Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Fatigue Reliability Functions in Semilogarithmic Coordinates

In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (lnN-lnS). Here, a similar transformation is established using a semi logarithmic (lnN-S) coordinate system. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life distribution.

A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential function of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various equipments. This paper deals with the system having components in series arrangement. Bayesian statistics is used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of reliability measures: 1) failure and repair rates, 2) mean time to failure, 3) mean time to repair, 4) reliability function and 5) availability. A sample problem is given to illustrate the methodology. The Bayesian estimation of the stepwise exponential distribution model is useful in the planning of equipment predictive maintenance.

Auger Elevator: Failure Modes and Effects Case Study

A fatal accident occurred when a right angle gear box on an auger elevator disintegrated freeing the outboard end of a rotating PTO shaft. The tractor, acting as a stationary power source, flailed the PTO shaft which then struck and killed a farmer. No similar occurrences have been reported for the nearly 2000 similar units which have been used for over a decade. This paper studies a number of fundamental failure modes in order to determine which failure modes created the accident. Systematic analysis showed that the accident was caused by unusual misuse of the product. Known safety control concepts do not preclude this unforeseeable event.

DIscrepancy of Gear Tooth Allowable Bending Stress Using the Extreme Value Distribution From Different Test Methods

The allowable bending stress Se of a gear tooth is one of the basic factors in gear design. It can be determined by either the pulsating test or the gear-running test. However, some differences exist between the allowable bending stress Se obtained from these different test methods. In this paper, the probability distribution functions corresponding to each test method are analyzed and the expressions for the minimum extreme value distribution are presented. By using numerical integration, Se values from the population of the same tested gear tooth are obtained. Based on this investigation it is shown that the differences in Se obtained from the different test methods are significant. A proposed correction factor associated with the different experimental approaches is also presented.

Prediction of the Strength of Ceramic Tubular Components: Part II — Experimental Verification

The strength distribution of reaction bonded silicon carbide tubes that failed by internal pressurization was predicted from strength distributions obtained from simple laboratory test specimens at room temperature. The strength distributions of flexure bars, C-rings tested in tension, C-rings tested in compression, diametrally compressed O-rings, and internally pressurized short tubes were compared to the strength distribution of internally pressurized long tubes. The methodology involved application of Weibull statistical theory using elasticity theory to define the stress distributions in the simple specimens. The flexural specimens did not yield acceptable results, since they were ground prior to testing, thereby altering their flaw population in comparison with the processing induced flaw populations of the tubular specimens. However, the short tube internal pressure test, the c-ring tested in tension and the diametrally compressed o-ring test configurations yielded accurate predictions, since these specimens more accurately represent the strength limiting flaw population in the long tubes.

Electric Resistive Heat Curing of the Fiber-Matrix Interphase in Graphite/Epoxy Composites

A novel method for tailoring the interphase of carbon fiber-polymer composites by resistive electric heating is presented. The single fiber-epoxy resin tensile test is used to investigate the adhesion and fracture properties of the interphase. Electric resistive heating is shown to increase adhesion and toughness at the interphase region. In analyzing the results, the strength and fracture energy of the interphase are related to the thermal postcure conditions created by resistive electric heating. For this purpose, difference analysis method is used to obtain numerical solution for heat conduction problem in the single fiber test specimen and the temperature distributions are plotted. Improvements obtained using resistive electric heating via carbon fiber are compared with those obtained by postcuring of the whole sample via convective thermal postcuring. The results obtained using these two different postcure methods seem to be similar with electric heating procedure producing superior benefits in both increased toughness and adhesion.

A Probabilistic Methodology for Random Stress-Strain Curves

This paper presents a methodology for analyzing structures with random stress-strain behavior. Uncertainties in the stress-strain curve of a structure are simulated by letting a small number of engineering parameters which describe the stress-strain curve be random. Certain constraints are imposed on the engineering parameters in order to have a physically realizable material. A general procedure to handle correlation among the stress-strain parameters has also been developed. This methodology has been integrated into the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) probabilistic structural analysis system. With this system, probabilistic finite element analysis of structures with random stress-strain behavior can be analyzed in an accurate, automated fashion. An example problem is presented to demonstrate the capabilities of the code. The problem analyzed is that of a pressure vessel fabricated with a material exhibiting random stress-strain behavior.

Estimation of Structural Reliability Under Random Fatigue Conditions

A procedure for determining the reliability of a structural element or machine part is presented. The solution assumes that the stress history in the part can be described by a narrow band, stationary, Gaussian random process and that the fatigue behavior of the part is governed by the classical S-N curve. Endurance limit modifications are discussed and a procedure is presented for determining the mean and standard deviation of the static stresses acting throughout a structure. A numerical example is presented showing the method applied to estimate the fatigue reliability of a power wheelchair frame.

Combined Stress and Resistance Modeling With the Nessus Software System

Computing the reliability of structural components with uncertainties in both stress and resistance variables is investigated. The NESSUS™ probabilistic software is used to perform the reliability computations using both Fast Probability Integration (FPI) and Monte Carlo methods. Results are compared for an example reliability analysis using both closed-form expressions and finite elements. The Advanced Mean Value probabilistic algorithm is used and is shown to yield highly accurate results, even for highly nonlinear response functions. The results show clearly the effectiveness of the newly incorporated algorithms available in the NESSUS software for computing structural reliability.