Journal of Engineering Mechanics

Linear buckling of column structures is an important design constraint in many structures, particularly where weight is a primary concern. Active strengthening is the application of feedback control to increase the critical buckling load of the structure. An important feature of this control problem is that the structure is inherently unstable when the axial load surpasses the critical buckling load. This research presents a design method for creating optimal buckling control systems using state or static output feedback. The primary feature of this method is the ability to select the designed closed loop, actively strengthened, critical buckling load. The stability of the resulting controllers is determined using Lyapunov methods. Simulation and experimental demonstration of this algorithm is performed using a column employing piezoelectric actuators, and MEMS-based strain sensors. The optimal buckling controllers developed are able to increase the critical buckling load by a factor of 2.9. The closed loop system is able to support lower axial loads indefinitely (>30 min).

After a few years of successful application of the fiber beam element to the analysis of reinforced concrete (RC) frames, the introduction of the mechanisms of shear deformation and strength appears to be the next necessary step toward a realistic description of the ultimate behavior of shear sensitive structures. This paper presents a new finite-beam element for modeling the shear behavior and its interaction with the axial force and the bending moment in RC beams and columns. This new element, based on the fiber section discretization, shares many features with the traditional fiber beam element to which it reduces, as a limit case, when the shear forces are negligible. The element basic concept is to model the shear mechanism at each concrete fiber of the cross sections, assuming the strain field of the section as given by the superposition of the classical plane section hypothesis for the longitudinal strain field with an assigned distribution over the cross section for the shear strain field. Transverse strains are instead determined by imposing the equilibrium between the concrete and the transverse steel reinforcement. The nonlinear solution algorithm for the element uses an innovative equilibrium-based iterative procedure. The resulting model, although computationally more demanding than the traditional fiber element, has proved to be very efficient in the analysis of shear sensitive RC structures under cyclic loads where the full 2D and 3D models are often too onerous.

The fiber beam element with shear modeling developed in the companion paper is calibrated and verified by comparison with test data. The verification is carried out for the material constitutive behavior and for single beam and column elements using available test results from literature. A structural analysis of a shear sensitive viaduct pier subjected to ground input motion is presented. Details of the algebraic expressions used for the concrete and steel constitutive behaviors are provided.

The roughness of a natural rock joint was measured in different directions using a laser profilometer. Two stationary roughness parameters and a nonstationary roughness parameter (all fractal based) were used to quantify anisotropic roughness. A plaster of Paris based model material was used to make model material replicas of the natural rock joint. Direct shear tests were performed at five different normal stresses, in each of the directions that were used for the roughness measurements, to measure the anisotropic peak shear strength of the model joint. Required observations and experiments were conducted to estimate (1) the asperity shear area as a proportion of the total surface area of the joint, for each tested joint; (2) the basic friction angle of the model material; and (3) the joint compressive strength. Tests were also conducted to develop a peak shear-strength criterion for the intact model material. Part of the direct shear test data was used to develop a new peak shear-strength criterion for joints including the aforementioned parameters. The other part of the data was used for model validation.

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. The model allows simulation of the observed phenomena of hydration, aging, damage, and creep. It is formulated within an appropriate thermodynamic framework, from which the state equations are derived. In this first part, the formulation and assessment of the thermochemical aspects of the model are presented. It is based on the reactive porous media theory, and it can accurately predict the evolution in time of the hydration degree and the hydration heat production. The evolution of the compressive and tensile strengths and elastic moduli is related to the aging degree, a concept introduced to account for the effect of the curing temperature in the evolution of the mechanical properties. The short- and long-term mechanical behavior is modeled by means of a viscoelastic damage model that accounts for the aging effects. The formulation and assessment of the mechanical part of the model are relegated to a companion paper.

In this work a coupled thermo-chemo-mechanical model for the behavior of concrete at early ages is proposed. This paper presents the formulation and assessment of the mechanical aspects of the model. Short- and long-term mechanical behaviors are modeled via a viscoelastic damage model that accounts for the aging effects. The short-term model is based on the framework of the continuum damage mechanics theory. A novel normalized format of the damage model is proposed, so that the phenomenon of aging is accounted for in a natural fashion. Long-term effects are included by incorporating a creep model inspired in the microprestress-solidification theory.

