Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models

Score-based generative models (SGMs) is a recent class of deep generative models with state-of-the-art performance in many applications. In this paper, we establish convergence guarantees for a general class of SGMs in 2-Wasserstein distance, assuming accurate score estimates and smooth log-concave data distribution. We specialize our result to several concrete SGMs with specific choices of forward processes modelled by stochastic differential equations, and obtain an upper bound on the iteration complexity for each model, which demonstrates the impacts of different choices of the forward processes. We also provide a lower bound when the data distribution is Gaussian. Numerically, we experiment SGMs with different forward processes, some of which are newly proposed in this paper, for unconditional image generation on CIFAR-10. We find that the experimental results are in good agreement with our theoretical predictions on the iteration complexity, and the models with our newly proposed forward processes can outperform existing models

Stability of twin circular tunnels in cohesive-frictional soil using the node-based smoothed finite element method (NS-FEM)

This paper presents an upper bound limit analysis procedure using the node-based smoothed finite element method (NS-FEM) and second order cone programming (SOCP) to evaluate the stability of twin circular tunnels in cohesive-frictional soils subjected to surcharge loading. At first stage, kinematically admissible displacement fields of the tunnel problems are approximated by NS-FEM using triangular elements (NS-FEM-T3). Next, commercial software Mosek is employed to deal with the optimization problems, which are formulated as second order cone. Collapse loads as well as failure mechanisms of plane strain tunnels are obtained directly by solving the optimization problems. For twin circular tunnels, the distance between centers of two parallel tunnels is the major parameter used to determine the stability. In this study, the effects of mechanical soil properties and the ratio of tunnel diameter and the depth to the tunnel stability are investigated. Numerical results are verified with those available to demonstrate the accuracy of the proposed method

Generating Procedural Controls to Facilitate Trade: The Role of Control in the Absence of Trust

Over the years, Trust has been recognized in the Bled community as a key enabling factor to stimulate Electronic Commerce. Authors have discussed formal aspects of trust, the role trust plays in the adoption of both B2B and B2C Electronic Commerce, as well as mechanisms to build trust and/or overcome the lack of it. This article first provides a brief overview of the Trust-related articles in the Bled eConference. It then focuses on one specific aspect of the facilitation of trade in absence of trust: the development of procedural controls that enable Electronic Commerce at arms’ length, summarizing the contributions of the authors on this theme at the Bled Conference since the early 1990s. The paper concludes with the authors’ current view on developing procedural controls, focusing on the design process itself, which is often a rather lengthy process consisting of trial-and -error. Here a more analytical approach is proposed to the identification of control requirements for inter-organizational procedures. The approach involves abstracting the process to identify its basic deontic elements. A model checking approach is then applied to identify needed controls