Developments in stochastic structural mechanics

EUROCODE 1: Basis of Design and Actions on Structures. CEN/TC250/N105, 6th draft, env edition, March (1991)

AISC: Load and Resistance Factor Design Specification for Structural Steel Buildings (LRFD). AISC, Chicago, IL, USA (1993)

API: Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms. API, Washington, D.C., API recommended practice 2a (rp 2a, 19edn) edition, Aug. 1991. 159p (1991)

Atalik T.S., Utku S. (1976) Stochastic linearization of multi-degree-of-freedom nonlinear systems. Earthquake Eng. Struct. Dyn. 4, 411–420

Au S.K,, Beck J.L, (2003) Subset simulation and its application to seismic risk based on dynamic analysis. J. Eng. Mech. ASCE 129, 901–917

Au S.-K., Beck J.L. (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab. Eng. Mech. 16(4): 263–277

Bea R.G.: Reliability based requalification criteria for offshore platforms. In: Proceedings International Conference on Offshore Mech. Arct. Eng. vol. II, Safety and Reliability, pp. 351–361, New York, ASME (1993)

Bergman L.A., Spencer Jr.B.F. (1992) Robust numerical solution of the transient Fokker–Planck equation for nonlinear dynamical systems. In: Bellomo N., Casciati F. (eds) Proceedings IUTAM Symposiam. on Nonlinear Stochastic Mechanics. Springer, Berlin Heidelberg New York

Bergman L.A., Wojtkiewicz S.F., Johnson E.A., Spencer Jr.B.F. Some reflections on the efficiency of moment closure methods. In: Spanos P.D. (ed.) Computational Stochastic Dynamics, pp. 87–96 (1995)

Bitzarakis S., Papadrakakis M., Kotsopulos A. (1997) Parallel solution techniques in computational structural mechanics. Comput. Meth. Appl. Mech. Eng. 148(1–2): 75–104

Bjerager P. (1988) Probability integration by directional simulation. J. Eng. Mech. 114(8): 1285–1302

BMFT.: Deutsche risikostudie kernkraftwerke. Technical report, Verlag TÜV Rheinland, Germany (1980)

Cai G.Q., Lin Y.K. (1988) A new approximate solution technique for randomly excited non-linear systems. Int. J. Nonlin. Mech. 23(2/3): 409–420

Cai G.Q., Lin Y.K. (1994) On statistics of first passage failure. J. Appl. Mech. ASME 61, 93–99

Cai G.Q., Lin Y.K. (1996) Generation of non-Gaussian stationary processes. Phy. Rev. E 54(1): 299–303

Cameron R., Martin W. (1947) The orthogonal development of nonlinear functionals in series of Fourier–Hermite functionals. Ann. Math 48, 385–392

Caughey T.K. (1959) Response of a linear string to random loading. J. Appl. Mech. ASME 26, 341–344

Caughey T.K. (1986) On the response of non-linear oscillators to stochastic excitacion. Prob. Eng. Mech. 1(1): 2–4

Chang T.-P., Mochio T., Samaras E. (1986) Seismic response analysis of nonlinear structures. Prob. Eng. Mech. 1(3): 157–166

COSSAN.: COmputational Stochastic Structural ANalysis, Part A, User’s Manual. Institute of Engineering Mechanics, Leopold–Franzens University, Innsbruck, Austria (1996)

Crandall S.H. (1963) Perturbation techniques for random vibration of nonlinear systems. J. Acoust. Soc. Am. 35, 1700–1705

Crandall S.H. (1985) Non-Gaussian closure techniques for stationary random vibration. Int. J. Non-Lin. Mech. 20, 1–8

Crandall S.H., Chandiramani K.L., Cook R.G. (1966) Some first passage problems in random vibration. J. Appl. Mech. ASME 33, 624–639

Daubechies I. (1992) Ten Lectures on Wavelets. Wiley, New York

Deodatis G. (1991) Weighted integral method. I: Stochastic stiffness matrix. J. Eng. Mech. ASCE 117(8): 1851–1864

Deodatis G., Shinozuka M. (1991) Weighted integral method. II: Response variability and reliability. J. Eng. Mech. ASCE 117(8): 1865–1877

Der Kiureghian A., Li C.-C.: Statistics of fractional occupation time for nonlinear stochastic response. In: Lin Y.K., Su T.C. (eds.) Proceeding ASCE Engineering Mechanics Conference, pp. 116–119. Fort Lauderdale, USA, May 19–22 (1996)

DNV.: Structural Reliability Analysis of Marine Structures. Det Nortske Veritas Classification AS, Norway, classif. notes no. 30.6 edn (1992)

