Journal of Engineering Mechanics

A relatively simple stochastic optimization procedure based on the adaptive random search algorithm is presented to train artificial neural networks of the type encountered in applied mechanics applications. After discussing some essential features of the algorithm that influence its search efficiency, a procedure is outlined for replacing the back-propagation training approach by the new method in order to train networks involving high-dimensional parameter vectors. The method is successfully used in conjunction with a multilayer network involving a parameter vector of very high dimension. It is shown that the adaptive random search approach shifts the training effort from the user to the computer by exchanging additional computer search effort for easier training tasks on the part of the user. Extensive simulation studies are presented to provide statistically significant results related to the characteristics of the stochastic training approach. Guidelines are provided for applying the method to generic neural network training episodes.

A method based on adaptive estimation approaches is presented for the on-line identification of hysteretic systems under arbitrary dynamic environments. The availability of such an identification approach is crucial for the on-line control and monitoring of time-varying structural systems. Previous work by the writers is extended to handle the general case when no information is available on the system parameters, even the mass distribution. A robust, least-squares-based adaptive identification algorithm, incorporating a Bouc-Wen hysteresis element model with additional polynomial-type nonlinear terms, is used to investigate the effects of persistence of excitation and of under- and overparameterization: challenging problems in realistic applications. In spite of the challenges encountered in the identification of the hereditary nature of the restoring force of such nonlinear systems, it is shown through the use of simulation studies of single-degree-of-freedom and certain multi-degree-of-freedom systems that the proposed approach can yield reliable estimates of the hysteretic restoring force and the hysteretic element model parameters.

A locking-assessment procedure for shear-deforming beam elements is proposed that is suitable for inelastic material behavior. By way of example, the procedure is used to motivate the formulation of a nonlocking element in the context of an isotropic but inelastic (e.g., J₂-flow theory with isotropic hardening) constitutive model. In particular, constraints among the nodal degrees of freedom (dof) are introduced to ensure uniform, non-shear-locking element behavior. The locking-assessment procedure distinguishes between locking, stiffening, and uniform element behavior in the thin-beam limit by comparing the dimensions of the function spaces containing the bending strains, both in the presence and absence of the thin-beam constraints. Inter-dof constraints that lead to uniform behavior are seen to arise naturally from this element-assessment procedure. Also, a novel cross-sectional numerical integration scheme is presented that is highly accurate in relation to the number of stress-sampling points on the cross section.

Thermodynamic formulation of elastoplastic or viscoplastic models using the internal variable approach currently does not include models using the plastic work as a hardening variable. This means that many realistic material models do not fit into the current thermodynamic framework. An approach to extend the thermodynamic framework to include models where plastic work is used as a hardening variable is considered. This approach can even be extended to viscoplasticity where the change of the quasistatic yield function is controlled by the plastic work. As an application of the approach, the Lade-Kim model is considered. This nonassociated plasticity model uses plastic work as a hardening variable, and it is capable of predicting the behavior of frictional materials, in particular soils. It is shown that the model can be described in a general thermodynamic framework and that it is well defined in a thermodynamic sense.

It has been suggested that the reinforcing fiber size and the spacing between the reinforcing fibers play a dominant role in determining the fracture properties of cementitious composite materials. In the present study, 48 specimens were tested under fatigue loading to investigate the effect of fiber size and the corresponding spacing between the reinforcing fibers on the fracture behavior of mortar composites. The specimen dimensions of 125 × 600 × 25 mm (5 × 24 × 1 in.) and the volume fraction of the reinforcement were kept constant at 0.04 while the cross-sectional area of the reinforcing fibers was varied at 0.79, 1.77, and 3.14 mm² (0.00122, 0.00274, and 0.00487 in.²) with a corresponding spacing between the fibers of 37.5, 15, and 5.8 mm (1.5, 0.6, and 0.23 in.) and a corresponding number of fibers of 3, 6, and 14. The tension-tension flexural fatigue testing was performed at stress levels of 80%, 65%, and 50% of the ultimate flexural strength of similar specimens tested under static loading conditions. The fatigue testing was performed at a constant frequency of 2 Hz. The crack initiated simultaneously as the loading cycles ensued at 80% and 65% stress levels; however, a large scatter in the number of cycles to failure (N_f) was observed. Number of cycles to failure ranged from 240 to 3,069 at the 80% stress level and from 10,165 to 35,070 at the 65% stress level. At the 50% stress level, none of the specimens failed or had appreciable crack growth for up to 500,000 cycles. As in the static case, fiber size and spacing appear to have an influence on the fatigue crack growth behavior; however, as is typical of concrete fatigue testing, the large scatter in the fatigue crack growth data engulfed any apparent trend. The Weibull probability distribution function compared well with the experimental data. A statistical model based on the inclusion model and the Weibull distribution was proposed to account for the fiber spacing effect.

