Journal of Engineering Mechanics

Growing deformable solids increase their mass during the deformation process by way of the gradual addition of material onto the external surface of the solids. Only the processes of continuous growth (accretion) are under consideration in this paper. The mathematical formulation of the boundary‐value problem for continuously growing solids has some general distinctive features, which differentiate it from the formulation for solids of constant mass. First, the full strains within the growing body are incompatible due to arbitrary straining of each material element before its attachment to the body. Second, the boundary conditions on the surface of growth must prescribe the total stress state of the surface element, i.e., the full stress tensor on this part of the external boundary of the body. The writer undertakes an attempt to display such features and to present a brief historical sketch of the topic.

In this study, a passive control system has been proposed to protect structures from earthquake damages. In particular, the influence of an absorber on the dynamics of base‐isolated structures has been investigated in detail. Two different types of base‐isolation systems have been considered. These include rubber‐bearing and sliding‐friction isolators. The base isolators are represented by hysteretic models. The absorber consists of a linear spring mass attached to the base. Simulation studies were conducted for various models subjected to the 1971 San Fernando earthquake excitation. An optimization subroutine based on the simplex method was utilized to determine the best absorber parameters for a given situation. It is concluded that the base isolators can be much more effective in protecting conventional structures from earthquake damages if they are used in conjunction with an absorber. The optimum mass of these absorbers is found to be quite small as compared to the mass of the ground structures. It is anticipated that the results obtained in this study could be put in practice in the near future and serve as a meaningful design technique in preventing earthquake damages.

The linear fictitious crack model with linear softening law is a very important special case of the general fictitious crack model proposed by Hillerborg. When the traction‐separation softening curve is assumed linear, the peak load can be determined through the proposed linear eigenvalue problem formalism, referred to as the boundary eigenvalue problem. A detailed description is given of the finite element implementation of the proposed algorithm. It is shown that the first eigenvector can be used to calculate the peak load of the linear fictitious crack model. Furthermore, the first eigenvalue can be related to the critical nondimensional specimen size. Finally, it is elucidated that in the linear fictitious crack model, the peak‐load solutions can be presented in a nondimensional fashion with proper consideration of material properties and specimen sizes. The nondimensional peak‐load solution graphs can be used effectively for quantifying the size effect in the linear fictitious crack model.

To identify the pattern of changes in vibrational signatures of a structure is a promising approach for on‐line structure monitoring. Artificial neural networks, developed by researchers in cognitive sciences and artificial intelligence, can be used for this purpose. The main benefit of using artificial neural networks is their ability to diagnose signals that are fuzzy or imprecise. In this paper, neural networks were used to analyze the changes in vibrational signatures of a five‐story, three dimensional, steel frame. The neural networks were first trained with a set of experimental data obtained from shake‐table test results of the model. The capability of the neural networks to diagnose new signals was then tested against a separate set of experimental data. The results show that application of artificial neural networks in analyzing the changes in vibrational signatures of structures has considerable potential to structural damage diagnosis and condition monitoring.

A generalization of the linear quadratic regulator control theory for seismic‐excited linear structures is presented. The generalization includes the effect of actuator dynamics and a penalty for the acceleration response of the structure. A nonlinear control method is also proposed for nonlinear or hysteretic structural systems with emphasis placed on the applications to aseismic hybrid control systems. In protecting nonstructural components housed in the building against strong earthquakes, the reduction of the building acceleration response is important. The adverse effect of a system time delay due to the actuator response can be alleviated by taking into account the actuator dynamics in the optimization process. Simulation results are presented to demonstrate the advantages of generalized optimal control. Numerical results further indicate that the performance of the proposed nonlinear control method is better than that of the linear control law for hybrid control systems.

Three‐dimensional solutions are presented for the buckling and free vibrations of sandwich panels with composite face sheets subjected to combined temperature change and applied edge compression. Sensitivity coefficients are also evaluated and used to study the sensitivity of the buckling and free‐vibration responses to variations in the different lamination and material parameters of the panel. The temperature is assumed to be uniform, and the material properties are assumed to be independent of temperature. Numerical results are presented showing the effects of variations in geometric, material, and lamination parameters on the stability boundary, vibrational response, and sensitivity coefficients of initially stressed, simply supported sandwich panels. Also, the contributions of the in‐plane and transverse stresses, in the face sheets and the core, to the strain energy associated with the buckling and vibration modes are studied, thereby providing insight into the permissible approximations in modeling of structural sandwiches.

