JOURNAL ARTICLES

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1. Rahman, S., "Probabilistic Frequency Response Analysis of Linear Dynamical Systems by Spline Chaos Expansion," submitted, 2022.
2. Rahman, S., "Global Sensitivity Analysis by a Generalized Polynomial Dimensional Decomposition," submitted, 2022.
3. Rahman, S., "Higher-order Moments of Spline Chaos Expansion," Probabilistic Engineering Mechanics, Vol. 77, 2024, Article 103666, pp. 1-15.
4. Lee, D. and Rahman, S., "High-Dimensional Stochastic Design Optimization under Dependent Random Variables by a Dimensionally Decomposed Generalized Polynomial Chaos Expansion," International Journal for Uncertainty Quantification, Vol. 13, 2023, pp. 23-59.
5. Jahanbin, R. and Rahman, S., "Stochastic Isogeometric Analysis on Arbitrary Multipatch Domains by Spline Dimensional Decomposition," Computer Methods in Applied Mechanics and Engineering, Vol. 393, 2022, Article 114813, pp. 1-36.
6. Rahman, S. and Jahanbin, R., "A Spline Dimensional Decomposition for Uncertainty Quantification in High Dimensions," SIAM/ASA Journal on Uncertainty Quantification, Vol. 10, 2022, pp. 404-438.
7. Lee, D., Jahanbin, R., and Rahman, S., "Robust Design Optimization by Spline Dimensional Decomposition," Probabilistic Engineering Mechanics, Vol. 68, Article 103218, pp. 1-27., 2022
8. Lee, D. and Rahman, S., "Reliability-based Design Optimization under Dependent Random Variables by a Generalized Polynomial Chaos Expansion," Structural and Multidisciplinary Optimization , Vol. 65, Article 21, pp. 1-29, 2022
9. Rahman, S. and Jahanbin, R., "Orthogonal Spline Expansions for Uncertainty Quantification in Linear Dynamical Systems," Journal of Sound and Vibration, Vol. 512, Article 116366, pp. 1-25, 2021.
10. Dixler, S., Jahanbin, R. and Rahman, S., "Uncertainty Quantification by Optimal Spline Dimensional Decomposition," International Journal for Numerical Methods in Engineering, Vol. 122, pp. 5898-5934, 2021.
11. Jahanbin, R. and Rahman, S., "Isogeometric Methods for Karhunen-Loeve Representation of Random Fields on Arbitrary Multi-patch Domains," International Journal for Uncertainty Quantification, Vol. 11, pp. 27-57, 2021.
12. Lee, D. and Rahman, S., "Robust Design Optimization under Dependent Random Variables by a Generalized Polynomial Chaos Expansion," Structural and Multidisciplinary Optimization , 2021.
13. Lee, D. and Rahman, S., "Practical Uncertainty Quantification Analysis Involving Statistically Dependent Random Variables," Applied Mathematical Modelling, Vol. 84, 2020, pp. 324-356.
14. Jahanbin, R. and Rahman, S., "Stochastic Isogeometric Analysis in Linear Elasticity," Computer Methods in Applied Mechanics and Engineering, Vol. 364, Article 112928, 2020, pp. 1-38.
15. Rahman, S., "A Spline Chaos Expansion," SIAM/ASA Journal on Uncertainty Quantification, Vol. 8, 2020, pp. 27-57.
16. Rahman, S., "Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces," Applied Mathematics and Computation, Vol. 362, Article 124538, 2019, pp. 1-19.
17. Rahman, S., "Uncertainty Quantification under Dependent Random Variables by a Generalized Polynomial Dimensional Decomposition," Computer Methods in Applied Mechanics and Engineerings, Vol. 344, 2019, pp. 910-937.
18. Jahanbin, R. and Rahman, S., "An Isogeometric Collocation Method for Efficient Random Field Discretization," International Journal for Numerical Methods in Engineering, Vol. 117, 2019, pp. 344-369.
19. Ren, X. and Rahman, S., "Stochastic Design Optimization Accounting for Structural and Distributional Design Variables," Engineering Computations, Vol. 35, No. 8, 2018, pp. 2654-2695.