Ellingwood B. (1994) Probability-based codified design: past accomplishments and future challenges. Struct. Saf. 13, 159–176

Freudenthal A.M. Safety and the probability of structural failure. Trans. ASCE 121(Proc. Paper 2843), 1337–1397 (1956)

Gasser M., Schuëller G.I. (1997) Reliability-based optimization of structural systems. Math. Meth. Oper. Res. 46, 287–307

Ghanem R., Kruger R. (1996) Numerical solution of spectral stochastic finite element systems. Comput. Meth. Appl. Mech. Eng. 129, 289–303

Ghanem R., Spanos P. (1991) Stochastic Finite Elements: A Spectral Approach. Springer, Berlin Heidelberg NewYork

Grigoriu M., Waisman F. (1997) Linear systems with polynomials of filtered Poisson processes. Probab. Eng. Mech. 12(2): 97–103

Hisada T., Noguchi H.: Development of a nonlinear stochastic FEM and its application. In: Ang A.H.-S., Shinozuka M., Schuëller G.I. (eds.) Structural Safety and Reliability, Proceedings of the 5th ICOSSAR, pp. 1097–1104, San Francisco, 1989. ASCE

Hoshiya M. (1995) Kriging and conditional simulation of Gaussian field. J. Eng. Mech. ASCE 121(2): 181–186

Hoshiya M., Kuwana T.: Complementary discussions on theory of conditional stochastic field. J. Struct. Mech. Earthq. Eng. Jpn. Soc. Civil Eng. No. 477/I-25:93–96 (in Japanese), (1993)

Hsu C.S. (1986) A cell mapping method for non-linear deterministic and stochastic systems—part I. the method of analysis. J. App. Mech. 53, 695–701

Hsu C.S. (1986) A cell mapping method for non-linear deterministic and stochastic systems—part II. examples of application. J. App. Mech. 53, 702–710

Iwan W.D., Yang I.M. (1972) Application of statistical linearization technique to nonlinear multi-degree-of-freedom systems. J. Appl. Mech. ASME 39, 545–550

Liu J.S. (2001) Monte Carlo Strategies in Scientific Computing. Springer Series in Statistics. Springer, Berlin Heidelberg NewYork

Kafka P. (1996) Probabilistic safety assessment: quantitative process to balance design, manufacturing and operation for safety of plant structures and systems. Nucl. Eng. Des. 165, 333–350

Kameda H., Morikawa H. (1992) An interpolating stochastic process for simulation of conditional random fields. Probab Eng. Mech. 7(4): 242–254

Kameda H., Morikawa H. (1993) Conditioned stochastic processes for conditional random fields. J. Eng. Mech. 120(4): 855–875

Kanda J., Ellingwood B. (1991) Formulation of load factors based on optimum reliability. Struct. Saf. 9(3): 197–210

Kijawatworawet W., Pradlwarter H.J., Schuëller G.I.: Structural reliability estimation by adaptive importance directional sampling. In: Shiraishi N., Shinozuka M., Wen Y.K. (eds.) Proceedings of the 7th International Conference on Structural Safety and Reliability (ICOSSAR’97), pp. 891 – 897, Kyoto, Japan, November 1998. A.A. Balkema, Rotterdam, The Netherlands (1998)

Kloeden P.E., Platen E. (1992) Numerical Solution of Stochastic Differential Equations. Springer, Berlin Heidelberg New York

Kontorovich V.Y., Lyandres V.Z. (1995) Stochastic differential equations: an approach to the generation of continuous non-Gaussian processes. IEEE Trans. Signal Process. 43(10): 2372–2385

Koutsourelakis P.S., Pradlwarter H.J., Schuëller G.I. (2004) Reliability of structures in high dimensions, part I: algorithms and applications. Probab. Eng. Mech. 19(4): 409–417

Lin Y.K. (1976) Probabilistic Theory of Structural Dynamics. Robert E. Krieger, Huntington

Lin Y.K., Cai G.Q. (1995) Probabilistic Structural Dynamics, Advanced Theory and Applications. McGraw–Hill, Inc., New York

Lind N.C. (1976) Approximate analysis and economics of structures. J. Struct. Div. 102(ST6): 1177–1196

Liu W.K., Belytschko T., Mani A. (1986) Probabilistic finite elements for nonlinear structural dynamics. Comput. Meth. Appl. Mech. Eng. 56, 61–81

Loève M. (1977) Probability Theory, 4th edn. Springer Berlin Heidelberg, New York

