【作者】 杨吉新；

【导师】 陈定方； 沈成武；

【作者基本信息】 武汉理工大学 ， 机械设计及理论， 2002， 博士

【摘要】 元胞单元法是新近出现的一种数值计算方法，它引用元胞自动机的思想将有限元对结构的整体分析变成局域求解，对计算机容量要求低，在大型复杂结构的计算方面具有良好的前景，同时可望形成一种高度并行的算法，适用于未来并行机的要求，是一种富有发展潜力的新的数值方法。 论文以弹性力学平面应力应变问题的求解为例，对元胞单元法进行了全面的、系统的理论描述，阐述了元胞单元法的基本原理和计算步骤，给出了相关定义，并据此对该方法与其它计算方法尤其是有限元法的异同点进行了讨论。为考察该方法的正确性，论文进行了数值试验，列出了详细的计算过程和计算结果，以实际算例对元胞单元法的有效性作出了数值论证。同时，以对大型结构的实际分析为依据，讨论了该方法在大规模计算方面的优势和发展前景。 为探讨元胞单元法的广泛适用性，论文将元胞单元法的应用领域从杆系结构、平面问题拓展到其它结构。首先应用该方法分析弹性薄板的小挠度弯曲问题。依据元胞单元法的基本原理和薄板弯曲理论，提出了用元胞单元法分析薄板弯曲问题的计算步骤，并进行数值试验，论证了其可行性和有效性。同时，还应用该方法分析三维实体结构，以8节点六面体等参元为例进行了数值试验和讨论，证明该方法在弹性力学空间问题中的应用同样是有效的。 为丰富元胞单元法理论，论文开展了非线性元胞单元法研究。根据有限元求解弹塑性问题的基本思想，提出了元胞单元法分析弹塑性问题的方法和步骤，用数值算例对其可行性进行了论证，从而将元胞单元法的应用从线性问题延伸到非线性问题。 元胞单元法是面向未来用于大规模计算的并行计算机而提出的计算方法，但其作为并行算法是否切实可行尚待考证，论文对此进行了讨论，认为古典的力矩分配法是元胞单元法求解连续梁和无侧移刚架的一种特殊形式，并按力矩分配法对连续梁作了局域并行和全域并行分析，对元胞单元法作为并行计算方法的可行性进行了理论探讨。 此外，论文在元胞单元法的可视化实现方面作了一定的工作，研制了一套具有自主知识产权、功能强大、集元胞单元法和有限元于一体的可视化结构分析软件，有良好的建模、分析、结果显示与查询模块，自带绘图功能，全中文界面，具有计算正确、速度快、结构规模大、可视化程度高、使用方便、容错性好等优点。 在软件研制过程中，提出一种基于前沿生成法的速度快、稳定性好的平面元胞元网格自动生成方法和三维六面体网格的线段转换法;根据元胞元模型的特点，提出一种稳健性较好的三维元胞元模型消隐方法;通过对应力图生成技术的研究，提出一种对等值线、色带图、浓淡图均适用的应力图快速生成算法。更多还原

【Abstract】 Cellular element method is a new numerical computing method .In this method the integer analysis of structure is changed into a series of part analysis by using the idea of Cellular Automata. It may have a good future in the aspect of large structure because it hardly have any special request on the capability of computer. Simultaneity,It can be developed into a high parallel arithmetic to suit for the request of parallel computer in the future. Therefore, the new method is a good numerical method with great potential.Cellular element method was described completely and systemically in this paper by through the solving of elastic plane stress and strain problems. The basic principle , calculating and the correlative definitions steps were described. The similarities and differences between cellular element method and other numerical methods such as finite element method were discussed. In order to check the correctness, some numerical examples were carried through. The detailed calculating course and results were listed. At the same time, the advantages of the new method on the aspect of analysis large structures were put forward after two large structures were computed.In order to find the applying area of cellular element method, it was used to analyses the structures besides truss, beam and plane problem. Elastic thin plate in small yield was firstly calculated by using cellular element method. The approach was researched on the basis of the principle of cellular and the theory of thin plate, and its feasibility and validity were proved through numerical instances. Similarly, the new method was applied to analyses three-dimensional entity structures. The hexahedron element with 8 nodes was selected to solve the structures. Some examples were listed, and the results show that cellular element method can solve space problems well.Nonlinear cellular element method was also studied for enriching its theory. According to its principle, the techniques of computing elastic-plastic structures were researched and a numerical example was given.Though cellcular element method is put forward to face parallel computer, its feasibility has not been studied. The problem was discussed in this paper. Theclassic moment distributing method can be regarded as a special form in calculating continuous beams or rigid frames with no line displacement. So moment distributing method was used as cellular element method to do part parallel compute and full parallel compute.Moreover, a few things on the visualized cellular element method were finished. A visual structure analysis system with might function was researched. The system can do computing by using both cellular element method and finite element method. It has good modeling module, analysis module and results showing module. It has full Chinese interface. Above all, the system has some advantages such as high compute precision, high speed and suited for large structure analysis.During the process of the system researching, A new mesh approach based on advancing front technique for triangle elements was studied. A practical method of generating hexahedron mesh for cellular element method through transfering lines into volumes was worked out. Moreover, a new hidden method for cellular models and a approach of forming stress images were also researched.更多还原