Finite Element Method for Stochastic Beams Based on Variational Principles

1997 ◽  
Vol 64 (3) ◽  
pp. 664-669 ◽  
Author(s):  
Y.-J. Ren ◽  
I. Elishakoff ◽  
M. Shinozuka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Covariance Function ◽  
Variational Principles ◽  
Joint Probability ◽  
Accurate Solution ◽  
Joint Probability Distribution ◽  
Covariance Functions ◽  
The Mean ◽  
Element Method

This paper proposes a new version (fundamentally different from the existing ones) of finite element method for the mean and covariance functions of the displacement for bending beams with spatially random stiffness. Apart from the conventional finite element method for stochastic problems, which utilizes either perturbation or series expansion technique or the Monte Carlo simulation, the present method is based on the newly established variational principles. The finite element scheme is formulated directly with respect to the mean function and covariance function, rather than perturbed components of the displacement. It takes into account an information on joint probability distribution function of the random stiffness to obtain the covariance function of the displacement. Therefore, the accurate solution can be obtained even if the coefficient of variation of the random stiffness is large, in contrast to conventional technique. Several examples are given to illustrate the advantage of the proposed method, compared with the conventional ones.

scholarly journals Optimization Method of the Car Seat Rail Abnormal Noise Problem Based on the Finite Element Method

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Huijie Yu ◽  
Xinkan Zhang ◽  
Chen Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Joint Probability ◽  
Element Model ◽  
Joint Probability Distribution ◽  
Natural Frequencies And Modes ◽  
Car Seat ◽  
Finite Element Software ◽  
Element Method

The finite element model of the seat rail is established with a spring-damping element to simulate the ball in the rail joint part. The stiffness and damping parameters of the joint part are determined by the combination of finite element method and experiment. Firstly, the natural frequencies and modes of the guide rail are obtained by modal experiment. The stiffness of the spring-damping element is optimized in the finite element software to make the natural frequencies and modes of the system consistent with the experimental ones. Secondly, the dynamic response curve of the key nodes is obtained through sweeping experiment, and the damping of the spring-damping element is optimized in the finite element software to make the nodal response of the system output consistent with the experiment. Then, the gap of the joint part of the car seat rail is studied considering the factors of load and structure randomness. The influence factors of the gap are selected by Hammersley experimental design method. The results show that the gap is normally distributed, and therefore the confidence interval of the gap is obtained. Finally, the joint probability distribution of the gap is obtained under the condition that the load and the structure are all random, which provides the theoretical guidance for determining the reasonable gap of the joint.

Generalized variational principles in the finite-element method.

AIAA Journal ◽  
1969 ◽  
Vol 7 (7) ◽  
pp. 1254-1260 ◽  
Author(s):  
B. E. GREENE ◽  
R. E. JONES ◽  
R. W. McLAY ◽  
D. R. STROME
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Principles ◽  
The Finite Element Method ◽  
Generalized Variational Principles ◽  
Element Method

Mean Strain Effect on Crack Initiation Lives for Notched Specimens Under Biaxial Nonproportional Loading Paths

1997 ◽  
Vol 119 (1) ◽  
pp. 104-112 ◽  
Author(s):  
Ming-Chuen Yip ◽  
Yi-Ming Jen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Initiation ◽  
Strain Effect ◽  
Nonproportional Loading ◽  
Notched Specimens ◽  
Loading Paths ◽  
The Mean ◽  
Mean Strain ◽  
Element Method

This paper discusses the mean strain effect on the crack initiation lives for notched specimens under biaxial nonproportional loading paths. Elastic-plastic finite element method was used to evaluate the local stresses and strains. Several prediction models related to the mean stress/strain effect were employed to correlate the experimental results with reference fatigue data for smooth specimens. It is found that Fatemi-Socie model gives good prediction for the present research with the assistance of finite element method. The stress behavior in this deflection-controlled tests is discussed in this study, and the failure surfaces are also examined after tests.

Effective shear modulus of a damaged ply in laminate stiffness analysis: Determination and validation

2019 ◽  
Vol 54 (9) ◽  
pp. 1161-1176
Author(s):  
Mohamed Sahbi Loukil ◽  
Janis Varna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Modulus ◽  
Crack Density ◽  
Accurate Solution ◽  
Effective Stiffness ◽  
Crack Face ◽  
Plane Shear ◽  
Stiffness Reduction ◽  
Element Method

The concept of the “effective stiffness” for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson’s ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described.

Resonance Reliability Assessment of Turbine Blade with Parametric Uncertainty

2007 ◽  
Vol 353-358 ◽  
pp. 2636-2639 ◽  
Author(s):  
Yong Qing Ge ◽  
Li Qiang An ◽  
Zhang Qi Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Turbine Blade ◽  
Parametric Uncertainty ◽  
Stochastic Finite Element Method ◽  
Stochastic Finite Element ◽  
Probabilistic Characteristic ◽  
The Mean ◽  
Mean Variance ◽  
Element Method

Stochastic finite element method and reliability technique are used to determine the safety degree of the turbine blade with parametric uncertainty. The material, geometric parameters and rotating speed of blade exhibit notable random fluctuations, so the conventional deterministic analysis of blade can’t provide complete information. The stochastic analysis can tackle the uncertainties in structural parameters and obtain the probabilistic characteristic of the vibration characteristic. In this paper, the study focuses on the reliability assessment of the blade with uncertainty parameters based on the stochastic finite element method (SFEM) and the mean-variance method. The perturbation stochastic finite element method (PSFEM) is used to calculate probabilistic characteristic of the natural vibration of the turbine blade. Based on the stochastic finite element method, the mean-variance method is used to calculate the resonance reliability of the blade. The example shows that the present method is valid.

Sign in / Sign up

Export Citation Format

Share Document