Marti K. (ed): Stochastic Optimization Techniques – Numerical Methods and Technical Applications, vol. 513 of Lecture Notes in Economics and Mathematic Systems. Springer, Berlin Heidelberg New York (2002)

Mayer M. (1926) Die Sicherheit der Bauwerke und ihre Berechnung nach Grenzkräften anstatt nach zulässigen Spannungen. Springer, Berlin Heidelberg New York

Metropolis N., Ulam S. (1949) The Monte Carlo method. J. Am. Stat. Assoc. 44, 335–341

Moan T.: Reliability and risk analysis for design and operations planning of offshore structures. In: Schuëller G.I. Shinozuka M., Yao J.T.P. (eds.) Structural Safety and Reliability, vol. 1, pp. 21–43. Balkema, Rotterdam (1994)

Muscolino G. (1995) Linear systems excited by polynomial forms of non-Gaussian filtered Poisson processess. Probab. Eng. Mech. 10(2): 35–44

Newland D.E. (1994) An introduction to Random Vibration, Spectral and Wavelet Analysis. Wiley, New York

Nie J., Ellingwood R. (2000) Directional methods for structural reliability. Struct. Safety 22, 233

Nowak A.S. (1995) Calibration of LRFD bridge code. J. Struct. Eng. 121(8): 1245–1251

Pellissetti M.F., Fransen S.H.J.A., Pradlwarter H.J., Calvi A., Kreis A., Schuëller G.I., Klein M.: Stochastic launcher–satellite coupled dynamic analysis. J. Spacecr. Rocket. (2006) (to appear)

Pellissetti M.F., Schuëller G.I. (2006) On general purpose software in structural reliability. Struct. Saf. 28(1–2): 3–16

Pradlwarter H.J., Li W. (1991) On the computation of the stochastic response of highly nonlinear large MDOF-systems modeled by finite elements. Probab. Eng. Mech. 6(2): 109–116

Pradlwarter H.J., Schuëller G.I. (1993) Equivalent linearization—a suitable tool to analyse MDOF-systems. Probab. Eng. Mech. 8, 115–126

Pradlwarter H.J., Schuëller G.I. (1997) On advanced MCS procedures in stochastic structural dynamics. J. Nonlin. Mech. 32(4): 735–744

Pradlwarter H.J., Schuëller G.I. (1999) Assessment of low probability events of dynamical systems by controlled Monte Carlo simulation. Probab. Eng. Mech. 14, 213–227

Pradlwarter H.J., Schuëller G.I., Székely G.S. (2002) Random eigenvalue problems for large systems. Comput. Struct. 80, 2415–2424

Pugsley A.G.: A philosophy of aeroplane strength factors. Rep. Mem. Br. Aeron. Res. Comm. no. 1906, 1942

Rice S.O.: Mathematical analysis of random noise. In: Wax N., (ed.) Selected Papers on Noise and Stochastic Processes, pp. 133–294. Dover, 1954. originally appeared in two parts in the Bell System Technical Journal in Vol. 23, July 1944 and in Vol. 24, January 1945

Roberts J.B. (1976) First passage probability for nonlinear oscillators. J. Eng. Mech. ASCE 102, 851–866

Roberts J.B. (1977) Stationary response of oscillators with nonlinear damping to random excitation. J. Sound Vib. 30, 145–156

Roberts J.B. (1986) First passage time for randomly excited non-linear oscillators. J. Sound Vib. 109(1): 33–50

Rocha M.M., Schuëller G.I. (2005) Markoff chain modeling of NDI techniques. Fatigue Fract. Eng. Mater. Struct. 28, 267–278

Schenk C.A., Schuëller G.I. (2003) Buckling analysis of cylindrical shells with random geometric imperfections. J. Non-Lin. Mech. 38(7): 1119–1132

Schittkowski K.: Theory, implementation, and test of a nonlinear programming algorithm. In: Proceedings of Euromech-Colloquium 164 on “Optimization Methods in Structural Design”. Universität Siegen, 1982, Bibliographisches Institut, Mannheim (1983)

Schuëller G.I.: Engineering applications of stochastic mechanics -achievements and prospects. In: Naess A., Krenk S. (eds.) Proceedings of the IUTAM-Symposium on Advances in Nonlinear Stochastic Mechanics, pp. 383–402. Kluver, Doordrecht (1996)

Schuëller G.I. (2006) Uncertainty and reliability analysis of structural dynamical systems. In: Mota Soares C.A., Martins J.A.C., Rodrigues H.C., Ambrósio J.A.C. (eds), Computational Mechanics—Solids, Structures and Coupled Problems. Springer, The Netherlands, pp. 541–554

