氏   名
Duan Mei
段   梅
本籍(国籍)
中 国
学位の種類
博士(工学)
学位記番号
甲 第30号
学位授与年月日
平成12年3月23日
学位授与の要件
学位規則第4条第1項該当
専  攻
生産開発工学専攻
学位論文題目
Study of Adaptive Hybrid/Mixed Finite Element Method for Structural Analysis of Plates and Shells
(板及びシェル構造解析のためのアダプティブハイブリット/混合有限要素法)

論文の内容の要旨

  It is known that the application of plate and shell are very widespread in engineering.
Finding a most effective numerical analysis method has very important theoretical and practical meanings in the design and optimization of structure. The hybrid-stress method has widely been accepted as one of the most effective approach to the formulation of C 1_continuous plate bending problem since it was presented by Professor Theodore H. H. Pian of Massachusetts Institute of Technology in 1964. Its emergence made the solutions of plate and shell analyses be greatly improved. Hybrid/mixed Finite Element Method (HHFEM) is the development of hybrid stress method and has been proved to be a more effective method than displacement finite element method (DFEM), which is traditionally called as finite element method, by a large number of numerical analyses. HMFEM has the superiority of hybrid stress method and mixed finite element method. The "locking"phenomenon of numerical results is overcome in the case of thin plate, the remarkable accurate displacement and stress results are p rovided, and so on. During the last thirty years, HMFEM has been well developed and a good historkical survey of HMFEM has beengiven by Profeseor Theodore H. H. pian at the Third Asian-Pacific Conference on Computational Mechanics (1996). But so far some of iicient elements are only presented for HMFEM in scientific paper and there is no paper published regarding adaptive hybrid/mixed finite element analysis for plate and shell. This research has very important theoretical and practical meanings in the computational mechanics and the civil engineering.
Therefore, the following researches have been finished based on above the state-of-the-art of research in this diseertation.

  l) Some new efficient hybrid/mixed thin〜moderately thick plate bending elements with 5- node (HP5) and 6-node (HM6-l4) and shell elements (SHEL4-l6-0, SHEL4-18-2, SHEL4-l6-2, SHEL4-18-0) are presented based on the Helling-Reissner variational principle . The convergence of elements are proved. The rate of convergence is achieved for very low number of degrees of freedom. Some remarkable properties of elements are shown that the elements have invariability to geometric distorted mesh situations, to axial rotation, and to node positions and no extra zero-energy modes and Shear locking phenomenon in thin plate limit. Numerical studies show these elements can provide acceptable results even if coarse meshes are used Some efficient elements have been established to develop adaptive hybrid/mixed finite element method.

  2) Some a-posteriori error estimates of HMFEM for two-dimension, three-dimension plate and shell bending problems are developed, tested and swown that they are asymptotically exact estimate. Numerical analyses show that the rate of convergence of presented error estimates is exponential with respect to the number of fteedom degree. A local version of the presented a-posteriori error estimates was used to optinize mesh and to improve the accuracy of solution The study of effectiveness of a-posteriori error estimates provides an important basis for the development of AHMFEM.

  3) The presented HMFEM of plate and shell bending problems can evaluate stresses and deflections in the shell structures of arbitrary form subjected to arbitrary loads and boundary conditions.

  4) Variable-node elements for plate and shell bending problems are developed for HMFEM. The h-version, p-version and hp-version AHMFEM for plate and shell are presented, respectively. The various types of geometric meshes are designed with quadrilateral and curvilinear quadrilateral elements.

  5) The formulation of HMFEM for orthotropic and circular plate under polar coordinate, three-dimension axisymmetrical and solid problems are derived, respectively. The four-node, eight-node nine-node quadrilateral elements and eight-node solid element are preeented for HMFEM. The numerical results indicate that the presented method has favorable accuracy and computational efficiency.

  6) Preprocessing and post-processing of numerical analyses are developed for HMFEM. The meshes of model are demonstrated to clearly see the analysis process and results. The computational problem of AHMFEM is implemented for elasticity problems.

  7) Many engineering problems have been settled by the presented AHMFEM and appeared in this doctoral dissertation, such as the stress analyses of adhesive-bonded cylindrical lap joints, structural, modal and dynamic analyses of press-ress timbered bridge, structural analysis of continuous footing made with EPS styrofoam, etc.

  8) The presented method has wide application in structural engineering. The most of contents of above researches have been published by author.