ISSN: 0975-766X CODEN: IJPTFI Available Online through ...IJPT| Sep-2016 | Vol. 8 | Issue No.4 |...

Pavel V.Bol'shakov*et al. /International Journal of Pharmacy & Technology

IJPT| Dec-2016 | Vol. 8 | Issue No.4 | 24242-24251 Page 24242

ISSN: 0975-766X

CODEN: IJPTFI

Available Online through Research Article

www.ijptonline.com

EVALUATION OF THE STRENGTH OF ROTARY ORTHOPEDIC EXTERNAL

FIXATION DEVICE Pavel V.Bol'shakov

1, Ruslan F.Khasanov

2, Petr S. Andreyev

2, Aleksey D.Lustin

3, Oskar A. Sachenkov

1,3

1Kazan Federal University, 18, Kremlyovskaya St., Kazan, (420008) Russia.

2Republican clinical hospital, 138, Orenburg tract, Kazan, Russia.

3Kazan National Research Technical University, 10, K. Marksa st., Kazan, Russia.

Email: [email protected]

Received on 14-08-2016 Accepted on 20-09-2016

Abstract:

This paper presents the calculation results of the strength and stiffness of external fixation device used within the

framework of the concept of three-plane spatial correction of pathological orientation of the proximal femur subject

to the disease stage, localization of a degenerative-dystrophic process and its severity. We have created a three-

dimensional parametric model of the device and performed its finite element sampling with the use of quad-nodal

tetrahedral finite element with linear approximation and the quad-nodal hexagonal hub finite element with linear

approximation. We have determined the stress-strain state of the structure in a linear position based on the method of

finite elements for different turn values of a swivel bracket. We have also determined the stress localization areas and

dangerous zones of junctions of the threaded joints. We have calculated the values of maximum shear stress and

stress intensity for different states of the structure under the influence of elementary forces in different directions.

Based on these data, we have determined the directed maximum operating loads, which were 160 N and 7,000 Nm.

Structural plasticity envelope carries loads depending on their direction. The results obtained allowed us to evaluate

structural integrity upon exposure to the elementary forces, which will ensure a more detailed analysis of the

structure.

Keywords: Biomechanics, rotational osteotomy, external fixation device, strength.

Introduction

High incidence of the hip joint disease in children determines the medical and social significance of the problem.

Among the hip joint diseases in childhood, the Perthes disease was noted in 25-30% of cases.Treating the Perthes

disease in case of severe lesion of the pineal gland leads in 89.5% to the residual deformation of the femoral head and

the acetabulum, and the development of coxarthrosis. Objective of this research is to study and calculate the strength

IJPT| Sep-2016 | Vol. 8 | Issue No.4 | 24242-24251 4243

of the external fixation device used for medical rehabilitation of children and adolescents [1-4], As well as to

determine the stress-strain state of the external fixation device at different angles between the rotary and supporting

parts, and evaluate external force action on the structural strength. This paper describes an external fixation device

used within the framework of the concept of three-plane spatial correction of pathological orientation of the proximal

femur subject to the disease stage, localization of a degenerative-dystrophic process and its severity. As part of

treatment, an intertrochanteric femoral osteotomy is performed along the lower contour of the femoral neck, parallel

to its longitudinal axis, outwards. A bone wedge is resected from the distal fragment of the femur at an angle equal to

the difference between the neck-shaft angle (NSA) on both the affected and the healthy limb segments. The base of

the bone wedge is turned inward, performing a “slant” behind to the angle of an excessive femoral torsion (FT) with

respect to the first osteotomy so that when joining together the bone fragments there would be a complete correction

of the FT and NS angles [3, 4]. Two intraosseous rods are placed into the femoral neck [5, 6]. The rods are fixed in

the neck support, which is connected to the device applied on the thigh and the iliac bone in the FT and NS correction

position. The affected area is released from load by turning the neck support by gradual rotation of the femoral neck.

This method provides a correction of biomechanical angles of the proximal femur, prevention of the development of

the hip joint contracture after rotating the femoral neck, and stable fixation of the femur fragments in the adjusted

position [3, 4, 6, 7]. Loads arising in the joint after the performed osteotomy are primarily transferred to the external

fixing device, which should provide sufficient strength, otherwise, the action of muscle forces may lead to flexion

and reverse rotation in the joint followed by degradation in the quality of treatment, and even by dislocation [5, 8-10].

Methods: The external fixation device is a three-dimensional structure with the rods serving as the support and

interconnected with brackets and pins (see Fig. 1). Structurally, the device can be divided into two parts: rotating

(part L in Fig. 1) and supporting (part R in Fig. 1). The angle between these parts can be varied depending on the

disease localization and surgical approach. All structural components are interconnected by a threaded joint, which

reliability is subject to the basic requirements.

