【作者】 黄明；

【导师】 申长雨； 赵振峰；

【作者基本信息】 郑州大学 ， 材料加工工程， 2005， 硕士

【摘要】 橡塑模具制品一般具有厚度方向尺寸较面内尺寸很小且形状复杂等特点,所以在对制品进行翘曲变形分析时,就可采用薄壳有限元法。目前用于薄壳翘曲变形分析的单元主要有平板壳元、退化壳元和多变量壳元,其中平板壳元应用最为广泛,也最为成熟。所谓的平板壳元就是用许多小平板元构成的多面体去逼近真实的曲面,许多著名软件如ABAQUS、ADINA、ANSYS、MARC、NASTRAN、SAP的壳体分析都主要应用平板壳单元。但是平板壳元也有自身的问题:膜刚度近似差,膜板结合:为壳单元和一维单元与二维单元连接时困难。 解决上述问题的最好办法无疑是在膜元中引入垂直于该膜单元平面绕单元平面法线旋转的旋转自由度。关于此类单元的构造,Allman采用的插值方法得到广泛的采用,具有里程碑的意义。目前,引入旋转自由度后的膜元都不同程度的提高了膜单元的计算精度,但是在一些带旋转自由度的膜元中存在一多余的零能模式,几乎所有此类膜元所引入的旋转自由度都不具有连续介质力学中关于旋转自由度的定义,同时鲜有对旋转自由度自身的正确性进行考核。因此在解决一维与二维连接问题时结果很不理想、甚至是没法解决,并且有些单元推导过程过于繁琐、不实用。 为了给注塑模CAE中的制件翘曲分析提供一个可靠的单元,基于以上带旋转自由度膜元存在的问题,本文在生成平板壳元时的工作主要集中在对带旋转自由度膜元的研究上,总结如下: 1.在6节点三角形单元的基础上,通过对切向位移一次插值和法向位移二次插值消除了边中间节点,成功地引入了旋转自由度。同时引入了一个待定系数α,并由连续介质力学中关于转动分量的定义确定其取值,同时给出了一个附加方程,进而得到一个简洁有效的带有旋转自由度的平面三角形单元,记为OAT3。单元推导简单,列式简洁。具体算例表明,此单元无多余的零能模式,仍保持了原有Allman单元的精度,引入的旋转自由度具有连续介质力学关于转动分量的定义,且首次对旋转自由度自身的正确性进行了校核。 2.在10节点三角形单元的基础上,通过对切向位移一次插值和法向位移三次插值,成功地消除了边中间节点和单元中心节点,推导得到另一个带旋转自由度的3节点三角形单元,记为AT4。算例表明,此单元无多余的零能模式,精度较无旋转自由度的膜元有所提高,不足之处是单元较刚。 3.生成了基于离散Kirchhoff理论的板弯曲单元和空间一维杆单元。具体算例证明了以单元OAT3为膜元的平板壳元具有良好的计算精度,很好的解决了膜板结合为壳单元和一维单元与二维单元连接时的问题。更多还原

【Abstract】 Most injection-molded parts are complicated thin-shell like structure, so the thin shell finite element method is usually used to analyze the warpage and deformation of the parts. Generally, we have several types of thin shell elements to be used: flat-shell element, degenerated shell element and multi-variable shell element, of which the flat-shell element is adopted most widely due to its simplicity and is also selected by most famous finite element softwares, such as ABAQUS, ADINA, ANSYS, MARC, NASTRAN and SAP. However, the flat-shell has its own disadvantages: The precision of membrane element is not perfect and it is difficult to connect one-dimensional element and two-dimensional element.To resolve the problems, some scholars thought that the drilling degree of freedom should be added to membrane element. In all of the related researches, Allman’s work is doubtlessly a milestone. Since he successfully introduced the drilling degree of freedom for planar triangle element in 1984, some representative elements with the drilling degree of freedom have been developed quickly. It has been proved that the membrane element with the drilling degree of freedom could effectively improve element precision. On the other hand, those elements have also been found some shortcomings: some of them have the so-called spurious zero energy mode and the drilling degree of freedom in most elements has no exact physical meaning. At the same time the correctness of the drilling degree of freedom has never been proved, so it is doubtful whether the drilling degree of freedom could correctly connect one-dimensional and two-dimensional elements and pass the twist moment.The above problems seem to exist in most membrane elements with drilling degree of freedom. To provide a robust element for warpage and shrinkage analysis in CAE of the polymer processing, the paper is mainly concentrated on the study of membrane element with drilling degree of freedom, and at the same time develops a flat-shell element. The main work is as follows:1. Based on the 6-node linear triangular element, the middle nodes of edges were removed, and an element with drilling degree of freedom was derived by means of linear interpolation in tangential and quadratic interpolation in normal. At the same time a parameter was introduced. By letting the drilling degree offreedom at the elemental nodes equal to the rotation defined in elasticity, the value of the parameter was determined, which also led to an additional equation that eliminated the spurious zero energy mode. The concrete examples show that the new element OAT3 has same precision as the original Allman’s element did, but no spurious zero energy mode. Most importantly, it is proved that the drilling degree of freedom in the present element can correctly pass the twist moment.2. Based on the 10-node linear triangular element, an element with drilling degree of freedom (AT4) was derived. The nodes on the element sides were removed by means of linear interpolation in tangential and cubic interpolation in normal. The examples show that the new element AT4 has better precision than the element without the drilling degree of freedom, and no spurious zero energy mode. Its disadvantage is that stiffness matrix is too rigid to use in some cases.3. According to the discrete Kirchhoff theory, a bending plate element was derived, and the one-dimensional beam element was also derived in 3-D space. The concrete examples show that the flat-shell element whose membrane element adopted the element OAT3 has better precision than the other flat-shell element. The problems of mentioned above are also resolved.更多还原