Improved Response Function Research Articles

An Improved Response Function Based Stochastic Meshless Method for Reliability Analysis of Euler-Bernoulli Beam

Abstract - An improved response function (IRF) based stochastic meshless method is proposed for the reliability analysis of Euler-Bernoulli beam. Spatial variation in Young's modulus is modelled as a homogeneous normal random field which is discretized using shape function method. The IRF method decomposes the displacement response into a deterministic part and an improved response function (IRF) and the stiffness matrix using Taylor series expansion. Limit state function of deflection is considered and a cantilever beam exposed to uniformly distributed load over the entire span is solved. Probabilities of failure and reliability indices are evaluated using the IRF method and compared with those obtained from direct Monte Carlo simulation (MCS) on the discretized system of equations. Failure probability values and reliability indices are found comparable even at higher coefficient of variation (CV) of input random field. The results are observed to be independent of the correlation length parameters. Computational times for the execution of the proposed method and MCS are also compared.

An improved response function based stochastic meshless method for problems in elasto-statics

The current study proposes an improved response function (IRF) based stochastic element free Galerkin method (SEFGM) for the analysis of problems in elasto-statics, wherein Young’s modulus is modelled as a homogeneous random field with symmetric distribution characteristics. The proposed SEFGM approximates displacement as the sum of a deterministic part and a stochastic part. The stochastic part is modelled with the help of an IRF, which is a function of discretized set of random variables. Moving least square shape functions are employed to discretize the random field. Utilizing Taylor series expansions of stiffness matrix and force vector and IRF approximation of displacement, explicit expressions for system responses in terms of random variables are derived. Stochastic informations of system responses are evaluated by employing Monte Carlo Simulation (MCS) on the response function, which eliminates the need of construction and simulation of system matrices at each set of sample generation. 1D and 2D numerical examples in elasto-statics are solved using proposed method. Results are validated with those obtained by direct simulation of system of equations using MCS and also compared with other methods like second order perturbation and ad-hoc response function based SEFGM. Normalized computational times required for all the methods are also compared. It is found that the proposed method is computationally efficient and can produce accurate results even for higher coefficient of variation of input random fields.

An Improved Response Function Based Stochastic Meshless Method for Reliability Analysis of Euler-Bernoulli Beam

An improved response function (IRF) based stochastic meshless method is proposed for the reliability analysis of Euler-Bernoulli beam. Spatial variation in Young’s modulus is modelled as a homogeneous normal random field which is discretized using shape function method. The IRF method decomposes the displacement response into a deterministic part and an improved response function (IRF) and the stiffness matrix using Taylor series expansion. Limit state function of deflection is considered and a cantilever beam exposed to uniformly distributed load over the entire span is solved. Probabilities of failure and reliability indices are evaluated using the IRF method and compared with those obtained from direct Monte Carlo simulation (MCS) on the discretized system of equations. Failure probability values and reliability indices are found comparable even at higher coefficient of variation (CV) of input random field. The results are observed to be independent of the correlation length parameters. Computational times for the execution of the proposed method and MCS are also compared.