A simplified optimization procedure is described for a novel fiber reinforced plastic bridge system. The bridge system is modeled using a transformed anisotropic plate that is discretized using the Ritz method. This provides a structural model that is incorporated into a stiffness-based optimization algorithm using the optimality criteria method. The resulting procedure provides a useful design tool that can be used to produce a minimum weight design without resorting to finite-element analysis, which is only used to check the strength of the final design. A two-lane highway bridge serves as a demonstration problem.

The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar/porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical impedance, axial force, and pore pressure profiles are presented to portray the influence of bar stiffness and length/radius ratio, frequency of excitation, and poroelastic properties.

We present a rapid and simple evaluation of an individual's ability to control exertions in quasi-isometric conditions. This evaluation is based on a closed loop that consists mainly of a single-axis force measurement system and a computer screen. This provides simultaneously a visual input command and visual feedback to monitor the output exertions. Specific parameters (stability, period duration, deviation, and velocity) were defined and measured to describe the dexterity, accuracy, precision, and endurance associated with the concept of fine control. Tests undertaken by subjects revealed that it is easier to maintain exertion at 30 and 35% of MVC rather than 15 or 20% of MVC. Subjects who exercised provided the best performances. Fatigue seems to affect exertions at 45% of the MVC. The rhythmic activity of the muscle was also evaluated by showing specific frequencies associated with a subject's exertion, which range from 20 Hz up to 25 Hz. When documented, the obtained information is expected to be of interest in clinical practice.

In this paper, the domain integrals due to uniform load or self-weight that appear in the boundary element method (BEM) formulation for thick plates resting on elastic foundations are transformed to boundary integrals. The Reissner plate bending model is used to model the plate behavior, and the two-parameter Pasternak model is used to model the behavior of the foundation. The necessary particular solutions are derived, and the explict forms for the new boundary kernels are given. Two different collocation procedures are considered—external and boundary collocations. In the case of the boundary collocation and internal collocation (for computing internal functions) procedures, an additional free term is obtained, due to the discontinuity of the transformed kernels. The new boundary integrals are hypersingular integrals. However, it will be shown that these hypersingular terms vanish when integrated around a closed contour. Three numerical examples are presented with several parametric studies to demonstrate the accuracy of the present formulation.

Most engineering material behaviors can be described by using nonassociated plasticity models, but their use leads to the formation of unsymmetric matrices that have, to date, been resolved by nonsymmetric solvers, the initial stiffness method, and, more recently, some symmetrization techniques. Some of these methods have proved to be inefficient due to large core storage requirements, excessive iteration, and slow rate of convergence; or the existence of regions of numerical instability within the mapping process. Some robust techniques are outlined in this paper that are capable of providing solutions of acceptable accuracy for nonassociated plasticity problems, by adapting them for banded, symmetric solvers and by returning CPU times comparable to the best available solution techniques. Numerical solutions to problems in both soil and nongranular plasticity are provided to illustrate the capability of the proposed techniques, and the problem of numerical instability inherent in a previous symmetrization technique is addressed.

The nonlinear response of laminated fiber reinforced plastic (FRP) plates modeled with finite elements and excited by stochastic loading is studied. FRPs are being used widely for structural applications in recent years due to their outstanding mechanical properties. Most FRP materials have strong anisotropic properties and exhibit significant nonlinearity in the shear stress-strain law. A high-order shear theory is used to account for the variation of strains through the thickness, since Kirchhoff and Mindlin plate theories are usually inadequate for modeling laminated FRP plates of reasonable thickness. Nonlinear random vibration analysis is performed using the method of equivalent linearization to account for material nonlinearity. A formulation for deterministic dynamic analysis is also developed and performed to verify the accuracy of the approximate nonlinear random vibration method. The random vibration analysis is found to be sufficiently accurate and is considerably more cost-effective than the use of deterministic simulations.

In the setting of thermomechanical transient analysis of concrete using isotropic damage, the writers noted the consistent occurrence of spurious bifurcations of the deformation field, for thermal and mechanical loading of panel specimens. The cause of the problem is discussed, noting that bifurcation occurs in a simple uniaxial problem, in tension or compression, when there is any (small) difference in material properties. With a transient analysis there are always small momentum effects, and these generate slight variations in strain. For a strain-based isotropic damage model, this results in slight variations in damage, hence stiffness, and so bifurcation is inevitable in the symmetric homogeneous problem. A simple cure to the problem is adopted and the model is tested on three point bend specimens. Apart from its known deficiencies, the local damage model is shown to be very sensitive to the choice of model parameters, mesh size and structure, and the level of numerical error. A nonlocal formulation, on the other hand, is shown to be quite robust.