Bolted joints are probably the most common jointing method in machine design over others like riveting, welding, interference fit and adhesives. Modeling bolt pretension is of importance in simulation driven design, for example to have a proper preload and residual preload on flanges to avoid leakage or to obtain the stress variation in bolt under external loads to estimate the fatigue life or to take account stress stiffening for modal properties, etc.
Calculix provides two ways of modeling bolt pretension. One is by linear beam element (type B31) and MPCs (Multiple Point Constraint), and no bolt geometry is needed.
*PRE-TENSION SECTION,ELEMENT=61000,NODE=60004
0,0,1
The other is by a surface, which is usually a cross section of the bolt, and for 3D bolts.
*PRE-TENSION SECTION,SURFACE=Spre_load2,NODE=49999
0,0,1
A vector, along which the pretension load is applied, can be defined underneath the *PRE-TENSION SECTION card. If the vector is specified away from the pretension surface (3D bolts) or in the direction going from node 1 to node 2 in the element definition (for the beam element), a positive force or positive displacements correspond to tension in the underlying structure.
Both approaches need a reference node. This node should not be used elsewhere in the model.The coordinates of this node are immaterial. The first degree of freedom of this node is used to define a pre-tension force with *CLOAD or a differential displacement with *BOUNDARY.
*CLOAD
49999,1,1.0e4
1.Pre-tension by a beam element
The beam element is shown in green in the following and can be specified with dimensions to represent bolt shank in beam section.
*ELEMENT,TYPE=B31,ELSET=Ebolt
61000,60000,60001
*BEAM SECTION,ELSET=Ebolt,MATERIAL=steel,SECTION=CIRC
16,16
The nodes of beam then connect to the nodes of structures (shown in magenta above) to be held together by linear equations or a *Distributing coupling card.
*ELEMENT,TYPE=DCOUP3D,ELSET=DC_nut
61001,60001
*DISTRIBUTING COUPLING,ELSET=DC_nut
nut_edge,1
*ELEMENT,TYPE=DCOUP3D,ELSET=DC_head
61002,60000
*DISTRIBUTING COUPLING,ELSET=DC_head
head_edge,1
2.Pre-tension by a surface
The surface is usually the cross section of the bolt and must be defined by element faces, it cannot be defined by nodes. It is a bit tricky. The bolt could be partitioned by a plane as shown in below, which means that the lower and upper part of bolt are connected by a number of sharing element faces, of which the parameter surface required in *pre-tension section card can be composed by *surface card
*SURFACE, name=Sname
<element>, <face label>
Max. 1 entry of element and corresponding face label per line, therefore, it is not practical to input manually. And it can’t be done by comp set do and send command to generate face becasue CGX can’t deal with internal faces (becasue of this is an internal face, the free bounary faces can be done by this, e.g. the magenta face for contact pairs).
However, it could be done by writing a subset of elements of bolt,e.g. lower part, with the
send command to the filesystem (send set frd c)and open this file again in a second cgx session. There the desired set of faces can be added (qadd set t1) and export them in the usual way (send set abq sur).
The contact pairs between bolt and bracket can be bonded (
*TIE) or other type of surface behavior, which is not the scope of this article.
Finally, we can check the results by two approaches, the following shows the result of pretension by beam element, whereas the picture at the beginning of this artical shows the result of pretension by 3D bolt.
Thank you for your attention.
