title: Web crippling design of cold-formed stainless steel channels under interior-two-flange loading condition using deep belief network

authors: Fang, Zhiyuan (Arthur)

subjects: stainless steel

abstract: This research presents a deep-learning framework, namely a deep belief network (DBN), for analyzing the interior-two-flange web crippling performance of cold-formed stainless steel channels with centered and offset web holes. An elastoplastic finite element (FE) model, validated using 101 experimental results which were previously reported in the literature, generates a total of 43,200 data points for training the DBN. When compared to a total of 54 experimental results published in the literature, the DBN predictions were shown to be approximately 10% more conservative. Using the same large training data, the developed DBN model outperformed the Backpropagation Neural Network (a typical shallow artificial neural network) and the PaddlePaddle-based linear regression model. A parametric analysis was then performed using the DBN predictions to explore the effect of section size, web holes and bearing length. Design equations for (reduced) web crippling strength are proposed for the cold-formed stainless steel perforated channels, and the feasibility of the proposed equations was assessed by the conducted reliability analysis.

text: Web crippling design of cold-formed stainless steel channels under interior-two-flange loading condition using deep belief network This research presents a deep-learning framework, namely a deep belief network (DBN), for analyzing the interior-two-flange web crippling performance of cold-formed stainless steel channels with centered and offset web holes. An elastoplastic finite element (FE) model, validated using 101 experimental results which were previously reported in the literature, generates a total of 43,200 data points for training the DBN. When compared to a total of 54 experimental results published in the literature, the DBN predictions were shown to be approximately 10% more conservative. Using the same large training data, the developed DBN model outperformed the Backpropagation Neural Network (a typical shallow artificial neural network) and the PaddlePaddle-based linear regression model. A parametric analysis was then performed using the DBN predictions to explore the effect of section size, web holes and bearing length. Design equations for (reduced) web crippling strength are proposed for the cold-formed stainless steel perforated channels, and the feasibility of the proposed equations was assessed by the conducted reliability analysis.

year: 2023-01

title: Hamilton-Jacobi Theory and Superintegrable Systems

authors: Armstrong, Craig Keith

subjects: Hamilton-Jacobi theory

abstract: Hamilton-Jacobi theory provides a powerful method for extracting the equations of motion out of some given systems in classical mechanics. On occasion it allows some systems to be solved by the method of separation of variables. If a system with n degrees of freedom has 2n - 1 constants of the motion that are polynomial in the momenta, then that system is called superintegrable. Such a system can usually be solved in multiple coordinate systems if the constants of the motion are quadratic in the momenta. All superintegrable two dimensional Hamiltonians of the form H = (p_x)sup2 + (p_y)sup2 + V(x,y), with constants that are quadratic in the momenta were classified by Kalnins et al [5], and the coordinate systems in which they separate were found.

 We discuss Hamilton-Jacobi theory and its development from a classical viewpoint, as well as superintegrability. We then proceed to use the theory to find equations of motion for some of the superintegrable Hamiltonians from Kalnins et al [5]. We also discuss some of the properties of the Poisson algebra of those systems, and examine the orbits.

text: Hamilton-Jacobi Theory and Superintegrable Systems Hamilton-Jacobi theory provides a powerful method for extracting the equations of motion out of some given systems in classical mechanics. On occasion it allows some systems to be solved by the method of separation of variables. If a system with n degrees of freedom has 2n - 1 constants of the motion that are polynomial in the momenta, then that system is called superintegrable. Such a system can usually be solved in multiple coordinate systems if the constants of the motion are quadratic in the momenta. All superintegrable two dimensional Hamiltonians of the form H = (p_x)sup2 + (p_y)sup2 + V(x,y), with constants that are quadratic in the momenta were classified by Kalnins et al [5], and the coordinate systems in which they separate were found.

 We discuss Hamilton-Jacobi theory and its development from a classical viewpoint, as well as superintegrability. We then proceed to use the theory to find equations of motion for some of the superintegrable Hamiltonians from Kalnins et al [5]. We also discuss some of the properties of the Poisson algebra of those systems, and examine the orbits.

year: 2007

title: Waikato shallow lakes modelling

authors: Lehmann, Moritz K.

subjects: Lakes

abstract: The principal aim of this study is to apply a modelling approach to identify, evaluate and prioritise specific in-lake and catchment restoration options which could be applied to improve the water quality and ecological health of peat and riverine lake types across the Waikato Region. Four representative lakes have been selected as case studies for this work based on their social, cultural and ecological significance, as well as the availability of historical monitoring data and the potential transferability of the study findings to similar lake systems. The lakes include Rotomānuka, Ngāroto, Waahi and Waikare.

text: Waikato shallow lakes modelling The principal aim of this study is to apply a modelling approach to identify, evaluate and prioritise specific in-lake and catchment restoration options which could be applied to improve the water quality and ecological health of peat and riverine lake types across the Waikato Region. Four representative lakes have been selected as case studies for this work based on their social, cultural and ecological significance, as well as the availability of historical monitoring data and the potential transferability of the study findings to similar lake systems. The lakes include Rotomānuka, Ngāroto, Waahi and Waikare.

year: 2017