1. Introduction The introduction section provides an overview of the research topic and its significance. It aims to introduce the reader to the research problem and explain why it is important to investigate.

2. Overview The overview section presents a general understanding of the flange-spigot connection system and its contact pressure distribution. It introduces the basic concepts, theories, and models related to this system.

3. Contact pressure distribution of flange-spigot connection This section focuses on analyzing the contact pressure distribution of flange-spigot connection through sub-region division. The simplified analysis of flange-spigot structure is presented first, followed by the sub-region division of flange bearing surface and spigot overfill surface.

2.1 Simplified analysis of flange-spigot structure This subsection explains how the flange-spigot structure can be simplified for analysis purposes.

2.2 Sub-region division of flange bearing surface This subsection presents a model for one bolted region under axial load and analyzes the contact pressure distribution considering the bolt influence zone.

2.2.1 Model of one bolted region under axial load This paragraph describes how a model for one bolted region can be established when analyzing contact pressure distribution in flange bearing surfaces.

2.2.2 Contact pressure distribution considering the bolt influence zone This paragraph discusses how to take into account the bolt influence zone when calculating contact pressure distribution in flange bearing surfaces.

2.3 Sub-region division of spigot overfill surface This subsection presents a model for spigots constrained by overfill material and analyzes the contact pressure distribution considering gaps at the root of spigots.

2.3.1 Model under spigot overfill constraint This paragraph describes how to establish a model for spigots constrained by overfill material when analyzing contact pressure distribution in spigot overfill surfaces.

2.3.2 Contact pressure distribution considering the gap at the root of spigot This paragraph discusses how to take into account gaps at the root of spigots when calculating contact pressure distribution in spigot overfill surfaces.

1. Circumferential stiffness model The circumferential stiffness model aims to predict the behavior of flange-spigot connection system under different loading conditions. This section presents two types of models: a fractal contact model and a discretized Iwan model.

3.1 Fractal contact model The fractal contact model is used to describe the contact between asperities on the flange-spigot surface. This subsection covers three types of purely elastic, purely plastic, and elastoplastic contacts, and explains how sub-regions can be defined based on their mechanical states and real contact areas.

(1) Purely elastic contact This paragraph explains what purely elastic contact means in terms of flange-spigot connections.

(2) Purely plastic contact This paragraph explains what purely plastic contact means in terms of flange-spigot connections.

(3) Elastoplastic contact This paragraph explains what elastoplastic contact means in terms of flange-spigot connections.

3.1.2 Parameters of the sub-regions This paragraph describes how parameters can be determined for each sub-region based on its mechanical state and real contact area.

(1) Mechanical states This sub-paragraph describes how mechanical states are defined for each sub-region in order to determine its parameters.

(2) Real contact areas This sub-paragraph describes how real contact areas are defined for each sub-region in order to determine its parameters.

3.2 Discretized Iwan model The discretized Iwan model is a method that uses Jenkins elements to describe the tangential response between flange-spigot interfaces. This subsection introduces this method and describes how parameters can be determined for the Jenkins element.

3.2.1 Determination of parameters in the Jenkins element This paragraph explains how to determine parameters in the Jenkins element used in discretized Iwan model.

3.2.2 Tangential response of Iwan model This paragraph describes how the tangential response between flange-spigot interfaces can be described using the discretized Iwan model.

1. Case study and discussion The case study and discussion section presents a practical example where the theoretical models are applied to analyze a specific flange-spigot connection system. It aims to validate the effectiveness and accuracy of the proposed models, as well as discuss their limitations and potential improvements.

2. Validity verification of theoretical model The validity verification section evaluates the validity of the proposed theoretical models by comparing them with experimental data or other established models in literature. It provides a comprehensive analysis of different factors that may affect the accuracy and applicability of the models, such as material properties, loading conditions, and geometric configurations.