Journal of Engineering Mechanics

Motions of particles in a simulated three‐dimensional random Gaussian flow field are numerically studied. The equation of motion of a solid particle (the generalized BBO equation), in addition to the Stokes drag, the Basset force, and the virtual mass effects, includes the three‐dimensional lift force. An ensemble of 300 particle trajectories are generated for evaluating various statistics. Turbulent diffusivity of small particles is calculated and its variations with nondimensional particle size, particle Reynolds number, density ratio, and particle response time are studied. Particle velocity autocorrelations and particle velocity‐fluid velocity cross‐correlations, as well as fluctuation energy transport from the fluid phase to the particulate phase, are evaluated. A simplified model for evaluating the particle response statistics is also described. The simulation results are compared with the predictions of the simplified model and the available experimental data and good agreement is observed. Effects of turbulence length scale, particle size, and density on particle diffusivity and various correlations and energy transports are also studied and discussed.

Exact modal analysis of structural systems, each consisting of a beam and various spring/mass oscillators, is presented. The Nicholson and Bergman mathematical model for such systems is considered, but altered by use of the particular integral approach to solve the model in favor of using Green's function. This alteration leads to a computer implementation of the model that runs significantly faster than the Green's function implementation in cases where the number of oscillators is sufficienfly large, and it exhibits a reduced tendency to erroneously predict nonexistent closely packed frequencies.

A dynamic finite element model, which incorporated a fracture process zone and a maximum tensile stress failure criterion, was used to simulate the results of impact tests on concrete and mortar three‐point bend specimens. When the measured impact load was used as an input boundary condition to this dynamic finite element model, it predicted with reasonable accuracy the measured crack propagation history, the midspan deflection, and the notch tip strain. However, the numerical simulation showed that, in contrast to the modulus of rupture strengths obtained with impact loading, the dynamic tensile strengths appropriate for the fracture process zone model were relatively insensitive to the strain rate variations of $0.1-;0.4{\sec }^{-1}\text{.}$ The predicted reaction forces at the supports, the energy balance, and dynamic energy release rate versus crack velocity results are also presented.

A study of the effect of the mode of geometric imperfection on the carrying capacity of an elastic discretized structure is presented. Optimization of the mode of imperfection that causes maximum reduction in the carrying capacity of a structure is formulated. This optimization is different compared to the common practice in which a fixed mode of the paths emanating from the first critical point on the equilibrium path of a perfect structure is used as the mode of initial imperfection. The objective function to be minimized is the loading intensity at which the tangential stiffness matrix becomes singular for the first time. The constraint equations consist of equilibrium equations, singularity of the tangential stiffness matrix, and the norm of imperfections. Numerical examples are presented on elastic trusses, including a reticulated truss simulating a spherical shell, to illustrate the formulation. It was found that there was a case in which the use of a mode of paths not from the first critical point as the mode of initial guess imperfection converged to the lowest carrying capacity.

A simple mixed method is formulated for elasticas. The total displacements are decomposed into large rigid‐body motions and small elastic deformation in total Lagrangian approach. The elementwise linear moment field and the rigid‐body rotations of straight elements are introduced as independent variables in the mixed functional. The compatibility equations for nodal slopes consequently become linear in terms of these rotational parameters. The nodal bending moments will then be eliminated from the discretized elastica equations. The number of the rotational degrees of freedom is finally equal to the number of elements. An integration procedure proposed by Shinohara is applied to solve the nonlinear governing equations. The major interest is to develop a nonlinear scheme that is able to trace the snap‐back and the looping behavior in load‐deflection history. Numerical examples suggest that the mixed method in the present study is quite accurate despite its simplicity. Shinohara's procedure also proved to be efficient, and may be applied to nonlinear plate and shell analysis.

Data on creep behavior of nailed joints between lumber and sheathing are essential to improve the design of light‐frame wood buildings. Two theoretical models were developed to predict creep of joints under variable loads from test data on creep under constant loads. The models incorporated the strain‐hardening principle and the modified superposition principle; the latter was further modified to include plastic creep in nailed joints. Tests were conducted to develop specific models for nailed joints between Douglas‐fir lumber and plywood. The experimental data for three constant‐load functions were used to formulate the specific models, and the data for four stepwise load functions were used to assess the accuracy of those models. Predicted and experimental data agreed closely for all solutions, but the simplest and most accurate predictions were based on the modified superposition principle. Thus, the models can provide accurate estimates of stiffness loss under long‐term loads in nailed wood components of light‐frame wood buildings.

In the framework of modal analysis the dynamic correction method is applied to evaluate the response of elastic perfectly plastic systems having numerous degrees of freedom. According to this method, the nodal structural response is evaluated as the sum of a pseudo‐static response, which is the particular solution of the differential equations of motion in nodal coordinates, and a dynamic response evaluated using a reduced number of natural modes. Once the modal analysis is applied, the elastoplastic response is evaluated by using a stepwise approach in modal space and by solving at each step a linear complementarity problem or equivalent quadratic programming problems. In a numerical example it is shown that by using the dynamic correction method greater accuracy, especially for elastoplastic systems, is obtained with respect to the traditional mode‐displacement methods, without considerable increase in the computational effort.

The solution of transient inverse elastoviscoplastic deformation problems is the topic of this paper. The inverse problems described here involve solving for boundary tractions and displacements given only approximate measurements of displacements at internal points to the body. A finite element formulation for the solution of these inverse problems, in conjunction with the regularization and future‐time methods, is presented here. Several one‐dimensional examples are given to demonstrate the method and to investigate the effect of various parameters on the solution.

