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Finite deformation geomechanics: developing a meshless scaled boundary method

有限变形地质力学：开发无网格尺度边界方法

基本信息

批准号：
EP/D077117/1
负责人：
Charles Augarde
金额：
$ 43.04万
依托单位：
Durham University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD077117%2F1
关键词：
Finite deformation geomechanics developing meshless

项目摘要

Civil engineers make regular use of computational tools to predict the behaviour of the things they wish to build, prior to construction. The most popular computational method is the Finite Element Method (FEM) which works by dividing a complex structure (building or foundation, for example) into smaller elements. These elements are connected to each other by their corner nodes. Each element follows a set of rules that ensures the laws of equilibrium and compatibility (i.e. the fact that elements cannot overlap) are satisfied. Combining a large number of elements allows the (complicated) complete structure to be simulated in an approximate (but potentially highly accurate) sense.The FEM is widely used but has some disadvantages; in particular, infinite boundaries cannot be modelled. Furthermore, generating the mesh of elements can be problematic when working in three-dimensions. For cases where there is considerable deformation, the elements can change shape so much that their accuracy deteriorates. An example where one wishes to model large deformations is pushed-in pile foundations (essentially a tube of steel or concrete pushed into the ground, which later supports part of a building). Another example is a test known as the Cone Penetrometer test that determines the soil's stiffness and strength.This project will develop a new method for modelling these types of problem which overcomes many of the difficulties associated with FEs. The approach is a combination of a meshless method and a scaled boundary method. Meshless methods entriely remove the problem of generating the mesh of elements; one simply generates a distribution of nodes inside the boundaries of the model. The Scaled Boundary technique allows accurate modelling of the infinite boundaries (representing the soil extending vertically downwards and laterally). A key part of this project is concerned with creating a realistic simulation capability for large ( finite ) deformations in the soil. In conventional small deformation theory we assume that we can calculate stresses and strains on the basis that it has not changed its original shape. This simplification works well in many cases, but when the loads applied cause large deformations, errors appear unless we keep track of the changing shape of the problem. The permanent (large) displacements will be represented by a new formulation that takes account of the different soil compressibilities in different directions (anisotropy). We will combine this rather fundamental work with the new computational method to create a general tool that can handle many problems in geomechanics (particularly those that pose real difficulties for the FEM).

土木工程师在施工之前，经常使用计算工具来预测他们想要建造的东西的性能。最流行的计算方法是有限元方法，它通过将复杂的结构(例如，建筑或基础)划分为较小的单元来工作。这些元素通过它们的角节点相互连接。每个元素都遵循一套规则，以确保满足平衡和兼容定律(即元素不能重叠的事实)。将大量单元组合在一起，可以近似(但可能非常精确)地模拟(复杂的)完整结构。有限元被广泛使用，但有一些缺点；特别是不能模拟无限大的边界。此外，在三维环境中工作时，生成元素网格可能会出现问题。对于存在相当大变形的情况，单元的形状可能会改变得太多，以至于它们的精度会恶化。一个想要模拟大变形的例子是挤入桩基础(基本上是一根推入地面的钢筋或混凝土管，后来支撑着建筑物的一部分)。另一个例子是一种被称为锥形贯入仪的测试，它可以确定土壤的硬度和强度。这个项目将开发一种新的方法来模拟这类问题，它克服了与FES相关的许多困难。该方法是无网格法和尺度边界法的结合。无网格方法彻底消除了生成单元网格的问题；只需在模型边界内生成节点的分布即可。定标边界技术允许对无限边界(表示土壤垂直、向下和横向延伸)进行精确建模。该项目的一个关键部分是为土壤中的大(有限)变形创建逼真的模拟能力。在传统的小变形理论中，我们假定可以在不改变其原始形状的基础上计算应力和应变。这种简化在许多情况下都很有效，但当施加的载荷引起大变形时，除非我们跟踪问题的变化形状，否则会出现错误。永久(大)位移将用一个新的公式表示，该公式考虑了不同方向(各向异性)不同的土壤压缩系数。我们将把这项相当基础的工作与新的计算方法结合起来，创建一个通用工具，可以处理地质力学中的许多问题(特别是那些给有限元带来真正困难的问题)。