One of the goals of this research is to apply nonlinear fracture mechanics to design problems encountered by the engineering society. Nonlinear fracture mechanics makes it possible to study the size effect with respect to the pullout cone failure of headed anchors embedded in concrete under various boundary conditions. This investigation shows that the fictitious crack approach can be extended with two orthogonal rod elements to become a new technique that can successfully predict the size effect on the pullout tests. In this study the numerical investigation that describes the behavior of headed anchors under tension loading has been carried out by a computer simulation using our original program ANACS (Advanced Nonlinear Analysis of Concrete Structures). To judge the validity of the results, the numerical results were compared with Eligehausen and Sawade's empirical equation and test results of a report by the Reunion International des Laboratoire d'Essais et de Recherches sur les Materiaux et les Constructions.

Further theoretical analysis is presented on the instability of superconducting magnets. A three-coil superconducting partial torus with two pin supports is described by a nonlinear theoretical model, which is composed of the theory of curved beams and the Biot-Savart law. A semianalytical and seminumerical program is used to obtain the solution to the nonlinear boundary-value equations of the coil. The influence of the location of two pin supports on the critical current is investigated in detail. The numerical results show that the deformation procedure can be well simulated by the theoretical model, and the critical current values of magnetoelastic stability of the coil are in good agreement with the existing experimental data.

A theoretical study of bending and buckling of ferroelastic plates in the presence of magnetic fields is carried out based on the model that takes into account the nonlinear field-structure interaction. The resultant force system derived from the interaction between magnetic fields and ferromagnetic materials is composed of the body force only. Using this model, the bending and buckling problems of a cantilevered ferromagnetic plate and simply supported rectangular plates in transverse and oblique magnetic fields are investigated with the aid of a numerical approach. Numerical results reveal some interesting features of magnetoelastic bending and buckling phenomena due to the nonlinear nature of the field-structure interaction.

Multigrid and multigrid-preconditioned conjugate-gradient solution techniques applicable for unstructured 3D finite-element models that may involve sharp discontinuities in material properties, multiple element types, and contact nonlinearities are developed. Their development is driven by the desire to efficiently solve models of rigid pavement systems that require explicit modeling of spatially varying and discontinuous material properties, bending elements meshed with solid elements, and separation between the slab and subgrade. General definitions for restriction and interpolation operators applicable to models composed of multiple, displacement-based isoparametric finite-element types are proposed. Related operations are used to generate coarse mesh element properties at integration points, allowing coarse-level coefficient matrices to be computed by a simple assembly of element stiffness matrices. The proposed strategy is shown to be effective on problems involving spatially varying material properties, even in the presence of large variations within coarse mesh elements. Techniques for solving problems with nodal contact nonlinearities using the proposed multigrid methods are also described. The performance of the multigrid methods is assessed for model problems incorporating irregular meshes and spatially varying material properties, and for a model of two rigid pavement slabs subjected to thermal and axle loading that incorporates nodal contact conditions and both solid and bending elements.

In this paper, a general method, called the spline finite member element method, is developed for spatial buckling analysis of thin-walled eccentric compressive members with arbitrary cross sections, considering warping. A transformed B₃-spline function is used to simulate the longitudinal warping displacement field along the cross section of a thin-walled member. The method differs from Vlasov's classical theory of spatial buckling in that it takes into account the effects of shearing strains of the middle surface of walls on the buckling, which reflect the shear lag phenomenon. Compared with the results from the COSMOS/M finite element analysis program and another analysis method, the numerical results obtained in the paper demonstrate the versatility, accuracy, and efficiency of the proposed method. The fast convergence shown in numerical examples demonstrates the reliability of the results.

