3. MATERIALES Y MÉTODOS
3.3 PROCEDENCIA DEL MATERIALES UTILIZADO
The finite element package ABAQUS /I / version 5.5, 1995 was used to perform the internal pressure stress and strain analysis for ’ the validation of the analytical model
described in the previous section.
The ABAQUS system includes a general purpose finite element program, an interactive pre-processor used to create models for ABAQUS and an interactive post-processing program which displays and output lists from restart and results files written by ABAQUS.
Since the ABAQUS analysis modules are batch programs, the objective is to assemble an input file which describes a problem so that ABAQUS can provide an analysis. Input files for complex simulations can be large, but can be managed without too much difficulty by using the convenience features built into the program’s input structure.
An input file for ABAQUS contains model data and history data. Model data define a finite element model, the element nodes, element properties, material definitiolis, and so on. History data define what happens to the model - the sequence of events or loading. The definition of a step includes the procedure type such as static analysis, the modelling of transients as well as control parameters for time integration or for the non-linear solution methodology, the loading, and output options.
First, the single walled cross-section was solved based on the well-know analytical solution for the stress and strain distribution along the radius of a single walled cross-section. After that a finite element model was prepared to perform the comparison with the analytical | results. The construction of the input file will be described later in this section. Figure 6.1.1 in JSection 6 I illustrates a comparison
figure indicates excellent agreement as is to be expected.
The input file for ABAQUS follows a standard procedure. There are five blocks which define the problem to be solved by the program. The first is the node
definition and generation; the second defines the element mesh or the way the nodes are connected to form the elements that will compose the whole finite element model. The third block is the material or materials definition, which | has to be linked with a set of elements. The fourth block defines the loading case and the boundary conditions. Finally, the fifth block establishes the form and variables that will be printed in the output file.
The selection of the element type is one of the key i decisions of a finite element problem. ABAQUS offers a huge range of element types. After considering the merits and drawbacks of very many of these, it was decided to perform this analysis using two types of elements - the axisymmetric element CAX8H and the plane strain element CPE8H. The problem was solved with both element types and gave almost exactly the same results. However of these two, the axisymmetric element CAX8H was used to produce the results of several geometries because the nodes and element mesh for this element type is much easier to define.
Based on the input file of Listing number 3.2.6-A, the multi-layered ABAQUS model was built, solved and verified against the analytical model developed in section 3. In this file, it was necessary to define another material set to represent the different material properties of the core and a new element mesh to model core thickness as three layers. To perform analysis using the plane strain element, a FORTRAN code was written to generate the node mesh which was used later to form the elements and consequently the finite element model. This model could selectively be represented by half or a quarter of the cylinder. Using suitable boundary conditions, the symmetry of the half or quarter cylinderl is exploited to reduce both computer time and disk space. A simple FORTRAN code was produced for the mesh generation to calculate the cartesian co-ordinates of each node in a cylindrical form and write the results in a suitable format to be input directly in the
ABAQUS input file. This code gives the node numbers with the comma
data for this program are the inner and outer radius of each layer, the number of nodes in each layer, the generation angle and the total angle. The relation between the total angle and the generation angle will be the number of nodes in the
circumferential direction. It used 10 degrees for generation angle and 180 degrees for the total angle. The number o f elements in the thickness was fixed in 100. Figure 6.1.2 in section 6 presents a comparison between the results obtained with the input file for multi-layered cross-sections and the analytical model developed in section 3. Good agreement is demonstrated by the comparison.
The input file for the multi-layered analysis is described in detail below. The lines starting with an asterisk (*) denote a command line which demands a specific action from ABAQUS. The first block of the input file contains the information to define the finite element node mesh. The command * HEADING is reserved to input the title of the input file. The commands *NODE and *NGEN are used to define the co ordinates of the nodes. The command *NODE defines for each node number a co ordinate associated with it. The command *NGEN generates several nodes between two nodes already defined using equal distances between them. It is useful to use the *NSET command to give a name to a given node set.
• First block: ^HEADING
THICK CYLINDER - INTERNAL PRESSURE - COMPOSITE *RESTART,WRITE,OVERLAY *NODE 1,10.
201
,20
. 1001.10..0.05 1201.20..0.05 2001.10..0.1 2201,20.,0.1 *NGEN,NSET=SIDE 1,201 *NGEN 1001,12012001,2201
The second block defines the element mesh. The ^ELEMENT command defines the type of the element among those described in the element library of ABAQUS.
There are several types and the selection of the element is the most important information to be input to the finite element system. The element type is directly related with the solution of the problem. For this analysis the axisymmetric element CAX8H. The reasons to use the axisymmetric element type CAX8H are two. First, the node mesh and element mesh can be easily defined without using a node mesh generator, ABAQUS has built in all necessary features to generate the axisymmetric mesh. Secondly, the results showed for the single walled cylinder with a mesh composed of axisymmetric elements CAX8H demonstrated a good agreement with the analytical solution.
In addition, the selection of the element type is a difficult task and only experienced engineers are able to do so. Therefore, this analysis was performed based on
recommended and tested element type.
The command *ELGEN is used in the second block to generate the elements that will compose the structural model. This command has several features and
properties to make the mesh generation more user friendly. The command *ELSET is similar to the command *NSET, although, it is used only to define a name for a set of elements rather than nodes.
• Second block: *ELEMENT,TYPE=CAX8H 1,1,3,2003,2001,2,1003,2002,1001 *ELGEN 1,100,2 *ELSET,ELSET=INNER 1 *ELSET,ELSET=OUTER
100
*ELSET,ELSET=STE,GENERATE 1,40 81,100 *ELSET,ELSET=COM,GENERATE 41,80The third block is to define the material properties associated with element numbers. This block starts with the command * SOLID SECTION where the material name and the element set is defined. The next command is ^MATERIAL and ^ELASTIC
which define the material elastic properties for a given element set. An isotropic material is assumed if nothing is specified. In this multi-layered analysis, two elastic materials sets have been defined to represent the material of the skins (STEEL) and the core(COMPOS). The analysis is applied only to the elastic regime of the
materials. • Third block: *SOLID SECTION,MATERIAL=STEEL,ELSET=STE *MATERIAL,NAME=STEEL ^ELASTIC 30.E6,.3 *SOLIDSECTION,MATERIAL=COMPOS,ELSET=COM *MATERIAL,NAME=COMPOS ^ELASTIC 30.E4,.3
The fourth block is to impose the boundary conditions and the loading parameters. The command *BOUNDARY defines the constraints applied to the model based on a set of nodes. The constraints could be for displacement and rotation in any direction according to the three dimensional system of co-ordinates of the problem. The loading parameters start with the command *STEP which define a loading case. This problem uses only one loading case which is the internal pressure applied in the inner surface. The pressure used is 15,000 at the inner surface and zero at the outer surface. The command * STATIC defines a ramp to gradually build the load defined in the command *DLOAD.
• Fourth block: ^BOUNDARY SIDE,2 *STEP,NLGEOM,INC=50 *STATIC .1,1. *DLOAD IN N ER,P4,15000 OUTER,P2,0
The last block of commands is to define the output file. The finite element program ABAQUS allows several combinations of output. For this analysis, the output was prepared to output the radial and hoop stresses along the radius as well as the strain
in the centroidal position of each node.
• Fifth block:
*PRINT,RESIDUAL=NO *NODE PRINT
U
*EL PRINT,POSmON=NODES,SUM M ARY=NO S
*ELFILE,POSITION=CENTROIDAL,SUMMARY=NO S