20. Rahman, S., "Mathematical Properties of Polynomial Dimensional Decomposition," SIAM/ASA Journal on Uncertainty Quantification , Vol. 6, 2018, pp. 816-844.
21. Rahman, S., "A Galerkin Isogeometric Method for Karhunen-Loeve Approximation of Random Fields," Computer Methods in Applied Mechanics and Engineerings, Vol. 338, 2018, pp. 533-561.
22. Rahman, S., "A Polynomial Chaos Expansion in Dependent Random Variables," Journal of Mathematical Analysis and Applications, Vol. 464, 2018, pp. 749-775.
23. Rahman, S., "Wiener-Hermite Polynomial Expansion for Multivariate Gaussian Probability Measures," Journal of Mathematical Analysis and Applications, Vol. 454, 2017, pp. 303-334.
24. Rahman, S., "A Surrogate Method for Density-based Global Sensitivity Analysis," Reliability Engineering & System Safety, Vol. 155, 2016, pp. 224-235.
25. Rahman, S., "The f-Sensitivity Index," SIAM/ASA Journal on Uncertainty Quantification , Vol. 4, 2016, pp. 130-162.
26. Ren, X., Yadav, V., and Rahman, S., "Reliability-based Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition," Structural and Multidisciplinary Optimization, Vol. 53, No. 3, 2016, pp. 425-452.
27. Rahman, S., "A Generalized ANOVA Dimensional Decomposition for Dependent Probability Measures," SIAM/ASA Journal on Uncertainty Quantification , Vol. 2, 2014, pp. 670-697.
28. Yadav, V. and Rahman, S., "A Hybrid Polynomial Dimensional Decomposition for Uncertainty Quantification of High-Dimensional Complex Systems," Probabilistic Engineering Mechanics , Vol. 38, 2014, pp. 22-34.
29. Rahman, S., and Ren, X., "Novel Computational Methods for High-Dimensional Stochastic Sensitivity Analysis," International Journal for Numerical Methods in Engineering, Vol. 98, 2014, pp. 881–916.
30. Rahman, S., "Approximation Errors in Truncated Dimensional Decompositions," Mathematics of Computation, Vol. 83, No. 290, 2014, pp. 2799-2819.
31. Yadav, V. and Rahman, S., "Adaptive-Sparse Polynomial Dimensional Decomposition for High-Dimensional Stochastic Computing," Computer Methods in Applied Mechanics and Engineering, Vol. 274, 2014, pp. 56-83.
32. Rahman, S., "Uncertainty Quantification by Alternative Decompositions of Multivariate Functions," SIAM Journal on Scientific Computing, Vol. 35, 2013, pp. A3024-A3051.
33. Ren, X. and Rahman, S., "Robust Design Optimization by Polynomial Dimensional Decomposition," Structural and Multidisciplinary Optimization, Vol. 48, No. 1, 2013, pp. 127-148.
34. Yadav, V. and Rahman, S., "Uncertainty Quantification of High-Dimensional Complex Systems by Multiplicative Polynomial Dimensional Decompositions," International Journal for Numerical Methods in Engineering, Vol. 94, 2013, pp. 221-247.
35. Rahman, S., "Global Sensitivity Analysis by Polynomial Dimensional Decomposition," Reliability Engineering & System Safety, Vol. 96, No. 7, 2011, pp. 825-837.
36. Rahman, S. and Yadav, V., "Orthogonal Polynomial Expansions for Solving Random Eigenvalue Problems," International Journal for Uncertainty Quantification , Vol. 1, No. 2, 2011, pp. 163-187.
37. Rahman, S., "Decomposition Methods for Structural Reliability Analysis Revisited," Probabilistic Engineering Mechanics, Vol. 26, 2011, pp. 357-363.
38. Rahman, S. and Chakraborty, A., "Stochastic Multiscale Fracture Analysis of Three-dimensional Functionally Graded Composites," Engineering Fracture Mechanics, Vol. 78, No. 1, 2011, pp. 27-46.
39. Rahman, S. and Xu. H., "Comments on High-dimensional Model Representation for Structural Reliability Analysis," International Journal for Numerical Methods in Biomedical Engineering, Vol. 27, 2011, pp. 1652-1659.