A nonparametric identification method for nonlinear hysteretic systems is presented. Making use of the Duhem hysteresis operator, the multivalued relationship of hysteretic restoring force with respect to displacement and velocity of the phase plane is mapped onto two single-valued surfaces in an appropriate subspace in terms of the state variables of displacement and hysteretic restoring force. The functions describing the surfaces need not be specified in specific expressions, so that both the form and parameters of the functions can be fine-tuned to match experimental results. They are identified by fitting the surfaces with the generalized orthogonal polynomials in terms of displacement and hysteretic restoring force. The proposed method is applied to the modeling of hysteretic behavior of a wire-cable vibration isolator from experimental data. Excellent agreement between the predicted and experimental hysteresis loops is obtained. Based on the established hysteretic model, the dynamic response characteristics of a wire-cable isolation system are evaluated.

Physically based analytical models capable of describing the behavior of general hysteretic systems are formulated. The formulation includes the effects of pinching, stiffness degradation, and load deterioration. Two types of pinching, one due to the system encountering additional stiffness and one due to unequalness of strengths for loading in opposite directions, are considered. The latter pinching is represented in terms of strength ratios. Both stiffness degradation and load deterioration are described in terms of functions of total adsorbed hysteretic energy. Two possible forms for each of these functions are presented. All of the system parameters are in terms of definite physical materials or system properties that can be measured through tests. To show that the proposed analytical models provide realistic descriptions of the resistance-deformation behavior for general hysteretic systems, examples of bilinear and quatrolinear systems are presented, using harmonic excitations as examples of the applied forcing functions.

There are several key issues to be considered in the design of active control systems for civil structures, including robustness to pertubations of the structural parameters stability in the presence of nonlinear actuator saturation effects, and the use of output feedback methods when it is either impossible or impractical to obtain the full state of the system. This research presents a design algorithm to create robust H_∞ static output feedback controllers for seismically excited civil structures, which account for all these effects in a single design. Robust static acceleration feedback H_∞ controllers are created for a five-story structure with a bounded, structural parameter uncertainty model. A nonconvex optimization problem is formulated and solved using an iterative solution method to obtain the desired control gains. A primary advantage of this method is that an intuitive, feasible starting point is available using the open loop (uncontrolled) system and the worst case attenuation constant for the uncertain system. Simulation results using seismic excitations show controllers obtained using this design method to be effective with minimal control effort.

Understanding the behavior of steel-concrete interaction is of fundamental importance to the study of reinforced concrete structures. In this paper, a technique for the development of a constitutive model for that interaction is presented. In the experimental part of the study, rebar and wedge pull-out specimens were tested. The stress and displacement in the tangential direction near the rebar interface were measured; whereas phase measurement speckle interferometry was used for accurate surface displacement measurement and crack growth detection. A fracture mechanics-based numerical simulation was then used to evaluate the normal stress at the interface using the measured crack length and crack opening displacement. This hybrid numerical-experimental technique was shown to successfully predict the measured normal stress and crack profile of the wedge splitting specimen.

Spectral-element method (SEM) is applied for the vibration analysis of the Levy-type rectangular plates subject to distributed dynamic loads. In the solution procedure, both FFT and inverse FFT computer algorithms are efficiently used to obtain the dynamic responses in time domain. Distributed dynamic load is approximated, as the superposition of equivalent dynamic line loads and the spatial coordinate dependence of equivalent line loads is removed by (spatial) FFT. This procedure transforms the original plate (two-dimensional) problem into an effective beam (one-dimensional) problem so that the solution procedure for one-dimensional structures can be used. Numerical tests show that SEM provides very accurate solutions when compared with conventional finite element solutions.

In the literature, the symmetry of the element tangent stiffness matrix of a spatial elastic beam has been a subject of debate. The symmetry of the tangent stiffness matrices derived by some researchers are tenuously attributed to the use of Lagrangian formulations, while the asymmetry of corotational tangent stiffness matrices is commonly attributed to the noncommutativity of spatial rotations. In this paper, the inconsistency regarding the symmetry of element tangent stiffness matrices formulated in the Lagrangian and the corotational frameworks is resolved. It is shown that, irrespective of the formulation framework, the element tangent stiffness matrix is invariably asymmetric. A “correction matrix” that enforces the proper rotational behavior of nodal moments into the conventional geometric stiffness matrix of an Updated Lagrangian spatial beam element is presented. It is demonstrated through a numerical example that adoption of this correction matrix is necessary for the detection of the lowest buckling mode of a space dome. The fact that the structure tangent stiffness matrix becomes symmetric at the converged solution of each increment in the geometrically nonlinear analysis of a space frame is also explained.