Reliability Calculations with the Stochastic Finite Element

Considering the influence of fuzzy factors, the fuzzy reliability of single component maintenance system and the repairable series system is studied.

Two fuzzy methods for reliability allocation are proposed: one uses the second-order fuzzy comprehensive evaluation method, and the other one uses the fuzzy optimization method.

Considering the influence of random factors, such as material inhomogeneity and manufacturing and installation error, the reliability of rigid rotor balance is studied by using stress -strength interference model. Based on the sensitivity analysis, a Monte Carlo simulation for the reliability calculation of gears is proposed. Based on sensitivity analysis, an optimization method for reliability calculation is proposed. The reliability calculation of spring is studied by the HL-RF method.

Considering the influence of random factors, using the HL-RF method to calculate the reliability, the reliability optimization design of the gearbox is studied. The reliability optimization design of the gearbox is studied by using the importance sampling. This paper puts forward the method of reliability fuzzy optimum design, which is the deepening of reliability, optimum design, and fuzzy optimum design. Under the influence of fuzziness, a multi-objective reliability fuzzy optimization model of the gearbox is established. By using the multi-objective fuzzy optimization method, the reliability fuzzy optimization design of the gearbox is carried out.

Perturbation stochastic finite element of mechanical vibration is introduced. The vibration equation of a system is transformed into a static problem by using the Willson θ method. An improved method of perturbation stochastic finite element is proposed. The formulas of calculating perturbation stochastic finite elements are transformed into linear equations to avoid solving matrix inversion. A numerical example is given in order to demonstrate the proposed.

Samples of material property are generated by the calculation of the stochastic field. Differential equations are transformed into linear equations by the Willson θ method. Linear equations are solved by the Successive Over Relaxation method. Dynamic reliability of structure can be given by Monte Carlo simulation. A new method of calculating dynamic reliability using the Neumann stochastic finite element is proposed.

The optimal design of structural vibration based on the stochastic finite element is presented. The optimization design of the gearbox is proposed by using the stochastic finite element method for structural vibration. A new iterative method (NIM) is used to calculate the stochastic finite element for vibration.

When material property geometry parameters and applied loads of structure are assumed to be stochastic, four methods of nonlinear vibration are proposed. The Newton method is applied to nonlinear vibration. Taylor expansion is used to analyze nonlinear vibration. The perturbation technology is proposed to compute nonlinear vibration. A modified iteration formula by the homotopy perturbation method is presented to analyze nonlinear vibration.