40. Wei, D. and Rahman, S., "A Multi-Point Univariate Decomposition Method for Structural Reliability Analysis," International Journal of Pressure Vessels and Piping, Vol. 87, 2010, pp. 220-229.
41. Rahman, S., "Statistical Moments of Polynomial Dimensional Decomposition," Journal of Engineering Mechanics , Vol. 136, No. 7, 2010, pp. 923-927.
42. Rahman, S., "Extended Polynomial Dimensional Decomposition for Arbitrary Probability Distributions," Journal of Engineering Mechanics , Vol. 135, No. 12, 2009, pp. 1439-1451.
43. Rahman, S., "A New Computational Method for Probabilistic Elastic-Plastic Fracture Analysis," Journal of Pressure Vessels Technology , Vol. 131, 2009, pp. 061402-1-061402-8.
44. Rahman, S., "Multiscale Fracture of Random Heterogeneous Materials," Ships and Offshore Structures , Vol. 4, No. 3, 2009, pp. 261-274.
45. Chakraborty, A. and Rahman, S., "Probabilistic Multiscale Fracture of Functionally Graded Materials by a Moment-Modified Polynomial Dimensional Decomposition Method," International Journal of Engineering Under Uncertainty: Hazards, Assessment and Mitigation, Vol. 1, 2009, pp. 111-125.
46. Rahman, S., "Probability Distributions of Natural Frequencies of Uncertain Dynamic Systems," AIAA Journal, Vol. 47, No. 6, 2009, pp. 1579-1589.
47. Chakraborty, A. and Rahman, S., "A Parametric Study on Probabilistic Fracture of Functionally Graded Composites by a Concurrent Multiscale Method," Probabilistic Engineering Mechanics, Vol. 24, 2009, pp. 438-451.
48. Rahman, S., "Stochastic Sensitivity Analysis by Dimensional Decomposition and Score Functions," Probabilistic Engineering Mechanics , Vol. 24, 2009, pp. 278-287.
49. Rahman, S., "A Polynomial Dimensional Decomposition for Stochastic Computing," International Journal for Numerical Methods in Engineering, Vol. 76, 2008, pp. 2091-2116.
50. Rahman, S., "A Random Field Model for Generating Synthetic Microstructures of Functionally Graded Materials," International Journal for Numerical Methods in Engineering, Vol. 76, 2008, pp. 972-993.
51. Chakraborty, A. and Rahman, S., "Stochastic Multiscale Models for Fracture Analysis of Functionally Graded Materials," Engineering Fracture Mechanics, Vol. 75, 2008, pp. 2062-2086.
52. Rahman, S. and Wei D., "Design Sensitivity and Reliability-Based Structural Optimization by Univariate Decomposition," Structural and Multidisciplinary Optimization, Vol. 35, 2008, pp. 245-261.
53. Rahman, S., "Stochastic Dynamic Systems with Complex-Valued Eigensolutions," International Journal for Numerical Methods in Engineering, Vol. 71, 2007, pp. 963-986.
54. Zhang, T., Rahman, S., Choi, K. K., Cho, K., Baker, P., Shakil, M., and Heitkamp, D., "A Global-Local Approach for Mechanical Deformation and Fatigue Durability of Microelectronic Packaging Systems," ASME Journal of Electronic Packaging, Vol. 129, 2007, pp. 179-189.
55. Rahman, S. and Chakraborty, A., "A Stochastic Micromechanical Model for Elastic Properties of Functionally Graded Materials," Mechanics of Materials, Vol. 39, 2007, pp. 548-563.
56. Wei, D. and Rahman, S., "Structural Reliability Analysis by Univariate Decomposition and Numerical Integration," Probabilistic Engineering Mechanics, Vol. 22, 2007, pp. 27-38.
57. Zhang, T., Choi, K. K., Rahman, S., Cho, K., Baker, P., Shakil, M., and Heitkamp, D., "A Hybrid Surrogate and Pattern Search Optimization Method and Applications to Microelectronics," Structural and Multidisciplinary Optimization, Vol. 32, 2006, pp. 327-345.
58. Rahman, S., "A Dimensional Decomposition Method for Stochastic Fracture Mechanics," Engineering Fracture Mechanics, Vol. 73, 2006, pp. 2093-2109.
