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A general numerical solution method for Fokker-Planck equations with applications to structural reliability
4 references·11 citing·39 second hop
A general numerical solution method for Fokker-Planck equations with applications to structural reliability (1991)A general numerical solution method for F…Nonlinear Vibration Models for Extremes and Fatigue (1988)Nonlinear Vibration Models fo…A finite element method for the statistics of non-linear random vibration (1985)A finite element method for t…Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations (1984)Cumulant-neglect closure for …Method for Random Vibration of Hysteretic Systems (1976)Method for Random Vibration o…Bayesian neural network based probability density evolution approach for efficient structural reliability analysis (2025)Bayesian neural network based…The Duffing oscillator under combined periodic and random excitations (2012)The Duffing oscillator under …Stochastic elastic–plastic finite elements (2010)Stochastic elastic–plastic fi…A Multi-Resolution Approach for Steady State Uncertainty Determination in Nonlinear Dynamical Systems (2006)A Multi-Resolution Approach f…NUMERICAL SOLUTION OF THE STATIONARY FPK EQUATION USING SHANNON WAVELETS (2000)NUMERICAL SOLUTION OF THE STA…Lagrangian/Eulerian Description of Dynamic System (1998)Lagrangian/Eulerian Descripti…Fourier-based maximum entropy method in stochastic dynamics (1998)Fourier-based maximum entropy…Stationary and non-stationary random vibration of oscillators with bilinear hysteresis (1996)Stationary and non-stationary…A finite-element method for analysis of a non-linear system under stochastic parametric and external excitation (1996)A finite-element method for a…Robust Numerical Solution of the Transient Fokker-Planck Equation for Nonlinear Dynamical Systems (1992)Robust Numerical Solution of …Nonlinear Stochastic Mechanics (1992)Nonlinear Stochastic MechanicsStochastic averaging: An approximate method of solving random vibration problems (1986)Response statistics of nonlinear, compliant offshore structures by the path integral solution method (1993)Stochastic joint time–frequency response analysis of nonlinear structural systems (2013)Stochastic response determination of nonlinear structural systems with singular diffusion matrices: A Wiener path integral variational formulation with constraints (2020)Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on Laplace’s method of integration (2022)Approximate Method for Nonlinear Random Vibration (1975)Random Vibration: A Survey of Recent Developments (1983)Approximate solution of the Fokker–Planck–Kolmogorov equation (2002)Numerical solutions of Fokker–Planck equation of nonlinear systems subjected to random and harmonic excitations (2011)Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM (2023)Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Probabilistic Theory of Structural Dynamics (1976)Stochastic Finite Elements: A Spectral Approach (1991)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)Fokker–Planck linearization for non-Gaussian stochastic elastoplastic finite elements (2016)Time-domain stochastic finite element simulation of uncertain seismic wave propagation through uncertain heterogeneous solids (2016)Structural Reliability Analysis and Prediction (2017)Machine learning aided stochastic elastoplastic analysis (2019)Random vibration and statistical linearization (1990)Random vibration and statistical linearization (1990)Formulation of Statistical Linearization for M-D-O-F Systems Subject to Combined Periodic and Stochastic Excitations (2019)A Wiener path integral technique for determining the stochastic response of nonlinear oscillators with fractional derivative elements: A constrained variational formulation with free boundaries (2023)An extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems (2024)On stochastic differential equations (1951)Developments in stochastic structural mechanics (2006)Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects (2006)Solution of Fokker-Planck equation by finite element and finite difference methods for nonlinear systems (2006)Stochastic Differential Equations (2014)On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems (1993)The equivalent extreme-value event and evaluation of the structural system reliability (2006)The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters (2006)Monte Carlo techniques in computational stochastic mechanics (1998)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Stochastic Dynamics of Marine Structures (2012)A new philosophy for stochastic equivalent linearization (1993)Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique (1995)Modified Path Integral Solution of Fokker–Planck Equation: Response and Bifurcation of Nonlinear Systems (2009)Methods of nonlinear random vibration analysis (1995)Phase Space Reduction in Stochastic Dynamics (2000)
this work references cited by second hop

References

  • 1976Method for Random Vibration of Hysteretic Systems2,686 cited
  • 1988Nonlinear Vibration Models for Extremes and Fatigue535 cited
  • 1984Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations234 cited
  • 1985A finite element method for the statistics of non-linear random vibration110 cited

Cited by

  • 2012The Duffing oscillator under combined periodic and random excitations46 cited
  • 1996Stationary and non-stationary random vibration of oscillators with bilinear hysteresis35 cited
  • 2010Stochastic elastic–plastic finite elements33 cited
  • 1992Nonlinear Stochastic Mechanics33 cited
  • 1992Robust Numerical Solution of the Transient Fokker-Planck Equation for Nonlinear Dynamical Systems29 cited
  • 2000NUMERICAL SOLUTION OF THE STATIONARY FPK EQUATION USING SHANNON WAVELETS19 cited
  • 1998Lagrangian/Eulerian Description of Dynamic System17 cited
  • 1996A finite-element method for analysis of a non-linear system under stochastic parametric and external excitation17 cited
  • 2006A Multi-Resolution Approach for Steady State Uncertainty Determination in Nonlinear Dynamical Systems15 cited
  • 1998Fourier-based maximum entropy method in stochastic dynamics11 cited

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  • 2025Bayesian neural network based probability density evolution approach for efficient structural reliability analysis10 cited