Thick-walled cylinders exposed to high, static internal pressures may experience both elastic and plastic deformation. Primary design considerations include loads, geometry and material properties. However, variations in geometry and material properties due to conventional manufacturing processes, and variations of internal pressure due to actual usage patterns, propagate through the system resulting in off-design stresses and strains which may cause failure. These variations can be evaluated using probabilistic methods which are discussed in this paper. Von Mises-distortion energy yield theory is presented to predict elastic, plastic and residual stresses in thick-walled cylinders. The design variation simulation method using Monte Carlo simulation and available statistical information is used to design a pressure vessel for servo-hydraulic experiments. The use of autofrettage to induce favorable compressive stresses at the inner bore, thereby improving the margin of safety and overall reliability, is also presented.

1.
Balling, R. J., Free, J. C., and Parkinson, A. R., 1986, “Consideration of Worst-Case Manufacturing Tolerances in Design Optimization,” ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN, Vol. 108, No. 4, Dec.
2.
Crawford
R.
, and
Rao
S. S.
,
1987
, “
Reliability Analysis of Function Generating Mechanisms Through Monte Carlo Simulation
,”
ASME Advances in Design Automation
, Vol.
2
, pp.
197
202
.
3.
Doepker, P. E., and Nies, D., 1989, “Designing Brake Components using Variation Simulation Modelling,” Failure and Reliability 1989, ASME, DE-Vol. 16, pp. 131–138, Montreal, Canada.
4.
Early, R., and Thompson, J., 1989, “Variation Simulation Modelling-Variation Analysis using Monte Carlo Simulation,” Failure and Reliability 1989, ASME, DE-Vol. 16, pp. 139–144, Montreal, Canada.
5.
Eggert
R. J.
,
1992
, “
Robust Fatigue Design for Combined Bending and Steady Torsion
,”
ASME Advances in Design Automation
, Vol.
2
, pp.
335
342
.
6.
Eggert
R. J.
,
1991
, “
Quantifying Design Feasibility Using Probabilistic Feasibility Analysis
,”
ASME Advances in Design Automation
, Vol.
1
, pp.
235
239
.
7.
Eggert, R. J., and Mayne, R. W., 1990, “Probabilistic Optimal Design using Successive Probability Density Functions,” Proceedings of the 16th ASME Design Automation Conference, Vol. DE-Vol. 23-1, pp. 129–136, Chicago, IL, September.
8.
Eggert, R. J., 1989, “Probabilistic Optimization Using Successive Surrogate Probability Density Functions,” Ph.D. Dissertation, Department of Mechanical & Aerospace Engineering, State University of New York at Buffalo.
9.
Faupel, J. H., and Fisher, F. E., 1981, Engineering Design: A Synthesis of Stress Analysis and Materials Engineering, 2nd ed., John Wiley & Sons, New York, pp. 234–236, 444–452, 743–753, 790–794.
10.
Haugen, E. B., 1980, Probabilistic Mechanical Design, Wiley, New York.
11.
Kapur, K. C., and Lamberson, L. R., 1977, Reliability in Engineering Design, John Wiley & Sons.
12.
Mischke, C. R., 1989a, “Stochastic Methods in Mechanical Design: Part 1: Property Data and Weibull Parameters,” Failure and Reliability 1989, ASME, DE-Vol. 16, pp. 1–10, Montreal, Quebec, Canada.
13.
Mischke, C. R., 1989b, “Stochastic Methods in Mechanical Design: Part 2: Fitting the Weibull Distribution to the Data,” Failure and Reliability 1989, ASME, DE-Vol. 16, pp. 11–15, Montreal, Quebec, Canada.
14.
Mischke, C. R., 1989c, “Stochastic Methods in Mechanical Design: Part 3: A Methodology,” Failure and Reliability 1989, ASME, DE-Vol. 16, pp. 17–20, Montreal, Quebec, Canada.
15.
Mischke, C. R., 1989d, “Stochastic Methods in Mechanical Design: Part 4: Applications,” Failure and Reliability 1989, ASME, DE-Vol. 16, pp. 21–28, Montreal, Quebec, Canada.
16.
Mischke, C. R., 1987, “Prediction of Stochastic Endurance Strength,” ASME Paper No. 86-WA/DE-10, pp. 1–10.
17.
Mischke, C. R., 1986, “Some Guidance of Relating Factor of Safety to Risk of Failure,” ASME Paper No. 86-WA/DE-22, pp. 1–10.
18.
Mischke, C. R., 1980, Mathematical Model Building, 2nd. Rev. Ed., Iowa State University Press, Ames.
19.
Mischke
C. R.
,
1970
, “
A Method of Relating Factor of Safety and Reliability
,”
ASME Journal of Engineering for Industry
, Vol.