59. Rahman, S. and Rao, B. N., "A Mode Decoupling Continuum Shape Sensitivity Method for Fracture Analysis of Functionally Graded Materials," Computer Methods in Applied Mechanics and Engineering, Vol. 195, 2006, pp. 5962-5982.
60. Rahman, S., "A Solution of the Random Eigenvalue Problem by a Dimensional Decomposition Method," International Journal for Numerical Methods in Engineering, Vol. 67, 2006, pp. 1318-1340.
61. Rao, B. N. and Rahman, S., "A Continuum Shape Sensitivity Method for Fracture Analysis of Isotropic Functionally Graded Materials," Computational Mechanics, Vol. 38, 2006, pp. 133-150.
62. Rahman, S. and Wei, D., "A Univariate Approximation at Most Probable Point for Higher-Order Reliability Analysis," International Journal of Solids and Structures, Vol. 43, 2006, pp. 2820-2839.
63. Xu, H. and Rahman, S., "Decomposition Methods for Structural Reliability Analysis," Probabilistic Engineering Mechanics, Vol. 20, 2005, pp. 239-250.
64. Rao, B. N. and Rahman, S., "A Continuum Shape Sensitivity Method for Fracture Analysis of Orthotropic Functionally Graded Materials," Mechanics of Materials, Vol. 37, No. 10, 2005, pp. 1007-1025.
65. Rao, B. N. and Rahman, S., "Continuum Shape Sensitivity Analysis of a Mixed-Mode Fracture in Functionally Graded Materials," Computer Methods in Applied Mechanics and Engineering, Vol. 194, 2005, pp. 1913-1946.
66. Rahman, S. and Chen, G., "Continuum Shape Sensitivity and Reliability Analyses of Nonlinear Cracked Structures," International Journal of Fracture, Vol. 131, 2005, pp. 189-209.
67. Rahman, S. and Xu, H., "A Meshless Method for Computational Stochastic Mechanics," International Journal of Computational Methods in Engineering Science and Mechanics, Vol. 64, 2005, pp. 41-58.
68. Rahman, S. and Rao, B. N., "Continuum Shape Sensitivity Analysis of a Mode-I Fracture in Functionally Graded Materials," Computational Mechanics, Vol. 36, No. 1, 2005, pp. 62-75.
69. Xu, H. and Rahman, S., "A Generalized Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics," International Journal for Numerical Methods in Engineering, Vol. 61, 2004, pp. 1992-2019.
70. Rahman, S. and Xu, H., "A Univariate Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics," Probabilistic Engineering Mechanics, Vol. 19, 2004, pp. 393-408.
71. Rao, B.N. and Rahman, S., "An Enriched Meshless Method for Nonlinear Fracture Mechanics," International Journal for Numerical Methods in Engineering, Vol. 59, 2004, pp. 197-223.
72. Rao, B.N. and Rahman, S., "Stochastic Meshless Analysis of Elastic-Plastic Cracked Structures," Computational Mechanics, Vol. 32, No. 3, 2003, pp. 199-223.
73. Rao, B. N. and Rahman, S., "An Interaction Integral Method for Analysis of Cracks in Orthotropic Functionally Graded Materials," Computational Mechanics, Vol. 32, No. 1-2, 2003, pp. 40-51.
74. Rao, B. N. and Rahman, S., "Meshfree Analysis of Cracks in Isotropic Functionally Graded Materials," Engineering Fracture Mechanics , Vol. 70, No. 1, 2003, pp. 1-27.
75. Chen, G., Rahman, S., and Y. H. Park, "Shape Sensitivity Analysis of Linear-Elastic Cracked Structures," ASME Journal of Pressure Vessel Technology, Vol. 124, No. 4, 2002, pp. 476-482.
76. Rao, B. N. and S. Rahman, "Probabilistic Fracture Mechanics by Galerkin Meshless Methods - Part I: Rates of Stress-Intensity Factors," Computational Mechanics, Vol. 28, No. 5, 2002, pp. 351-364.
77. Rahman, S. and Rao, B. N., "Probabilistic Fracture Mechanics by Galerkin Meshless Methods - Part II: Reliability Analysis," Computational Mechanics, Vol. 28, No. 5, 2002, pp. 365-374.
