary integrals are needed. Several examples of solutions obtained by the present method are presented. Each solution has been compared with an analytical solution or a solution obtained by the finite-element method (FEM). By means of these examples, the method is shown to be effective for evaluating displacements and stresses resulting from body forces due to gravity or constant rotation.

A multiblock numerical method has been employed for the calculations of viscous flow around two appended submarine configurations used in the DARPA SUBOFF experiments. The method solves Reynolds-averaged Navier-Stokes equations in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model and a two-layer isotropic eddy viscosity model. Comparison of second-moment and two-layer calculations with experimental data clearly demonstrated the significant influence of Reynolds stress anisotropy in the vortex-induced spatial nonuniformity of the propulsor inflow. The second-moment solutions are shown to capture the most important features of submarine flows including the formation and evolution of the appendage root and tip vortices, the development of thick stern boundary layer, and the complex interaction among the horseshoe vortex system and appendage wakes.