Fig. 1.Structural scheme of the external fixation device.a – side view, b – top view, с – view at rotation. 1 – rod,

2 – brackets, 3 – stud, 4 – supports.

IJPT| Sep-2016 | Vol. 8 | Issue No.4 | 24242-24251 Page 24244

Turning the bracket (2L in Fig. 1) at a certain angle results in shift in relation to the bracket (2R in Fig. 1) of one of

the studs (3 in Fig. 1) down, the second, respectively, raises up in relation to the same bracket, with simultaneous

rotation of the fasteners, which connect the bracket (2L in Fig. 1) and studs (3 in Fig. 1).

As part of the study, we have created a three-dimensional parametric model of the external fixation device to conduct

the rotational osteotomy [3, 5]. To build the model, we selected different locations between the rotating and

supporting parts, namely angles of 5, 10, 15 and 20, and applied forces to the structure: Pz=10 N, Px=10 N, Py=10

N and the moments: Mz=100Н∙mm , Mx=100 N∙mm, My=100 N∙mmto the center of the rods (1L in Fig. 1)(see Fig.

2). Rods (1R in Fig. 1) are rigidly fixed [8].

For these positions the finite element sampling was conducted: brackets (2L and 2R in Fig. 1) and rods (1 in Fig. 1)

were separated with 8-node hexagonal finite element, and the supports (4 in Fig. 1), rods (3 in Fig. 1) and fasteners

that connect the bracket (2L in Fig. 1) and studs (3 in Fig. 1) – with 4-node tetrahedral finite element [8, 9, 10-13].

Node-to-node couplings were applied on all the rods (1 in Fig. 1) connected with the supports (4 in Fig. 1), on the

studs (3 in Fig. 1) fixed to the bracket (2R in Fig. 1), and between the fasteners that connect the studs (3 in Fig. 1) and

the bracket (2L in Fig. 1).

Constructing conditions for the additional one-dimensional binding grid were used as a central connection between

rods (1L in Fig. 1) for the application of forces [11-13]. The coordinate system, to which the forces have been

applied, is at the point where the additional one-dimensional binding grid was plotted [14-17]. The Z axis goes along

the rods (1L in Fig. 1), the Y axis goes along the rod 3 from right to left (see Fig. 1), the X axis is perpendicular to the

OZ plane so as to create a right-sided triplet of vectors.

Maximum power was derived from the formula:

[ ]T

Max

Max

F F

(1.1)

whereF is force applied.

Results and discussions

These results were obtained for the external fixation device with the arrangement between a rotating and supporting

parts in 10.

The structure is made of steel 12Х18Н10Т, with mechanical characteristics:

, . ,[ ] ,[ ]T cpE GPa MPa MPa 200 0 3 600 140


Fig. 3. Mises stress.

а – Pzapplication, b – Pxapplication, c – Pyapplication, d– Mz application, e – Mx application, f – My

application

We can conclude from these calculations that the maximum Mises stress of the whole structure, at a rotation angle of

10, is caused by Pz and Px loads, and by Mz and Mx moments (see Fig. 3). It follows from the formula (1.1) that

maximum load Pz must be not more than 160 N, and Px – not more than 165 N. The stress will not exceed the yield

point at the moment Mz = 20,000 N∙mm, and at Mx = 18,600 N∙mm.

a

b

c

d

e

f


We shall consider the junction graphics of right and left mounting bolts, right and left fasteners with a stud at a load

Pz = 10 N, Px = 10 N, Py = 10 N, and the moment Mz = 100 N∙mm, Mx = 100 N∙mm, My = 100 N∙mm with respect to

angle variation.

Fig. 4. Diagram of the left bolt load-caused Mises stress (MPa)

Load Px causes maximum stress in the left bolt in the interval 5-20. Loads Pzand Pyat rotation angle of 5 and 20

result in approximately the same stress. However, load Py causes substantially greater stress at 10-15. Load Px is the

most “undesirable” for the left bolt in the entire interval, the greatest stress of 10.6 MPa occurs at an angle of

10.Minimum stress-strain state of 2.4 MPa occurs at an angle of 15 with Pz.

Fig. 5. Diagram of the right bolt load-caused Mises stress (MPa)

Among all loads, load Px causes maximum stress in the right bolt in the entire range. Maximum stress of 10.9 MPa

occurs at an angle of 10 between the rotating and supporting parts. Load Py causes stress equal to 4 N in the entire

range. While load Pz causes stress in the interval of 3.1-6.43 Ma. Minimum stress equal to 3.1 MPa occurs at 10 with

Pz.


Fig. 6. Diagram of the left bolt moment-caused Mises stress (MPa)

The most critical moment for the left bolt is My. It causes maximum Mises stress equal to 0.584 MPa at an angle of 5

and 15.The minimum stress equal to 0.125 MPa is caused by the moment Mz at 10. This moment also causes

minimum stress in the left bolt at any angles being considered in this study.

