Keywords: flat shell, finite element method, pipe, discrete shear theory, free formulation.

In this paper is described an attempt to incorporate to standard drawing tools from OpenGL library and a evaluation tool related to finite element analysis of cylindrical shells with geometry approximated by triangular flat elements in a environment called DUTOGL. Hence, properties other than element geometry such as mechanical properties, element connectivity, and boundary constraints can be added to the drawing information, providing a more friendly and efficient pre-processing environment. Next the stiffness matrices and equivalent nodal forces related to bending plate finite elements can be evaluated.

The evaluation functions are written in the object oriented language C++ and they are compiled as dynamic link libraries, which can be run from the environment programmed with OpenGL. At last the analysis is completed as soon as the post-processing libraries are run.

The pre-processing is usually defined as a stage of the analysis where input data (such as geometry, node and element numbering, mechanical properties, boundary conditions, loading) are set to perform the calculation of the discretized problem. The DUTOGL environment provides all drawing capabilities necessary to incorporate the remaining finite element input data information. This procedure of compatibilization has usually been done using two strategies namely the OpenGL API [1] and the CaeFep++ library. In the first approach the source code must be written in C++. In the second approach the object oriented programming CaeFep++ library with more than 50 different function calls written in C++ programming language is used. It should be noted the OpenGL library has a compiled form and therefore the source code does not necessarily need to be shown to the users.

The processing is usually defined as a stage of the analysis in which the main calculations (such as elemental stiffness matrix evaluation, structural stiffness matrix assembling, nodal equivalent force vector evaluation, algebraic system solution, etc) are done. In present paper, the pipe problem is analysed by superposition of bending plate and membrane problems using the finite element method. For the membrane effects the free formulation finite element, originally developed by Bergman and Felippa [2] is used. The main characteristics of this element are: triangular flat geometry, three degrees-of-freedom by node (two displacements on the plane and one drilling rotation perpendicular to the plane) located at each triangle vertex. For plate bending two flat triangular elements are used namely the discrete Kirchhoff theory [3] and the discrete shear theory [4] elements. Both elements have three degrees-of-freedom (one transverse displacement and two slopes) by node located at each triangle vertex.

The post-processing is usually defined as a stage of the analysis in which the results are shown. In the DUTOGL environment the results can be accessed by the values shown in some dialogs. In addition, DUTOGL allows graphical outputs for the displacements and deformed shape.

1

Woo M., Neder J., Davis T., Shreiner D., "OpenGL Programming Guide", Addison-Wesley, 1999.

2

Bergman P.G., Felippa C.A., "A triangular membrane element with rotational degrees of freedom", Comp. Meths. in Applied Mech. Eng., v.50, p.25-69, 1985. doi:10.1016/0045-7825(85)90113-6

3

Batoz J.L., Bathe K.J., Ho L.W., "A study of three node triangular plate bending elements", Int J Numer Meth Engng, 15, 1771-812, 1980. doi:10.1002/nme.1620151205

4

Batoz J.L., Lardeur P., "A discrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates", Int J Numer Meth Engng, 28, 533-560, 1989. doi:10.1002/nme.1620280305

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)