Schuëller G.I., Pandey M.D., Pradlwarter H.J. (1994) Equivalent linearization (EQL) in engineering practice for aseismic design. J. Probab. Eng. Mech. 9, 95–102

Schuëller G.I., Pradlwarter H.J.: Benchmark study on reliability estimation in higher dimensions of structural systems – an overview. Struct. Safe. (2006) (to appear)

Schuëller G.I., Pradlwarter H.J., Koutsourelakis P.S. (2004) A critical appraisal of reliability estimation procedures for high dimensions. Probab. Eng. Mech. 19(4): 463–474

Schuëller G.I., Pradlwarter H.J., Vasta M., Harnpornchai N. (1998) Benchmark-study on non-linear stochastic structural dynamics. In: Shiraishi N., Shinozuka M., Wen Y.K. (eds), Proceedings of the 7th International Conference on Structural Safety and Reliability (ICOSSAR’97). A.A. Balkema, Rotterdam, pp. 355–361

Schuëller G.I., Stix R. (1987) A critical appraisal of methods to determine failure probabilities. J. Struct. Saf. 4, 293–309

Schuëller G.I. (ed) (1997) A state-of-the-art report on computational stochastic mechanics. J. Probab. Eng. Mech. 12(4): 197–313

Shinozuka M. (1972) Monte Carlo solution of structural dynamics. Comput. Struct. 2(5+6): 855–874

Shinozuka M., Deodatis G. (1996) Simulation of multi-dimensional Gaussian stochastic fields by spectral representation. Appl. Mech. Rev. 49(1): 29–53

Soize C. (1988) Steady state solution of Fokker–Planck equation in higher dimension. Probab. Engr. Mech. 3(4): 196–206

Soize C. (1994) The Fokker–Planck Equation for Stochastic Dynamical Systems and its Explicit Steady State Solutions. World Scientific, Singapore

Soong T.T. (1973) Random Differential Equations in Science and Engineering. Academic, New York

Soong T.T., Grigoriu M. (1993) Random Vibration of Mechanical and Structural Systems. Prentice-Hall, Englewood Cliffs

Spencer Jr.B.F., Bergman L.A. (1993) On the numerical solution of the Fokker–Planck equation for nonlinear stochastic systems. Nonlin. Dyn. 4, 357–372

Székely G.S., Schuëller G.I. (2001) Computational procedure for a fast calculation of eigenvectors and eigenvalues of structures with random properties. Comput. Meth. Appl. Mech. Eng. 191(8-10): 799–816

Takada T. (1990) Weighted integral method in stochastic finite element analysis. Probab. Eng. Mech. 5(3): 146–156

Thacker B.H., Riha D.S., Fitch S.H.K., Huyse L.J., Pleming J.B. (2006) Probabilistic engineering analysis using the nessus software. Struct. Saf. 28(1–2): 83–107

Torrie G.M., Valleau J.P. (1977) Non-physical sampling distributions in Monte Carlo free energy estimation: umbrella sampling. J. Comput. Phy. 23(2): 187–199

Vanmarcke E.H., Grigoriu M. (1983) Stochastic finite element analysis of simple beams. J. Eng. Mech. ASCE 109(5): 1203–1214

Vanmarcke E.H., Heredia-Zavoni E., Fenton G.A. (1993) Conditional simulation of spatially correlated earthquake ground motion. J. Eng. Mech. ASCE 119(11): 2333–2352

Vanzini R., Rossetto P., Conz L., Ferro G., Righetti G.: Requalification of offshore platforms on the basis of inspection results and probabilistic analyses. In: JCSS, Offshore Technology Conference, paper no. OCT 5930, pp. 481–492, Houston (1992)

Wen Y.K. (1980) Equivalent linearization of hysteretic systems under random excitation. J. Appl. Mech. ASME 42(2): 39–52

Wen Y.K. (1990) Structural Load Modelling and Combination for Performance and Safety Evaluation. Elsevier, Amsterdam

Wierzbicki W. (1936) Safety of Structures as a Probability Problem, p 690. Przeglad Techniczny, Warsaw

Wu W.F., Lin Y.K. (1984) Cumulant-neglect closure for nonlinear oscillators under parametric and external excitations. Int. J. Non-Lin. Mech. 19, 349–362

Yang J.-N. (1972) Simulation of random envelope processes. J. Sound Vib. 25(1): 73–85

Yang J.-N. (1973) On the normality and accuracy of simulated random processes. J. Sound Vib. 26(3): 417–428