78. Chen, G., Rahman, S., and Y. H. Park, "Shape Sensitivity and Reliability Analyses of Linear-Elastic Cracked Structures," International Journal of Fracture, Vol. 112, No. 3, 2001, pp. 223-246.
79. Rahman, S. and Rao, B. N., "An Element-Free Galerkin Method for Probabilistic Mechanics and Reliability," International Journal of Solids and Structures, Vol. 38, No. 50-51, 2001, pp. 9313-9330.
80. Rao, B. N. and Rahman, S., "A Coupled Meshless-Finite Element Method for Fracture Analysis of Cracks," International Journal of Pressure Vessels and Piping , Vol. 78, No. 9, 2001, pp. 647-657.
81. Rahman, S. and Kim, J. S., "Probabilistic Fracture Mechanics for Nonlinear Structures," International Journal of Pressure Vessels and Piping, Vol. 78, No. 4, 2001, pp. 261-269.
82. Chen, G., Rahman, S. and Park, Y. H., "Shape Sensitivity Analysis in Mixed-Mode Fracture Mechanics," Computational Mechanics, Vol. 27, No. 4, 2001, pp. 282-291.
83. Rahman, S. and Rao, B. N., "A Perturbation Method for Stochastic Meshless Analysis in Elastostatics," International Journal for Numerical Methods in Engineering, Vol. 50, No. 8, 2001, pp. 1969-1991.
84. Rahman, S., "Probabilistic Fracture Mechanics: J-estimation and Finite Element Methods," Engineering Fracture Mechanics, Vol. 68, 2001, pp. 107-125.
85. Rao, B. N. and Rahman, S., "An Efficient Meshless Method for Fracture Analysis of Cracks," Computational Mechanics, Vol. 26, 2000, pp. 398-408.
86. Rahman, S. and Chen. G., "Constraint Effects on Probabilistic Analysis of Cracks in Ductile Solids," Fatigue & Fracture in Engineering Materials & Structures, Vol. 23, No. 10, 2000, pp. 879-890.
87. Firmature, R. and Rahman, S., "Elastic-Plastic Analysis of Off-Center Cracks in Cylindrical Structures," Engineering Fracture Mechanics, Vol. 66, No. 1, 2000, pp. 15-39.
88. Francis, M. and Rahman, S., "Probabilistic Analysis of Weld Cracks in Center-Cracked Tension Specimens," Computers & Structures, Vol. 76, No. 4, 2000, pp. 483-506.
89. Rahman, S., Chen, G., and Firmature, R., "Probabilistic Analysis of Off-Center Cracks in Cylindrical Structures," International Journal of Pressure Vessels and Piping, Vol. 77, No. 1, 2000, pp. 3-16.
90. Rahman, S., "Probabilistic Elastic-Plastic Fracture Analysis of Circumferentially Cracked Pipes with Finite-Length Surface Flaws," Nuclear Engineering and Design, Vol. 195, No. 3, 2000, pp. 239-260.
91. Foxen, J. and Rahman, S., "Elastic-Plastic Analysis of Small Cracks in Tubes under Internal Pressure and Bending," Nuclear Engineering and Design, Vol. 197, No. 1-2, 2000, pp. 75-87.
92. Rahman, S. and Wilkowski, G., "Net-Section-Collapse Analysis of Circumferentially Cracked Cylinders - Part I: Arbitrary-Shaped Cracks and Generalized Equations," Engineering Fracture Mechanics, Vol. 61, No. 2, 1998, pp. 191-211.
93. Rahman, S., "Net-Section-Collapse Analysis of Circumferentially Cracked Cylinders - Part II: Idealized Cracks and Closed-Form Solutions," Engineering Fracture Mechanics, Vol. 61, No. 2, 1998, pp. 213-230.
94. Rahman, S., Brust, F. W., Ghadiali, N., and Wilkowski, G., "Crack-Opening-Area Analyses for Circumferential Through-Wall Cracks in Pipes - Part I: Analytical Models," International Journal of Pressure Vessels and Piping, Vol. 75, No. 5, April 1998, pp. 357-373.
