DESCRIPCIÓN DE LAS VARIABLES

Pressure profiles

To obtain values o f norm al pressure along the lim b/socket interface, a FORTRA N p ro g ram w as w ritten w hich p ro cessed the calcu la ted in terface reaction s. The com ponents o f the reactions, in a direction norm al to elem ent side, w ere found and sum m ed for each elem ent. Reactions at the com er nodes were shared between adjacent elem ents according to the ratio o f their side lengths. The area o f the elem ent face was the area around the side o f a frustrum for the conical part o f the m odel and the surface area o f a segm ent o f 2 bases at the distal end. Interface pressure was calculated as the total normal load divided by the face area.

(b)

F ig u r e 6 .3 - N o r m a l p r e s s u r e p r o f ile s fo r e n d b e a r in g m o d e ls .

(a) m o d e l 'A '

Chapter 6 - M odels o f idealised lim bs 129

F or a m eaningful com parison between models, pressure distributions w ere prepared for the case w here approxim ately h alf the body w eight o f the am putee subject is supported. An iterative process was used w here the bone displacem ent w as adjusted until a 350N vertical reaction (i.e. ju st over 5 stone, 70 lbs.) w as produced.

Figures 6.3 and 6.4 represent norm al pressure distributions under this applied load w ith and w ithout end bearing respectively. Both interface conditions are shown. In these figures, the shaded region describes the profile o f norm al pressure calculated at the interface with the socket wall. The boundary o f this region has been defined by a series o f vectors norm al to the surface o f the elastic layer at the m idside o f each elem ent. Each 1 mm length o f the vectors represents a pressure o f approxim ately 3.6 kPa. i (a) (b) F ig u r e 6 .4 - N o r m a l p r e s s u r e p r o f ile s fo r n o n -e n d b e a r in g m o d e ls. (a) m o d e l 'C ' ('t o t a lly r o u g h '). (b ) m o d e l 'D ' ( 'f r ic t io n le s s ') . Shear profiles

Shear forces at the interface in the 'totally rough' m odels were calculated by another FORTRA N program which took the com ponents o f reactions parallel to the surface of

Chapter 6 - Models o f idealised limbs 130

the socket wall. The distributions of shear force per unit area at the interface are shown in figure 6.5 for models 'A' and 'C'. Each 1 mm of normal displacement of the profile from the limb surface represents a magnitude of approximately 2.7 N mm-2 in these diagrams.

k

(b)

Figure 6.5 - Shear profiles.

(a) model 'A' (distal end-bearing). (b) model 'C' (no end-bearing).

A difference in the direction of shearing action is shown by the change of hatching in the diagram for the end-bearing model.

Chapter 6 - Models o f idealised limbs 131

A summary of the vertical stiffnesses the four linear models appears in figure 6.6

Interface conditions: Totally rough Frictionless

£nd-bearing 330 164

Non end-bearing 257 50

Figure 6.6 - Vertical stiffnesses calculated for models 'A' to ’D*. (units are N mm**)

6.2 Effect of limb shape.

To demonstrate how the general shape of the residual limb may influence the interface loading pattern, the 'average' geometry of the previous section was adjusted. A 'fleshy' residual limb shape was created in which the thickness of the tissue layer was doubled everywhere. For a 'bony' limb shape the thickness was halved. The external shape of the 'fleshy' limb was less tapered than the 'average' one. Taper angles, i.e. the angles of inclination to the vertical of the sides of the limb, were 5.3° and 8.6° respectively. For the 'bony' limb the taper angle was 11.6°. It is generally the case that 'fleshy' residual limbs are more cylindrical in shape with a flatter distal end and bony limbs are more tapered with a more pointed distal end.

In each of the models, the bone structure was as shown previously barring the inclusion of a recess at the knee joint. This was a closer approximation to the X-ray views. Six models were used which calculated interface loads for the 'average', 'fleshy' and 'bony' limbs under both interface conditions. In all models, there was no distal end bearing.

The continuity of stresses around the point where the socket and limb came into contact was checked to evaluate trial meshes as well as the behaviour of individual reactions. Triangular isoparametric elements were incorporated to cope with the 'undesirable' geometry of the knee-joint recess. Final meshes for each limb geometry appear in the diagrams (a) of figures 6.7, 6.8 and 6.9.

Normal pressure profiles were produced for each geometry, under 'totally rough’ and 'frictionless' conditions, from iterative runs using 10 increments of displacement.