Estimating the Probability Distribution of von Mises Stress for Structures Undergoing Random Excitation

1999 ◽  
Vol 122 (1) ◽  
pp. 42-48 ◽  
Author(s):  
Dan Segalman ◽  
Garth Reese ◽  
Richard Field, ◽  
Clay Fulcher
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Asymptotic Properties ◽  
Monte Carlo Sampling ◽  
Random Excitation ◽  
Von Mises Stress ◽  
Second Order Statistics ◽  
Analytic Expressions ◽  
Numerical Precision ◽  
Von Mises

The von Mises stress is often used as the metric for evaluating design margins, particularly for structures made of ductile materials. For deterministic loads, both static and dynamic, the calculation of von Mises stress is straightforward, as is the resulting calculation of reliability. For loads modeled as random processes, the task is different; the response to such loads is itself a random process and its properties must be determined in terms of those of both the loads and the system. This has been done in the past by Monte Carlo sampling of numerical realizations that reproduce the second order statistics of the problem. Here, we present a method that provides analytic expressions for the probability distributions of von Mises stress which can be evaluated efficiently and with good numerical precision. Further, this new approach has the important advantage of providing the asymptotic properties of the probability distribution. [S0739-3717(00)00801-1]

Parameterization of multifractal cascade models based on their breakdown coefficients

2020 ◽  
Author(s):  
César Aguilar Flores ◽  
Alin Andrei Carsteanu
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Rainfall Intensity ◽  
Probability Distributions ◽  
Asymptotic Properties ◽  
Distribution Functions ◽  
Marginal Probability ◽  
Probability Distribution Functions ◽  
Marginal Probability Distribution ◽  
Cascade Models

<p>Breakdown coefficients of multifractal cascades have been shown, in various contexts, to be ergodic in their (marginal) probability distribution functions, however the necessary connection between the cascading process (or a tracer thereof, such as rainfall) and the breakdown coefficients of the measure generated by the cascade, was missing. This work presents a method of parameterization of certain types of multiplicative cascades, using the breakdown coefficients of the measures they generate. The method is based on asymptotic properties of the probability distributions of the breakdown coefficients in “dressed” cascades, as compared with the respective distributions of the cascading weights. An application to rainfall intensity time series is presented.</p>

scholarly journals Seismic Tomography Using Variational Inference Methods

2020 ◽  
Author(s):  
Xin Zhang ◽  
Andrew Curtis
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Seismic Tomography ◽  
Posterior Probability ◽  
Sampling Methods ◽  
Probability Distributions ◽  
Monte Carlo Sampling ◽  
Variational Inference ◽  
Posterior Probability Distribution ◽  
Inference Methods

<p><span>In a variety of geoscientific applications we require maps of subsurface properties together with the corresponding maps of uncertainties to assess their reliability. Seismic tomography is a method that is widely used to generate those maps. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large data sets and high-dimensionality parameter spaces. To extend uncertainty analysis to larger systems, we introduce variational inference methods to conduct seismic tomography. In contrast to Monte Carlo sampling, variational methods solve the Bayesian inference problem as an optimization problem yet still provide fully nonlinear, probabilistic results. This is achieved by minimizing the Kullback-Leibler (KL) divergence between approximate and target probability distributions within a predefined family of probability distributions.</span></p><p><span>We introduce two variational inference methods: automatic differential variational inference (ADVI) and Stein variational gradient descent (SVGD). In ADVI a Gaussian probability distribution is assumed and optimized to approximate the posterior probability distribution. In SVGD a smooth transform is iteratively applied to an initial probability distribution to obtain an approximation to the posterior probability distribution. At each iteration the transform is determined by seeking the steepest descent direction that minimizes the KL-divergence. </span></p><p><span>We apply the two variational inference methods to 2D travel time tomography using both synthetic and real data, and compare the results to those obtained from two different Monte Carlo sampling methods: Metropolis-Hastings Markov chain Monte Carlo (MH-McMC) and reversible jump Markov chain Monte Carlo (rj-McMC). The results show that ADVI provides a biased approximation because of its Gaussian approximation, whereas SVGD produces more accurate approximations to the results of MH-McMC. In comparison rj-McMC produces smoother mean velocity models and lower standard deviations because the parameterization used in rj-McMC (Voronoi cells) imposes prior restrictions on the pixelated form of models: all pixels within each Voronoi cell have identical velocities. This suggests that the results of rj-McMC need to be interpreted in the light of the specific prior information imposed by the parameterization. Both variational methods estimate the posterior distribution at significantly lower computational cost, provided that gradients of parameters with respect to data can be calculated efficiently. We therefore expect that the methods can be applied fruitfully to many other types of geophysical inverse problems.</span></p>

