【作者】 岑松；

【导师】 龙驭球；

【作者基本信息】 清华大学 ， 结构工程， 2000， 博士

【摘要】 构造基于Mindlin-Reissner中厚板理论的厚薄板通用单元和复合材料层合 板单元一直是近四十年来学术界关心和感兴趣的问题。本文针对构造上述单元 中所遇到的难题，提出了独特、合理而且简便易行的解决方案，克服了单元构 造和计算过程中所遇到的困难，获得了较大的成功。本文的工作主要包括： 一、将三角形单元面积坐标法推广应用到四边形单元，建立四边形面积坐 标理论，为构造四边形单元提供了新工具。并将四边形面积坐标法与广义协调 法相结合，提出了两种新型四边形八结点平面膜元MQ8-Ⅰ和MQ8-Ⅱ，在规则 和不规则网格下都能保持良好的性态，同时也证明了四边形面积坐标方法的优 越性。 二、对中厚板单元的剪切闭锁现象进行了探讨，提出了可以从根本上消除 剪切闭锁现象的剪应变场合理插值方法；提出了两类构造厚薄板通用单元的新 方案：Ⅰ．直接假设剪应变场和挠度场：和Ⅱ．直接假设剪应变场和转角场。按 照上述方案Ⅰ，并结合广义协调及四边形面积坐标技术，构造了三角形和任意 四边形厚薄板通用广义协调元TCGC-T9和TACQ；按照上述方案Ⅱ，构造了三 角形和任意四边形厚簿板通用单元TMT和TMQ，都获得了较大成功。它们自 由度少，列式简单，精度高，收敛性好，对网格畸变不敏感，无需特殊的数值 技巧便可以自动彻底地消除剪切闭锁现象，对薄板和厚板都具有良好的性能。 三、在本文的四边形厚薄板通用单元TACQ和TMQ的基础上增加中面双 线性位移场，构造出两个基于一阶剪切变形理论并适用于任何铺设情形的位移 型四边形复合材料层合板单元CTACQ和CTMQ。针对位移型单元应力精度不 良的问题进行了一些探讨，提出了利用杂交元原理对位移型单元内力和应力解 进行重算的后处理方法，使本文的单元可以较为精确地确定层合板应力，特别 是横向剪应力。本文的单元既保持了位移型单元的简便性和计算位移的精确 性，又可以像杂交元一样较好地预测层合板应力，是一类简单高效实用的优质 单元。更多还原

【Abstract】 In the past 40 years, the construction of plate bending elements based on the Mindlin-Reissner theory (the first-order shear deformation theory) for isotropic and laminated composite plates has attracted many researchers. In this dissertation, several rational, simple methods are presented to overcome the difficulties in the construction and application of above elements. Good results can be obtained by the proposed approaches. The main contributions of this dissertation are as follows:Ⅰ.The area co-ordinate method, which has been successfully applied to construct triangular elements, is generalized to construct quadrilateral elements. An area co-ordinate theory for quadrilateral elements is systematically established. By using the quadrilateral area co-ordinate and the generalized conforming method, two eight-node quadrilateral membrane elements, MQ8-I and MQ8-II, are developed. They exhibit good performance for both regular and distorted meshes. It is also demonstrated that the area co-ordinate method is an efficient tool for developing quadrilateral elements.Ⅱ.The shear locking phenomenon in thick plate bending elements is discussed. A rational, simple interpolation method for shear strain field is presented. Two new approaches for constructing thin-thick plate bending elements are also suggested: (i) Assume shear strain field and deflection field; and (ii) Assume shear strain field and rotation field. According to (i), triangular and quadrilateral thin-thick plate bending elements, TCGC-T9 and TACQ, are successfully constructed by using area the co-ordinate and the generalized conforming method. According to (ii), triangular and quadrilateral thin-thick plate bending elements, TMT and TMQ, are also successfully constructed. These four elements and are robust and free of shear locking. They can be employed to analyze very thin to moderately thick plates.Ⅲ.Two new displacement-based laminated composite plate elements, CTACQ and CTMQ, based on the first-order shear deformation theory, are successfully constructed. They are generalized from elements TACQ and TMQ by adding bilinear in-plane displacement field of the mid-plane, respectively. A new simple hybrid procedure is also proposed to improve stress solutions. Thus, excellent results for both displacements and stresses, especially the transverse shear stresses, can be obtained. The proposed elements are excellent for moderately thick and thin composite plates.更多还原