A Weyl-Dirac Cosmological Model with DM and DE

In the Weyl-Dirac (W-D) framework a spatially closed cosmological model is considered. It is assumed that the space-time of the universe has a chaotic Weylian microstructure but is described on a large scale by Riemannian geometry. Locally fields of the Weyl connection vector act as creators of massive bosons having spin 1. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe. At the beginning the universe is a spherically symmetric geometric entity without matter. Primary matter is created by Dirac's gauge function very close to the beginning. In the early epoch, when the temperature of the universe achieves its maximum, chaotically oriented Weyl vector fields being localized in micro-cells create weylons. In the dust dominated period Dirac's gauge function is giving rise to dark energy, the latter causing the cosmic acceleration at present. This oscillatory universe has an initial radius identical to the Plank length = 1.616 exp (-33) cm, at present the cosmic scale factor is 3.21 exp (28) cm, while its maximum value is 8.54 exp (28) cm. All forms of matter are created by geometrically based functions of the W-D theory.Comment: 25 pages. Submitted to GR

Shock Compression in Granular Media Using Discrete Finite Element Method

Los Alamos National Laboratory Research Contract LANL 6911J00149

Neural Network-Based Material Modeling

A neural network - based material modeling methodology for engineering materials is developed in this study. With this approach, the complex stress - strain behavior of an engineering material can be captured within the weight structure of a multilayer feedforward neural network trained directly on the stress- strain data obtained from experiments. The feasibility of this approach is verified through constructing neural network-based constitutive models of plain concrete in biaxial stress states and in uniaxial cyclic compression. A composite material model simulating the stress-strain behavior of reinforced concrete as a generic composite material in a biaxial stress state is built with experimental data from Vecchio and Collins' tests on reinforced concrete panels in both pure shear and combined shear with normal stresses. An adaptive neural network simulator is developed by implementing a dynamic node creation scheme and a higher order learning algorithm. Representation schemes, network architectures. training and testing methods, stress- and strain -based approaches for material modeling are investigated. An elastic unloading mechanism is studied with a concrete material model in biaxial compression. Main issues concerning the implementation of neural network material models in finite element solution procedures arc discussed. The results on the stress-strain relations of a material predicted by a neural network-based model are compared with experimental data. All neural network material models developed in this study match well with experimental results and the network testing results are reasonable. The developed approach shows promise in the constitutive modeling of composite materials

Modeling of Hysteretic Behavior of Beam-Column Connections Based on Self-Learning Simulation

Current AISC-LRFD code requires that the moment-rotation characteristics of connections be known. Moreover, it requires that these characteristics be incorporated in the analysis and member design under factored loads (AISC, 2001). Conventional modeling approaches to improve the prediction of cyclic behavior starts with a choice of a phenomenological model followed by calibration of the model parameters. However, not only is the improvement limited due to inherent limitations of this approach, but also test results indicate a large variability in load-carrying capacity under earthquake loading. In this research, a new neural network (NN) based cyclic material model is applied to inelastic hysteretic behavior of connections. In the proposed model, two energy-based internal variables are introduced to expedite the learning of hysteretic behavior of materials or structural components. The model has significant advantages over conventional models in that it can handle complex behavior due to local buckling and tearing of connecting elements. Moreover, its numerical implementation is more efficient than the conventional models since it does not need an interaction equation and a plastic potential. A new approach based on a self-learning simulation algorithm is used to characterize the hysteretic behavior of the connections from structural tests. The proposed approach is verified by applying it to both synthetic and experimental examples. For its practical application in semi-rigid connections, design variables are included as inputs to the model through a physical principle based module. The extended model also gives reasonable predictions under earthquake loads even when it is presented with new geometrical properties and loading scenario as well.published or submitted for publicatio

Hybrid Mathematical-Informational Modeling of Beam-to-Column Connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this report, two distinct approaches???mathematical models and informational models???are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macroelement by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.unpublishednot peer reviewe