92
, pp.
537
542
.
20.
Parkinson, A., Pourhassan, N., and Sorenson, C., 1991, “Tolerances and Robustness in Engineering Design Optimization: Further Results,” Design Productivity International Conf., Hawaii, pp. 1–15.
21.
Rao, S. S., 1992, Reliability in Design, McGraw-Hill, Inc., New York.
22.
Rao
S. S.
,
1986
a, “
Automated Optimum Design of Wing Structures: A Probabilistic Approach
,”
Computers and Structures
, Vol.
24
, No.
5
, 1986, pp.
799
808
.
23.
Rao
S. S.
, and
Eslampour
H. R.
,
1986
b, “
Multistage Multiobjective Optimization of Gearboxes
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
108
, Dec., pp.
461
468
.
24.
Rao
S. S.
,
1985
, “
Optimization of Airplane Wing Structures Under Gust Loads
,”
Computers and Structures
, Vol.
21
, pp.
741
749
.
25.
Rao
S. S.
,
1984
a, “
Optimization of Airplane Wing Structures Under Landing Loads
,”
Computers and Structures
, Vol.
19
, pp.
849
863
.
26.
Rao
S. S.
,
1984
b, “
Multiobjective Optimization in Structural Design With Uncertain Parameters and Stochastic Processes
,”
AIAA Journal
, Vol.
22
, pp.
1670
1678
.
27.
Rao
S. S.
, and
Das
G.
,
1984
c, “
Reliability Based Optimum Design Gear Trains
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
106
, pp.
17
22
.
28.
Rao
S. S.
,
1981
, “
Reliability-Based Optimization Under Random Vibration Environment
,”
Computers and Structures
, Vol.
14
, pp.
345
355
.
29.
Rao
S. S.
,
1979
, “
Reliability Analysis and Design of Epicyclic Gear Trains
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
101
, Oct., pp.
625
632
.
30.
Rao
S. S.
, and
Hati
S. K.
,
1979
, “
Game Theory Approach in Multicriteria Optimization of Function Generating Mechanisms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
101
, pp.
398
406
.
31.
Rao, S. S., 1978, Optimization: Theory and Applications, Wiley.
32.
Rao
S. S.
, and
Reddy
C. P.
,
1977
, “
Reliability Analysis of Machine Tool Structures
,”
ASME Journal of Engineering for Industry
, Vol.
99
, Nov., pp.
882
888
.
1.
Rao
S. S.
,
1974
, “
A Probabilistic Approach to the Design of Gear Trains
,”
International Journal of Machine and Tool Design Research
, Vol.
14
, pp.
267
278
.
2.
Engineering for Industry
, Vol.
99
, Nov., pp.
882
888
.
1.
Shah, A. R., and Chamis, A. C., 1991, “Simulation of Probabilistic Wind Loads and Building Analysis,” Reliability, Stress Analysis and Failure Prevention, DE-Vol. 30, pp. 5–14, Miami, FL.
2.
Shigley, J. E., and Mischke, C. R., 1989, Mechanical Engineering Design, McGraw-Hill, 5th Ed.
3.
Siddall
J. N.
,
1986
, “
Probabilistic Modeling Design
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
108
, pp.
330
335
.
4.
Siddall
J. N.
,
1984
, “
A New Approach to Probability in Engineering Design and Optimization
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
106
, pp.
5
10
.
5.
Siddall, J. N., 1983, Probabilistic Engineering Design: Principles and Applications, Marcel Dekker, Inc., New York.
6.
Smith
C. O.
,
1984
, “
Probabilistic Design Criteria for Cylinders & Spheres under Thermal Stresses
,”
ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design
, Vol.
106
, Oct., pp.
523
528
.
7.
Smith
C. O.
,
1980
, “
Design of Ellipsoidal and Toroidal Pressure Vessels to Probabilistic Criteria
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
102
, Oct., pp.
787
792
.
8.
Teng, A., 1992, “Robust Optimal Design for Dynamic and Feedback Control Systems,” Ph.D. Dissertation, Brigham Young University, Provo, UT.
9.
Thacker, B. H., Harren, S. V., and Millwater, H. R., 1991, “Combined Stress and Resistance Modelling with the Nessus Software System,” Reliability, Stress Analysis and Failure Prevention, ASME, DE-Vol. 30, pp. 49–54, Miami, FL.
10.
Weber, M. A., and Penny, R. K., 1991, “Probabilistic Stress Analysis Methods,” Reliability, Stress Analysis and Failure Prevention, ASME, DE-Vol. 30, pp. 21–28, Miami, FL.
11.
Zibdeh, H. S., 1990, “Reliability of Thermally Loaded Cylinders,”
This content is only available via PDF.
You do not currently have access to this content.