The curvilinear mesh method for analysis of complex thin walled structures

摘要

Complex plate and shell type structures are frequently analysed numerically on the basis of a super-element method. The FEM is usually used to obtain the stiffness matrix of a super-element (sometimes in several stages). In this paper the Curvilinear Mesh Method (CMM) which can be efficiently used for the same purpose is presented. The method uses an approach similar to the finite difference method but has a number of important advantages. One is the higher speed of convergence of numerical solutions due to the exclusion of effects produced by approximating rigid body motion. Another advantage is the fact that the equations of the CMM remain valid on the lines of slope discontinuity of the median surface. This makes it possible to analyse sub-structures as a whole even if the sub-structures consist of several parts with different geometry. CMM is based on the equations of classis theory of thin shells in invariant form. The median surface of a sub-structure is described in general curvilinear co-ordinates. In the super-element procedure the structure considered to be geometrically linear and elastic. The interaction between sub-structures is modelled using a generalised displacement method, in which the unknown at boundary nodes of the sub-structure are of the same type as those at internal nodes and also because there is a need to determine the degree of static indeterminacy and no need to choose the primary structure. To verify the presented numerical technique, the stress-strain state of a cylindrical shell with diaphragms has been analysed. Results obtained using CMM in a super-element procedure are compared with results obtained by the FEM and CMM without sub structuring. A comparison of results shows that there is little difference between these three methods in terms of accuracy.