Journal of Engineering Mechanics

The extended Kalman filter, which is essentially a method of sequential least‐squares estimation, has been applied not only for dynamic parameter identification but also for static or dynamic system identification problems. In order to obtain the stable and convergent estimation in dynamic or static parameter identification problems, an extended Kalman filter‐weighted local iteration procedure with an objective function (EK‐WLI procedure) is previously proposed by writers. This paper investigates the procedure in geotechnical engineering problems, where the EK‐WLI procedure is incorporated with the finite element method in order to identify unknown parameters. For the effectiveness of this proposed procedure, parameter identification problems are numerically analyzed for an elastic plane strain field represented by finite element models under several conditions. And numerical examples show the usefulness of this method in parameter identification of a plain strain field.

The second mixed‐boundary‐value problem is solved by the classical theory of thin‐plate bending. The mixed boundary consists of a boundary of simple supported type and that of external forces. The boundary of simple support is straight and the remain is arbitrary configuration and a closed‐form solution is obtained. Complex stress functions and a rational mapping function are used for the analysis. As an example to derive a general solution, a half‐plane with a crack subject to uniform bending moment is considered. The crack initiates from an end of the simple support due to stress concentration. Stress distributions before and after the crack initiation are obtained. The influence of the simple support and a crack on the stress is investigated. Stress intensity factors are obtained from short to long crack and for some Poisson's ratio.

The present paper attempts to explain the significance of the various terms that must be included in an element stiffness matrix of a beam finite element to yield correct results in buckling analyses of spatial frames. The complete stiffness matrices for the buckling and post‐buckling analysis of three‐dimensional elastic framed structures are derived for the $C^0‐\mathrm{two}‐\mathrm{noded}$ straight prismatic beam element with doubly symmetric cross section. The assumed small‐strain hypothesis permitted closed‐form expressions to be arrived at. Derivations of the elastic and geometric matrices of a generic beam element are first reviewed. All stress resultants are included in the geometric stiffness matrix. The contribution of the conservative external surface loads having moment resultants to the stiffness matrix is then formulated. The so‐called energy method of stiffness derivation used commonly by engineers is argued to yield correct results when relevant load‐stiffness terms are included. The resulting expressions are easier to understand than their counterparts known from the papers advocating semitangential rotations and moments. Finally, the actual way of application of the external moments is included in the system stiffness matrix and it is shown that the tangential operator of the assembled system is symmetric. The present element stiffness matrices can be easily incorporated into finite‐element codes by only correcting those already implemented.

Viscoelastic structures that undergo an evolution of the structural system, which passes from an initial to a final configuration, with an increase at different times of the number of the redundant reactions, are analyzed. These actions, which restore the compatibility conditions at the delayed restraints, are time‐dependent. Moreover, they depend on the rheological properties of the material, which are, in general, different for each single part (heterogeneous structures). Under these circumstances, the general statement of the problem is presented. The mathematical formulation has demonstrated that the problem is governed by a coupled system of Volterra integral equations for each building stage, which, in general, may be solved only by a numerical procedure, with an overlarge number of calculations. A number of particular cases are also discussed. Subsequently, in order to investigate the influence of each single cause of heterogeneity a parametric analysis was performed by applying the numerical step‐by‐step procedure of the general method to an opportune simple structural model.

A theoretical framework for the buffeting analysis of incompleted bridges in the erection stage is first presented. The bounding cases of across‐deck and along‐deck wind flow are then treated. Intermediate considerations of skew winds are shown to be conservatively calculable from the two bounding cases. Flutter derivatives adapted from flat‐plate theory are demonstrated to provide reasonable estimates for the aerodynamic damping involved. Calculated results are compared to an experimental example reported by Kimura in 1991. The study emphasizes the roles of key structural and flow parameters and the accuracy of assessment needed to establish them for use in design evaluations. Earlier contributions to the study of this problem by Tanaka and Kimura are acknowledged.

This paper describes an approximate analytical method for estimating the stresses in planar tensile reinforcements due to shearing of the surrounding soil mass. The proposed formulation adapts the techniques of shear‐lag analysis, commonly used in the mechanics of composites, and considers plane‐strain compression shearing of the soil mass with the inclusion oriented parallel to the minor, external, principal stress. The analyses assume that the soil and reinforcement behave as linear, isotropic, and elastic materials, linked through a frictional interface. Closed‐form solutions are presented for the axial reinforcement stress and interface tractions as functions of the material properties and inclusion geometry. Comparisons with numerical finite‐element calculations demonstrate the accuracy of the analytical solutions for a wide range of practical geometric and material properties. The proposed formulation provides a simple and direct method for estimating the stress distribution within reinforced soil masses at working load conditions.

