基于三角小波有限元的桥梁稳定极限承载力自适应计算理论研究

项目名称： 基于三角小波有限元的桥梁稳定极限承载力自适应计算理论研究

项目编号： No.51478159

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 建筑科学

项目作者： 任伟新

作者单位： 合肥工业大学

项目金额： 83万元

中文摘要： 桥梁稳定极限承载力势必涉及材料非线性,然而结构的弹塑性总是在结构的局部形成，且随着荷载的增加，弹塑性区不断发展，这就要求有限元需要有这种自适应性，而常规有限元方法在跟踪和考虑结构弹塑性区逐步地发展有其本质的不足。项目将同时具有三角函数良好逼近特性和小波多分辨率与局部特性的Hermite插值型三角小波引入结构分析领域，采用三角小波作为插值函数，推导杆系结构的三角小波有限元列式，进行结构的变形、振动和稳定计算；在此模型基础上考虑桥梁的几何和材料非线性，基于三维虚功增量方程，建立桥梁结构非线性分析TL 和UL三角小波有限元列式；最后运用三角小波升阶谱有限元和多分辨率三角小波单元，实现三角小波有限元的自适应分析。项目旨在从理论、数值模拟和试验三个方面，解决桥梁稳定极限承载力分析中局部弹塑性和弹塑性区逐步发展的难题，实现桥梁结构稳定极限承载力更精细化分析，项目研究具有较大的理论意义和工程实用价值。

中文关键词： 桥梁结构；极限承载力；小波；有限元；自适应

英文摘要： The ultimate load-carrying capacity of bridge structures has to involve in the material nonlinearity. However, the structural elastic-plasticity always occures in the local zone of the structure and this elastic-plastic zone develops gradually with the increase in the applied loads. To consider these issues, it is required that the finite elements are adaptive. Unfortunately, the current conventional finite elements has a dificulty to automatically trace the occrence and development of structural elastic plastcity.In this project, the trigonometric Hermite wavelet, which has both good approximation characteristics of trigonometric function and multi-resolution, local characteristics of wavelet, is introduced into the field of structural analysis. Taking wavelet function as interpolation function, the trigonometric wavelet finite element formulation of beam, plane frame structure is derived, and the deformation, vibration and stability of beam and frame structure are calculated accordingly. Thereafter, to take into account for both structural geometric and material nonlinearities, the total Lagrange and updated Lagrange trigonometric wavelet finite element formulations for bridge nonlinear analysis are established based on three dimensional virtual incremental equations. By using trigonometric wavelet hierachical element and multi-resolution trigonometric wavelet element, the adaptive trigonometric wavelet element formulation is finally realized to carry out the adaptive structural nonlinear analysis. This project is aimed at solving the key problem on the localization and development of structural elastic-plasticity to perform the more accurate analysis of the ultimate-load carrying capacity of bridges.

英文关键词： bridge structure;ultimate load-carrying capacity;wavelet;finite element;adaptive