Journal of Engineering Mechanics

In this paper, probabilistic models for structural analysis are put forward, with particular emphasis on model uncertainty. Context is provided by the finite-element method and the need for probabilistic prediction of structural performance in contemporary engineering. Sources of model uncertainty are identified and modeled. A Bayesian approach is suggested for the assessment of new model parameters within the element formulations. The expressions are formulated by means of numerical “sensors” that influence the model uncertainty, such as element distortion and degree of nonlinearity. An assessment procedure is proposed to identify the sensors that are most suitable to capture model uncertainty. This paper presents the general methodology and specific implementations for a general-purpose structural element. Two numerical examples are presented to demonstrate the methodology and its implications for probabilistic prediction of structural response.

This paper presents a hybrid analytical–computational mechanics formulation for an arbitrarily curved Timoshenko beam undergoing planar finite deformation and subjected to kinematic constraints in the form of fixed displacement and cross-linking. On the basis of an analytical reduction of the governing equations, the system reduced to a single nonlinear differential equation coupled with integral equations associated with translational constraints. An effective numerical formulation of the problem with general distributed and pointwise constraints is shown to be possible by using a simple finite-element procedure. To illustrate the efficiency and accuracy of the method, several examples are introduced to study both stable and bifurcation problems and a system of interacting fibers with different types of cross-link constraints. Because of the reduction of discretization error and the dimension of the matrix system, the proposed formulation is likely to be an attractive computational platform for modeling large-scale multifiber problems, as in fibrous microstructure simulations and other applications.

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts.

In this paper, a damage assessment method for remotely inspecting the near-surface condition of multilayer composite systems is proposed. The method utilizes far-field steady-state electromagnetic waves reflected from the surface of multilayer composite systems and generates the in-depth profile of the inspected composite systems using inverse synthetic aperture radar (ISAR) imaging technique. Spatial imagery of the system can be reconstructed with the structural and geometric features of the multilayer system. These features are revealed by discrete scatterers in the imagery. Reconstructed imagery can be used for detecting construction defects and structural damages in the near-surface region of the system. The theoretical background of the method is described, followed by experimental measurements on glass-fiber-reinforced polymer (GFRP)-confined concrete cylinders with an artificial defect as an example of multilayer composite systems. Continuous waves in the frequency range of 8 to 12 GHz were used. The imaging results show that the proposed method can reveal the location and size of the embedded defect in the GFRP-concrete composite system, indicating the potential use of the method as a basis for distant radar/microwave nondestructive testing/evaluation techniques in civil engineering.

Design of infrastructure materials with inherent material damping may help dissipate energy during dynamic loading events such as earthquakes, thereby reducing structural damage and risk of collapse. One possible method to enhance damping of cementitious materials such as concrete is to utilize poromechanical damping. To evaluate the potential damping associated with the poromechanical effect and to aid in the design of high damping porous materials such as concrete, approximate closed-form solutions have been derived for poromechanical damping as a function of frequency, maximum damping, and critical damping frequency for axially loaded solid and hollow cylinders. The effect of inherent viscoelastic damping of the porous material body was included in the analysis, which indicated that inherent viscoelastic damping could be superposed on poromechanical damping to predict overall damping capacity. Simulations indicate that poromechanical damping may be significant for cementitious materials if designed appropriately.

Early time transient waves multireflected in a finite pile, governed by a damped wave equation, are analyzed by a reverberation-ray matrix. The pile is surrounded by compacted soil, and the composite is modeled by elastic springs and viscous dampers distributed along the length and at the tip of an elastic rod. Steady-state waves with complex frequencies and wave numbers that are generated by a source of harmonic time function at the top and reverberated between the top and bottom surface of the pile are sorted in matrix form into ray-groups, arriving at a receiver in successive orders of reflections from the bottom. The steady-state ray groups are synthesized into a series of nonsingular Fourier integrals that can be evaluated accurately with a fast Fourier-transform algorithm. The first integral (zeroth-order) has also been reduced by complex contour integration to the well-known closed-form solution in Bessel functions for a semi-infinite pile. Detailed time records of velocity response received at the top after three reflections are calculated to illustrate attenuation and damping; arrival times and amplitude-phase change on each reflection for various lateral and base supports. The calculated records resemble ultrasonic nondestructive testing data.

The cohesive crack model has been widely accepted as the best compromise for the analysis of fracture of concrete and other quasibrittle materials. The softening stress-separation law of this model is now believed to be best described as a bilinear curve characterized by four parameters: the initial and total fracture energies $G_f$ and $G_F$, the tensile strength $f_t^{\prime }$, and the knee-point ordinate ${\sigma }_1$. The classical work-of-fracture test of a notched beam of one size can deliver a clear result only for $G_F$. Here it is shown computationally that the same complete load-deflection curve can be closely approximated with stress-separation curves in which the $f_t^{\prime }$ values differ by 77% and $G_f$ values by 68%. It follows that the work-of-fracture test alone cannot provide an unambiguous basis for quasibrittle fracture analysis. It is found, however, that if this test is supplemented by size-effect testing, all four cohesive crack model parameters can be precisely identified and the fracture analysis of structures becomes unambiguous. It is shown computationally that size-effect tests do not suffice for determining $G_F$ and $f_t^{\prime }$, which indicates that they provide a sufficient basis for computing neither the postpeak softening of fracturing structures nor the peak loads of a very large structure. However, if the size-effect tests are supplemented by one complete softening load-deflection curve of a notched specimen, an unambiguous calculation of peak loads and postpeak response of structures becomes possible. To this end, the notched specimen tests must be conducted in a certain size range, whose optimum is here established by extending a previous analysis. Combination of the work-of-fracture and size-effect testing could be avoided only if the ratios $G_F/G_f$ and ${\sigma }_1/f_t^{\prime }$ were known a priori, but unfortunately their estimates are far too uncertain.