基于离散外微积分的薄壳复杂物理过程模拟

项目名称： 基于离散外微积分的薄壳复杂物理过程模拟

项目编号： No.61472170

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 计算机科学学科

项目作者： 孙晓鹏

作者单位： 辽宁师范大学

项目金额： 84万元

中文摘要： 薄壳物体的弯曲变形、折皱、碎裂、燃烧等复杂物理过程的动态模拟是图形学领域极具挑战性的难点问题。薄壳边界曲面的宽度与薄壳的厚度之比往往很高，其受力分析、能量分布与传导等数值模拟计算的收敛性和精准性均呈病态退化。常见薄壳物体如皮肤、纸张、树叶、布料、玻璃、铝罐、巧克力板等，具有弹性、塑性、脆性或者粘性等复杂物理性质，传统的有限元方法难以实现影视级真实感的高精度描述薄壳复杂物理过程在时间域和空间域的动态演变。 本项研究将基于离散外微积分理论建立薄壳物体弯曲变形、折皱、碎裂等复杂物理过程在时间域和空间域的动态几何演变的优化模型，并将给出有效、健壮、精度可控的离散数值解。薄壳轻便稳定坚固、承载力强、技术和经济效益显著、应用范围广泛，本项研究在提出新的图形学模拟理论和方法的同时，也将为土木建筑、机械化工、航空航天等领域的工程力学研究提供有效参考。

中文关键词： 薄壳；外微积分；复杂过程；物理模拟；离散模拟

英文摘要： Dynamic simulation of the bending, deformation, wrinkling, fracture, burning and other complex physical processes of thin shells is an extremely challenging and difficult problem of computer graphics.Because of the ratio of thin shell's boundary surface size to its thickness is very high, the convergence and accuracy of numerical simulation (such as stress analysis, energy distribution and transmitting, et al.) are pathological degradation. Common shell objects such as skin, paper, leaves, fabric, glass, aluminum cans, chocolate plates, etc., have some complex physical properties of elasticity, plasticity, brittleness, and viscidity, the classic finite element methods have lots of difficulties to address the dynamic evolution of the complex physical procedures of thin shells in the time domain and the spatial domain. Basing on the Discrete Exterior Calculus theory, this proposal will provide a dynamic optimization model to simulate a series of geometric evolutions of the complex physical procedures of thin shells both in the time domain and spatial domain, and will give some effective, robust discrete numerical solutions with controllable accuracy.Because of the firmness, lightweight, strong bearing capacity, significant technical efficiency and economic benefits, thin shells have a wide range of applications. The project will not only propose novel theory and methods for computer graphics simulation, but also provide a valid reference for the fields of civil, machinery, aerospace, engineering and mechanics.

英文关键词： Thin shell;Exterior calculus;Complex procedure;Physical simulation;Discrete simulation