Fig. 7. Diagram of the right bolt moment-caused Mises stress (MPa)

Similar to the left bolt, the same loads cause maximum Mises stress of 0.701 MPa and minimum 0.06 MPa in the

right bolt in the entire range of intervals. Unlike the left bolt, the moment My causes stress-strain state of 0.7 MPa at

angles of 5 and 20.Minimum stress equal to 0.06 MPa occurs at an angle of 15 and moment Mz.

Analyzing the Figures 4-7, we can conclude that the largest contribution to the stress of the left and right mounting

bolts is caused by load Px and the moment My. It is also obvious that the left and right bolts experience a state of

maximum load stress at an angle between the rotating and supporting parts equal to 10.However, the same angle for

the moments will be 5. Almost in every interval, all minimum stresses were caused by loads in the OZ direction.


Fig. 8. Diagram of the load-caused Mises stress (MPa) in the junction of the left stud and the fastener

Load Px causes maximum stress at an angle of 20. When the angle between the supporting and rotating parts is 15,

each of three loads causes the same stress in the junction of the left stud and the fastener. Stress in the interval of 5-

15 at loads Pzand Pxoccurs with little difference. The minimum stress occurs at load Pz.

Fig. 9. Diagram of the load-caused Mises stress (MPa) in the junction of the right stud and the fastener

Analyzing the load-caused Mises stresses in the junction of the right stud and the fastener we can note that loads Px

and Py cause roughly the same stresses in the entire interval of 5-15 degrees. Load Pz causes maximum stress-strain

state of 14 MPa at 20. We can also note that the stress charts have two intersections, which is due to the fact that

each of the loads causes the same stress at these angles.

Fig. 10. Diagram of the moment-caused Mises stress (MPa) in the junction of the left stud and the

fastener


The most critical moment for the junction of the left stud and the fastener is Mx. It causes maximum Mises stress

equal to 1.058 MPa at an angle of 15.The minimum Mises stress equal to 0.141 MPa is caused by the moment Mz at

10. This moment also causes minimum stress in the left bolt at any angles being considered in this study.

Fig. 11. Diagram of the moment-caused Mises stress (MPa) in the junction of the right stud and the

fastener

Similar to the left junction, the same loads cause maximum and minimum Mises stresses in the junction of the right

stud and the fastener in the entire range of intervals. However, unlike the left junction, the moment Mx causes stress

equal to 1.1 MPa at an angle of 15.Minimum stress equal to 0.102 MPa occurs at an angle of 20 and moment Mz.

Considering the Figures 10-11 we can see that the maximum stress occurs at the moment Mx. A more interesting case

can be seen in Figures 8-9, as at different rotation angles the maximum stress depends on various loads. Having

analyzed the Figure 7, we loads Px and Py cause nearly the same stress at angles of 5 and 10, but when an angle is

15, each of three loads equally contributes to the maximum stress. Load Px causes maximum stress in the interval of

15-20.

Diagram of the load-caused Mises stress in the junction of the right stud and the fastener (see Fig. 8) shows similar

stress caused by loads Pxand Py at an angle of 10, while Pz causes maximum stress at angles of 5, 15, and 20.

Summary

For the external fixation device, we have performed assembly, finite element sampling and calculations at different

rotation angles of 5, 10, 15, and 20 degrees with the use of Siemens NX package. We have determined the loads

occurring at these positions that cause the maximum stress-strained state. It follows from the analysis that the

maximum stress at any rotation angle both in the right and left bolt occurs under the influence of OX-directed load


(Px) and the moment (My) about OY-axis. We have also noted that the most “undesirable" loads for stress-strain state

at an angle between the rotating and the supporting parts of 5-15 degrees in the stud-fastener junction are Px, Py, and a

moment Mx. While at an angle of 20 degrees, the maximum stress in the left junction occurs under the influence of

Px, and in the right – Pz. It follows from the formula (1.1) that maximum load Pz must be not more than 160 N, and Px

– not more than 165 N. The stress will not exceed the yield point at the moment Mz = 20,000 N∙mm, and at Mx =

18,600 N∙mm; the maximum shear stress occurs at the moment Mz, which must not exceed 8216.49 N∙mm, and My

must not exceed 7777.77 N∙mm.

Acknowledgements

The work is performed according to the Russian Government Program of Competitive Growth of Kazan Federal

University and the work was partially supported by the Russian Foundation for Basic Research within scientific

projects No. 14-01-31291, 15-31-20602.

References

1. Abalmasova E.A. Balaba T.Ia., Lavrishcheva G.I. Towards the etiology and pathogenesis of juvenile

epiphysiolysis // Current problems of traumatology and orthopedics. – M., 1981. – Vol 23. – Pp. 87-91. 2.Weiner

SD, Weiner DS, Riley PM. Pitfalls in treatment of Legg–Calve–Perthes disease using proximal femoral varus

osteotomy. J Pediatr Orthop. 1991;11:20–24.