scholarly journals Probability distribution of von Mises stress in the presence of pre-load.

2013 ◽  
Author(s):  
Daniel Joseph Segalman ◽  
Field, Richard V., ◽  
Garth M. Reese
Keyword(s):  
Probability Distribution ◽  
Von Mises Stress ◽  
Von Mises

Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Sayan Gupta ◽  
P. H. A. J. M. van Gelder
Keyword(s):  
Probability Distribution ◽  
Gaussian Process ◽  
Joint Probability ◽  
Random Processes ◽  
Von Mises Stress ◽  
Analytical Approximations ◽  
Multidimensional Integration ◽  
Reliability Method ◽  
Non Gaussian ◽  
Von Mises

The problem of approximating the probability distribution of peaks, associated with a special class of non-Gaussian random processes, is considered. The non-Gaussian processes are obtained as nonlinear combinations of a vector of mutually correlated, stationary, Gaussian random processes. The Von Mises stress in a linear vibrating structure under stationary Gaussian loadings is a typical example for such processes. The crux of the formulation lies in developing analytical approximations for the joint probability density function of the non-Gaussian process and its instantaneous first and second time derivatives. Depending on the nature of the problem, this requires the evaluation of a multidimensional integration across a possibly irregular and disjointed domain. A numerical algorithm, based on first order reliability method, is developed to evaluate these integrals. The approximations for the peak distributions have applications in predicting the expected fatigue damage due to combination of stress resultants in a randomly vibrating structure. The proposed method is illustrated through two numerical examples and its accuracy is examined with respect to estimates from full scale Monte Carlo simulations of the non-Gaussian process.

Effects of occlusal scheme on All-on-Four abutments, screws and prostheses: A three-dimensional finite element study

2020 ◽  
Author(s):  
Nurullah Türker ◽  
Hümeyra Tercanlı Alkış ◽  
Steven J Sadowsky ◽  
Ulviye Şebnem Büyükkaplan
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Good Prognosis ◽  
Von Mises Stress ◽  
Element Analysis ◽  
Group Function ◽  
Occlusal Contact ◽  
Maximum Deformation ◽  
Contact Points ◽  
Von Mises

An ideal occlusal scheme plays an important role in a good prognosis of All-on-Four applications, as it does for other implant therapies, due to the potential impact of occlusal loads on implant prosthetic components. The aim of the present three-dimensional (3D) finite element analysis (FEA) study was to investigate the stresses on abutments, screws and prostheses that are generated by occlusal loads via different occlusal schemes in the All-on-Four concept. Three-dimensional models of the maxilla, mandible, implants, implant substructures and prostheses were designed according to the All-on-Four concept. Forces were applied from the occlusal contact points formed in maximum intercuspation and eccentric movements in canine guidance occlusion (CGO), group function occlusion (GFO) and lingualized occlusion (LO). The von Mises stress values for abutment and screws and deformation values for prostheses were obtained and results were evaluated comparatively. It was observed that the stresses on screws and abutments were more evenly distributed in GFO. Maximum deformation values for prosthesis were observed in the CFO model for lateral movement both in the maxilla and mandible. Within the limits of the present study, GFO may be suggested to reduce stresses on screws, abutments and prostheses in the All-on-Four concept.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

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