Development of flat shell elements with directly modified non-conforming modes and analysis of shell structures

Abstract

This dissertation presents the Direct Modification Method that eliminates the undesirable effect of strains due to various non-conforming modes so that the non-conforming element can pass the patch test. By the analytical calculation of correction constants, the direct correction for the derivatives of various types of non-conforming modes and/or for non-conforming modes themselves is possible. Thus, the presented method can substantially reduce the computation efforts when compared with `B-bar method``. Various non-conforming (NC) modes are classified into `basic NC modes``, `hierarchical NC modes``, and `higher order NC modes`` according to the correction constants of the presented Direct Modification Method. Based on the Direct Modification Method, a series of new non-conforming membrane elements with drilling degrees of freedom were developed by combined use of basic and hierarchical NC modes simultaneously. A series of new non-conforming plate bending elements were also developed by combined use of basic and higher order NC modes. In addition, a series of new non-conforming 4-node quadrilateral flat shell elements were established by combining the membrane and plate bending elements. A large number of numerical tests carried out in this study reveal that the presented flat shell elements show no sign of membrane locking and other defects even though the coarse meshes are used. A series of new variable-node non-conforming flat shell elements were also established. From results of the numerical tests, the following solutions for the problems in developing high performance flat shell element are suggested: (1) When the basic NC modes are combined by hierarchical or higher order NC modes, the elements become insensitive to mesh distortion. (2) One of the major problems of the non-conforming elements, i.e. failure of the patch test, can be effectively solved by using the presented Direct Modification Method. (3) When the membrane component of a flat shell has h...