3. Andreev P.S., Konoplev Iu.G., Sachenkov O.A., Khasanov R.F., Iashin I.V. Mathematical modeling of rotary

flexion osteotomy // Volga Region Scientific and Technical Journal. 2014. No. 5. Pp. 18-21.

4. Khasanov R.F., Andreev P.S., Skvortsov A.P., Sachenkov O.A., Iashina I.V. Biomechanical justification of

surgical treatment of Legg-Calve-Perthes disease // Practical Medicine. 2015. No. 4-1. Pp. 200-203.

5. Zaitseva T.A., Konoplev Iu.G., Mitriaikin V.I., Sachenkov O.A. Mathematical modeling of dislocation of the hip

joint implant // Bulletin of A.N. Tupolev Kazan State Technical University. 2013. No. 1. pp. 99-102.

6. Rublenyk I.M., Bilyk S.V., Shayko-Shaykovsky A.G. The Application of Metal and Polymer Fixing Systems for

Intramedullar Osteosynthesis // Russian Journal of Biomechanics, Volume 7, No. 1, 2003, Pp. 84-89.

7. Akulich Y.V., Akulich A.Y., Denisov A.S., Podgaets R.M. Adaptation Processes in the Bone Tissue of the

Femoral Neck After Its Osteosynthesis by Elastic Fixing Screws // Russian Journal of Biomechanics. - Volume

11, No. 3, 2007, Pp. 36-50.


8. Galiullin R.R., Sachenkov O.A., Khasanov R.F. and Andreev P.S. Evalution of external fixation device stiffness

for rotary osteotomy // International Journal of Applied Engineering Research Vol.10 No.24 Pp. 44855-44860

9. Shigapova F.A., Mustakimova R.F., Saleeva G.T. and Sachenkov O.A. Definition of the intense and deformable

jaw state ender the masseters hyper tone // International Journal of Applied Engineering Research Vol.10 No.24

Pp. 44711-44714

10. Konoplev Yu.G., Mazurenko A.V., Sachenkov O.A., Tikhilov R.M. Numerical study of the influence of the

degree of undercoverage of the acetabular component on the load-bearing capacity of hip joint endoprosthesis //

Russian Journal of Biomechanics. 2015. Vol. 19, No. 4: Pp. 283-295.

11. Sachenkov O.A., Mitryaikin V.I., Zaitseva T.A., Konoplev Yu.G. Implementation of Contact Interaction in a

Finite-Element Formulation // Applied Mathematical Sciences, Vol. 8, 2014, no. 159, 7889 - 7897.

http://dx.doi.org/10.12988/ams.2014.49769

12. A.I. Golovanov, L.U. Sultanov, Numerical investigation of large elastoplastic strains of three-dimensional

bodies, International Applied Mechanics, Vol. 41 (2005), 6, 614–620. doi: 10.1007/s10778-005-0129-x.

13. A.I.Golovanov, L.U.Sultanov, Postbucklingelastoplastic state analysis of three-dimensional bodies taking into

account finite strains, Russian Aeronautics, Vol. 51 (2008), 4, 362-368.doi: 10.3103/S106879980804003X

14. A.I. Golovanov, L.U. Sultanov, Numerical investigation of large elastoplastic strains of three-dimensional

bodies, PrikladnayaMekhanika, Vol. 41 (2005), 6, 36-43.

15. R.L. Davydov, L.U. Sultanov, Numerical algorithm of solving the problem of large elastic-plastic deformation

by fem, PNRPU Mechanics Bulletin, 1 (2013), 81-93.

16. L.U. Sultanov, R.L. Davydov Mathematical modeling of large elastic-plastic deformations, Applied

Mathematical Sciences, Vol. 8 (2014), 57-60, 2991-2996. doi: 10.12988/ams.2014.44272 ISSN: 13147552.

17. Berezhnoi D.V., Paimushin V.N. Two formulations of elastoplastic problems and the theoretical determination of

the location of neck formation in samples under tension // Journal of Applied Mathematics and Mechanics. 2011.

V. 75. № 4. P0. 447-462.

http://elibrary.ru/item.asp?id=18365353



http://elibrary.ru/contents.asp?issueid=1063412

http://elibrary.ru/contents.asp?issueid=1063412&selid=18365353

ISSN: 0975-766X CODEN: IJPTFI Available Online through ...IJPT| Sep-2016 | Vol. 8 | Issue No.4 |...

Documents

Transcript of ISSN: 0975-766X CODEN: IJPTFI Available Online through ...IJPT| Sep-2016 | Vol. 8 | Issue No.4 |...