Probability Distribution of von Mises Stress in the Presence of Pre-load

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]

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Probability Distribution of Peaks for Nonlinear Combination of Vector Gaussian Loads

Journal of Vibration and Acoustics ◽

10.1115/1.2890404 ◽

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.

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

Journal of Oral Implantology ◽

10.1563/aaid-joi-d-19-00334 ◽

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.

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

Reports in Mechanical Engineering ◽

10.31181/rme200101093s ◽

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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Numerical Investigation of the Deformable Porous Media Treated by the Intermittent Microwave

Processes ◽

10.3390/pr9050757 ◽

2021 ◽

Vol 9 (5) ◽

pp. 757

Author(s):

Tianyi Su ◽

Wenqing Zhang ◽

Zhijun Zhang ◽

Xiaowei Wang ◽

Shiwei Zhang

Keyword(s):

Porous Media ◽

Heat Transport ◽

Liquid Water ◽

Von Mises Stress ◽

Temperature Deformation ◽

Local Maxima ◽

Whole Process ◽

Surface Areas ◽

Pulse Ratio ◽

Von Mises

A 2D axi-symmetric theoretical model of dielectric porous media in intermittent microwave (IMW) thermal process was developed, and the electromagnetic energy, multiphase transport, phase change, large deformation, and glass transition were taken into consideration. From the simulation results, the mass was mainly carried by the liquid water, and the heat was mainly carried by liquid water and solid. The diffusion was the dominant mechanism of the mass transport during the whole process, whereas for the heat transport, the convection dominated the heat transport near the surface areas during the heating stage. The von Mises stress reached local maxima at different locations at different stages, and all were lower than the fracture stress. A material treated by a longer intermittent cycle length with the same pulse ratio (PR) tended to trigger the phenomena of overheat and fracture due to the more intense fluctuation of moisture content, temperature, deformation, and von Mises stress. The model can be extended to simulate the intermittent radio frequency (IRF) process on the basis of which one can select a suitable energy source for a specific process.

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Finite Element Analysis of Composite Repair for Damaged Steel Pipeline

Coatings ◽

10.3390/coatings11030301 ◽

2021 ◽

Vol 11 (3) ◽

pp. 301

Author(s):

Jiaqi Chen ◽

Hao Wang ◽

Milad Salemi ◽

Perumalsamy N. Balaguru

Keyword(s):

Finite Element ◽

Shear Stress ◽

Hoop Stress ◽

Pipe Wall ◽

Von Mises Stress ◽

Repair System ◽

Composite Repair ◽

Steel Pipeline ◽

Von Mises ◽

Infill Material

Carbon fiber reinforced polymer (CFRP) matrix composite overwrap repair systems have been introduced and accepted as an alternative repair system for steel pipeline. This paper aimed to evaluate the mechanical behavior of damaged steel pipeline with CFRP repair using finite element (FE) analysis. Two different repair strategies, namely wrap repair and patch repair, were considered. The mechanical responses of pipeline with the composite repair system under the maximum allowable operating pressure (MAOP) was analyzed using the validated FE models. The design parameters of the CFRP repair system were analyzed, including patch/wrap size and thickness, defect size, interface bonding, and the material properties of the infill material. The results show that both the stress in the pipe wall and CFRP could be reduced by using a thicker CFRP. With the increase in patch size in the hoop direction, the maximum von Mises stress in the pipe wall generally decreased as the maximum hoop stress in the CFRP increased. The reinforcement of the CFRP repair system could be enhanced by using infill material with a higher elastic modulus. The CFRP patch tended to cause higher interface shear stress than CFRP wrap, but the shear stress could be reduced by using a thicker CFRP. Compared with the fully bonded condition, the frictional interface causes a decrease in hoop stress in the CFRP but an increase in von Mises stress in the steel. The study results indicate the feasibility of composite repair for damaged steel pipeline.

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