Identification of modal parameters of a vibrating structure is a primary concern in structural dynamics. A time‐domain method for identification of modal parameters is presented in this paper. The relationship between the eigenvalues of a vibrating structure and poles of its autoregressive, moving‐average (ARMA) model is derived. The eigenvalues are then identified by an estimate of the poles of a univariate ARMA model. The relationships between the autoregressive (AR) model and the moving‐average (MA) model of the vibrating structure are derived. The coefficient matrix sequence of the AR model is estimated using the excitation and response data and the impulse response function matrix sequence of the structure is then calculated through the relationship between the AR and MA models. The estimated impulse response function matrix sequence and poles are used for the identification of the eigenvectors of the structure. Freedecay vibration data, white‐noise excitation, or general excitation and corresponding response data can be used with this method.

A stochastic finite element method is developed for reliability studies of problems such as beam‐columns under axial loading with random geometric imperfections, uncertain material properties, and uncertain moduli of elastic foundations. The random geometric imperfections are described by an explicit form of autocorrelation function or a given initial displacement function with amplitude described as a random variable. The effects of random initial geometric imperfections are treated as a set of equivalent random initial forces. This concept enables the direct employment of existing stochastic finite element methods developed for treating random forces. This formulation can be straightforwardly used to study the reliability of practical beam‐column problems with complex loadings, realistic boundary conditions, arbitrary geometries, and imperfections, for which analytical solutions are difficult to obtain. To establish the validity of the present formulation, a series of examples including random loadings and uncertain material properties were solved. Since existing alternative solutions are limited, analytical solutions are also obtained for comparison. The last of the series of examples is a simply supported beam‐column with four simultaneous uncertain parameters: geometric imperfection, modulus of elasticity, moment of inertia, and modulus of elastic foundation. All the four parameters cover ranges of values with practical significance.

A mixed variational principle for thin‐walled prismatic structures is formulated and a solution method is proposed. In this principle, the cross section of the thin‐walled prismatic structure is assumed to be rigid in its own plane, but flexible out of plane, and both the stresses and displacements are considered to be unknown variables in this function. The solutions are expanded in a series of co‐ordinate functions and the governing equations of the unknown functions are derived. The coordinate functions for bending problems can be deduced systemati and the solutions can be obtained in simple closed form. This method can be applied to members with rows of openings and to problems involving shear lag phenomena. Numerical examples show that only the first two terms in the solution series will give an approximate result in which the shear lag phenomenon has been reflected, while a three‐term solution will give a satisfactory result in comparison with the finite strip method.

The research work in this paper consists of a rigorous closed form solution regarding the deflection of thin rectangular plates with variable thickness in one dimension. The rigorous closed form solution is given in the form of an equivalent system of flat plates that replaces the original variable thickness plate. The sum of the deflections of the flat plates is equal to the deflection of the original variable thickness plate. A simplified equivalent system is also obtained in order to reduce the mathematical complexity of the problem. Various variable thickness rectangular plates have been solved by using the method stated above, and the results are compared with those obtained by using the finite difference method.

The force‐displacement relationship associated with the vertical vibration of a circular rigid disk resting on a saturated layered half‐space is derived using Biot's two‐phased linear theory. The analysis relies on the use of integral transform techniques in conjunction with axisymmetric potential theory by means of which Green's functions are derived. Using the latter, the determination of the force‐displacement relationship of the disk is reduced to the evaluation of a stress function that satisfies a Fredholm integral equation of the second kind similar to that obtained in relative studies involving uniform or layered dry media. Plots of vertical stiffness and damping coefficients in terms of frequency and saturation depth‐to‐disk radius ratio are given. Comparisons are also presented with results from the corresponding dry case. Numerical results obtained from a representative range of parameters show that the effect due to the saturation on the impedence functions is generally not significant. Specifically, at low dimensionless frequencies (i.e., less than 3), this effect is practically negligible, while at higher dimensionless frequencies (i.e., between 3 and 6), the departure from the dry case was about 30%.

A treatment of the mapping and synthesis of random pressure fields is presented that highlights the concepts of point, spatially and/or temporally averaged random pressure fluctuations in the context of local or integral aerodynamic loads. Space-time averaging techniques are examined that provide promising practical means to measure local random pressure fields acting on bluff structures exposed to complex flow fields and to synthesize their integral effects. Pneumatic manifolding devices utilizing a discrete or distributed matrix of pressure taps facilitate both uniform and nonuniform local spatial averaging. Alternatively, a continuous spatial averaging device utilizing a piezopolymer strip permits a similar local averaging provision. Uniform local averaging permits the evaluation of normal or lateral loads on prismatic structure, while, nonuniform local averaging facilitates expedient measurement of torsional and lateral aerodynamic loads on prismatic and cylindrical members, respectively. Synthesis of locally averaged random fields permits evaluation of mode-generalized aerodynamic loads. The design of pneumatic manifolding devices and their calibration procedures are presented. An example of torsional aerodynamic loads on prismatic structures exposed to simulated atmospheric flow conditions in boundary layer wind tunnels is presented.

Data processing techniques have been frequently used to minimize errors involved in the measurements of earthquake ground motion data and experimental structural responses. In this paper a frequency domain data processing (FDDP) method is modified on its integration interval so that the integrated velocity and displacement time histories will be real functions. Earthquake simulation tests are performed to validate the modified FDDP. The input ground acceleration is used as the input program source to the shaking table. The time histories of input ground motion are compared with those measured at the shaking table. Very high fidelity is obtained. The reliability of the use of modified FDDP is further verified by comparing the response spectra measured and the input ground accelerations. High accuracy is achieved over a broad period range.