95. Rahman, S., Brust, F. W., Ghadiali, N., and Wilkowski, G., "Crack-Opening-Area Analyses for Circumferential Through-Wall Cracks in Pipes - Part II: Model Validations," International Journal of Pressure Vessels and Piping, Vol. 75, No. 5, April 1998, pp. 375-396.
96. Rahman, S., Ghadiali, N., Wilkowski, G., Moberg, F., and Brickstad, B., "Crack-Opening-Area Analyses for Circumferential Through-Wall Cracks in Pipes - Part III: Off-Center Cracks, Restraint of Bending, Thickness Transition, and Weld Residual Stresses," International Journal of Pressure Vessels and Piping, Vol. 75, No. 5, April 1998, pp. 397-415.
97. Rahman, S. and Brust, F. W., "Approximate Methods for Predicting J-integral of a Circumferentially Surface-Cracked Pipe Subject to Bending," International Journal of Fracture, Vol. 85, No. 2, October 1997, pp. 111-130.
98. Rahman, S., Wilkowski, G., and Mohan, R., "Low-Cycle Fatigue Crack Growth Considerations in Pipe Fracture Analyses," Nuclear Engineering and Design, Vol. 168, 1997, pp. 105-118.
99. Rahman, S., "Probabilistic Fracture Analysis of Cracked Pipes with Circumferential Flaws, International Journal of Pressure Vessels and Piping, Vol. 70, 1997, pp. 223-236.
100. Rahman, S., Ghadiali, N., Wilkowski, G., and Paul, D., "A Computer Model for Probabilistic Leak-Rate Analysis of Nuclear Piping and Piping Welds," International Journal of Pressure Vessels and Piping, Vol. 70, 1997, pp. 209-221.
101. Rahman, S., Ghadiali, N., Wilkowski, G., and Bonora, N., "Effects of Off-Centered Cracks and Restraint of Induced Bending Caused by Pressure on the Crack-Opening-Area Analysis of Pipes" Nuclear Engineering and Design, Vol. 167, 1996, pp. 55-67.
102. Rahman, S., Wilkowski, G., and Brust, F., "Fracture Analysis of Full-Scale Pipe Experiments on Stainless Steel Flux Welds," Nuclear Engineering and Design, Vol. 160, 1996, pp. 77-96.
103. Rahman, S., "A Stochastic Model for Elastic-Plastic Fracture Analysis of Circumferential Through-Wall-Cracked Pipes Subject to Bending," Engineering Fracture Mechanics, Vol. 52, No. 2, September 1995, pp. 265-288.
104. Brust, F., Rahman, S., and Ghadiali, N., "Elastic-Plastic Analysis of Small Cracks in Tubes," ASME Journal of Offshore Mechanics and Arctic Engineering, Vol. 117, No. 1, February 1995, pp. 57-62.
105. Rahman, S. and Grigoriu, M., "Local and Global Models for Nonlinear Dynamic Analysis of Multi-Story Shear Buildings Subject to Earthquake Loading," Computers and Structures, Vol 53, No. 3, November 1994, pp. 739-754.
106. Leis, B. and Rahman, S., "Risk-based Considerations in Developing Strategies to Ensure Pipeline Integrity - Part I: Theory," ASME Journal of Pressure Vessel Technology, Vol. 116, No. 3, August 1994, pp. 278-283.
107. Rahman, S. and Leis, B., "Risk-based Considerations in Developing Strategies to Ensure Pipeline Integrity - Part II: Applications," ASME Journal of Pressure Vessel Technology, Vol. 116, No. 3, August 1994, pp. 284-289.
108. Rahman, S. and Grigoriu, M., "Markov Model for Seismic Reliability Analysis of Degrading Structures," Journal of Structural Engineering, Vol. 119, No. 6, June 1993, pp. 1844-1865.
109. Rahman, S. and Brust, F., "Elastic-Plastic Fracture of Circumferential Through-Wall Cracked Pipe Welds Subject to Bending," ASME Journal of Pressure Vessel Technology, Vol. 114, No. 4, November 1992, pp. 410-416.
110. Rahman, S. and Brust, F., "An Estimation Method for Evaluating Energy Release Rates of Circumferential Through-Wall Cracked Pipe Welds," Engineering Fracture Mechanics, Vol. 43, No. 3, October 1992, pp. 417-430.