A new and relatively simple constitutive theory that describes fracture and slip of an interface in cementitious composites such as concrete is presented. The constitutive model is developed and formulated in analogy to the theory of incremental plasticity. Adhesion, debonding and mobilized friction mechanisms are considered in the characterization of the interface behavior. The debonding mechanism in the presence of a combination of normal and shear stress, i.e., the degradation of tensile and shear strengths, is monitored via a work‐softening rule that entails tensile crack opening as well as tangential slip. As a result, a fracture energy release‐based plasticity model is obtained. The material parameters are physically transparent and are conveniently calibrated from characteristic response functions that can be observed experimentally in pure tension and in pure shear. Analytical predictions are compared with experimental results for the case when constant normal traction is applied while the slip displacement is monitored.

This paper focuses on the numerical treatment of an interface model that was presented in the companion paper. A generalized trapezoidal rule is proposed for integrating the slip rule. The new model is used in finite element predictions, whereby Newton iterations to achieve equIlibrium require the algorithmic tangent stiffness matrix that is pertinent to the incremental problem. In order to ensure convergence to a physically acceptable (stable) solution, one should employ a modified tangent stiffness that is always positive definite. The analysis of a simple composite microstructure confirms that the model is capable of predicting interface failure. Application of the interface model as a generalized fictitious crack model concludes the paper. Preliminary results show that it is possible Do obtain a crack pattern that extends from the Aggregate‐mortar boundary into the mortar itself along predefined interelement boundaries.

A family of trigonometric polynomials $X_n\left(t\right)$, $t\ge 0$, of order $n=1\text{,}2\text{,}\dots$ with correlated Gaussian coefficients is used to approximate a general nonstationary Gaussian process $X\left(t\right)$ on an arbitrary bounded interval $\left(0\text{,}T\right)$. The probabilistic characterization of the Gaussian coefficients of $X_n\left(t\right)$ can be obtained from the coefficients of the Fourier expansion of the covariance function of $X\left(t\right)$ on $\left(0\text{,}T\right)\times \left(0\text{,}T\right)$. It is shown that the polynomials $X_n\left(t\right)$ can match the finite dimensional distributions of $X\left(t\right)$ on $\left(0\text{,}T\right)$ to any degree of accuracy provided that the order $n$ is sufficiently large. An algorithm is developed for generating realizations of $X\left(t\right)$, based on the approximating trigonometric polynomials $X_n\left(t\right)$. The algorithm involves two phases. First, samples of the Gaussian coefficients of $X_n\left(t\right)$ have to be generated. Second, these samples can be used to calculate realizations of $X_n\left(t\right)$. The proposed simulation algorithm is simple, efficient and general. An example is presented to demonstrate the proposed simulation method.

Under the assumption that the second‐order random wave theory is valid, theoretical solutions for the probabilistic cumulants (or moments), in particular the third and fourth cumulants, of wave elevation associated with a deep‐water unidirectional random wave of arbitrary wave bandwidth are derived. In general, knowing the probability density function is not sufficient to obtain the corresponding power spectral density function, and vice versa. However, through the use of the second‐order random wave theory, the study shows that the probabilistic cumulants and spectral parameters of stationary random wave processes become closely related. In the present paper, numerical attention is given to random waves described by either Pierson‐Moskowitz, JONSWAP, or Wallops spectra. The paper also numerically verifies that the use of the second‐order random wave theory is appropriate only when the significant wave slope is less than about 0.02.

An analysis of the flow through an inclined‐plane pervious substratum coupled to a turbulent, steady, uniform, and fully developed open channel flow above it is introduced. The porous material is taken to be homogeneous, isotropic, and formed by a square‐arrayed lattice made of circular cylinders with axes normal to the flow direction. Starting from the Navier‐Stokes equation for the flow through the pores, a combination of the ensemble average method and the method of multiple scales is used to derive the equations governing the macroscale flow through the bed. From them, the vertical variation of the velocity in the substratum, as well as the boundary at the pervious interface are obtained. Application of the derived boundary condition, which guarantees continuity of the total stress across the interface, to the frontier between a laminar flow and a porous material, recovers the condition proposed by Beavers and Joseph in 1967. Joint use of the obtained equation for the velocity distribution and available data, suggests that the parameter controlling its exponential decay, from the slip‐velocity at the interface to the Darcy velocity away from it, may be a function of the properties of the porous material. The analysis also indicated that the nonlinearity of the flow through the substratum originates from the curvature of the streamlines and the flow separation around the solid particles at the microscale level.