A laterally loaded masonry pier or a masonry arch under gravity loads is investigated by considering the pier or arch composed of blocks that are infinitely rigid, infinitely strong, and that transmit no tension at the joints. The constraints against interpenetration of adjacent blocks, and against sliding when prevented by a sufficient frictional force, result in a set of kinematic constraints on the system. Although the energy input to the system is nonlinear and has multiple branches, the linear part can be written as a linear program of minimizing the potential energy plus the dissipated energy of the system subject to the kinematic constraints on the system. The system is found to be stable if a statically admissible distribution of internal forces can be found in which a nonzero compressive force is transmitted at each joint, and the tangential force nowhere exceeds the normal force times the coefficient of friction. The system is shown to be unstable under a set of loads for which the virtual work is nonpositive in a kinematically admissible displacement.

This paper presents an approach for a general laminated shell geometry describable by orthogonal curvilinear coordinates. The theory includes through‐the‐thickness parabolic distribution of transverse shear stress, transformation of Cauchy stress‐strain relations into Lagrangian coordinates, and a layered elastic‐plastic analyses. Additionally, a simplified approach that allows large displacements and rotations is incorporated. The theory is cast into a displacement‐based finite‐element formulation and then specialized to cylindrical and spherical geometry. The theory is then applied to the isotropic and transversely isotropic laminated shells. Results incorporating the Cauchy‐Lagrangian transformation with through‐the‐thickness strain show a slightly more flexible response than in published results that are based on inextensible assumptions. These problems also indicate that the usual locking associated with shell elements is eliminated.

A methodology for quantifying flow‐field characteristics from laser Doppler velocimeter (LDV) measurements was developed. This methodology was used to quantitatively investigate two mixing conditions (0.25 Hz and 0.75 Hz) in an oscillating grid reactor. The resulting time records of fluid velocity in the reactor verified that the fluid motion was significantly different for the two mixing conditions. A computer program was developed based on theoretical work of others to calculate the power spectral density function directly from the randomly sampled LDV data. These power spectra, calculated from velocity‐time records, were used to quantify the length scales occurring in the reactor and their associated frequencies, the differences in the fluid motion associated with the two mixing conditions, and the differences in fluid motion with respect to measurement plane and measurement position in the reactor. Significant differences were observed in the larger‐scale fluid motions and not in the smaller‐scale (higher frequency) fluid motions.

This paper provides a methodology for optimally locating sensors in a dynamic system so that data acquired from those locations will yield the best identification of the parameters to be identified. It addresses the following questions: (1) Given $m$ sensors, where should they be placed in a spatially distributed dynamic system so that data from those locations will yield best estimates of the parameters that need to be identified?; and (2) given that we have already installed $p$ sensors in a dynamic system, where should the next $s$ be located? The methodology is rigorously founded on the Fisher information matrix and is applicable to both linear and nonlinear systems. A rapid algorithm is provided for use in large multi‐degree‐of‐freedom systems. After developing the general methodology, the paper goes on to develop the method in detail for a linear $N‐\mathrm{degree}‐\mathrm{of}‐\mathrm{freedom}$, classically damped, system. Numerical examples are provided and it is verified that the optimal placement of sensors, as dictated by the methodology that is developed, could provide significantly improved estimates of the parameters to be identified.

Buckling of rectangular plates under uniaxial loading is considered. The plates are uniform and elastic, and the load is uniform. The unloaded edges are simply supported, whereas the loaded edges have no out‐of‐plane deflection and are elastically restrained against rotation. Based on observations reported in the literature, this rotational resistance may increase as the plate is compressed. To take this stiffening behavior into account, the rotational stiffness at the loaded edges is assumed to be a linear function of the load. The equilibrium equation is solved analytically, leading to two characteristic equations. One corresponds to buckling modes that are symmetric in the direction of loading, and the other to antisymmetric modes. Critical loads are computed and plotted as a function of the aspect ratio for various cases. Results for load‐dependent conditions are compared to those for loaded edges that are simply supported, clamped, or elastically restrained with load‐independent stiffness. It is found that the critical load of a rectangular plate may be increased significantly if the loaded edges stiffen as they are compressed.