Glen H. Besterfield

Transient probabilistic systems

Abstract The probabilistic finite element method (PFEM) for the transient analysis of random field problems by the finite element method is presented with improved computational procedures. The theoretical development of PFEM is reviewed with the inclusion of a transformed uncorrelated random variable, the formulation of the decoupled PFEM equations, and the computations of the probabilistic distributions. A method is presented to reduce the PFEM equations to a smaller system of tridiagonal equations. The reduction scheme is based on a highly efficient Lanczos algorithm which forms a reduced basis from the system eigenproblem. The application of PFEM via a sensitivity method for transient problems can result in the emergence of undesirable secular terms. A method based on Fourier analysis is presented for removing secularities from the PFEM. The effectiveness of the Lanczos reduction technique and the secularity elimination scheme is demonstrated with application to a linear continuum problem and potential applications to nonlinear problems are discussed.

Fatigue crack growth reliability by probabilistic finite elements

Abstract Failure of components due to fatigue crack growth is a major problem in industry. The failure process initiates with the presence of small cracks which can cause catostrophic fracture or slow crack growth. When treating a problem of this type, many aspects of the problem should be treated as random variables. The probabilistic finite element method (PFEM) has been shown to be a practical approach for solving problems of this type. In this paper, the fusion of the PFEM and reliability analysis for probabilistic fatigue crack growth is presented. A comprehensive method for determining the probability of fatigue failure for mixed-mode cyclic loading is also presented. The loading is mixed-mode with randomness in the initial and final crack lengths, initial crack angle and position, material properties, crack growth law, crack direction law and loading. The methodology consists of calculating the reliability index via an optimization procedure, which is used to calculate the probability of fatigue failure. Performance of the methodology presented is demonstrated on a classical mode I fatigue problem.

Mechanics of multiple periodic brittle matrix cracks in unidirectional fiber-reinforced composites

Abstract A fracture model based on two-dimensional plane stress-strain elasticity theory is developed for the problem of periodic, interacting and regularly spaced matrix cracks in a unidirectional fiber-reinforced brittle matrix composite. The solution is obtained in terms of a hypersingular integral equation. The effects of the fiber reinforcement, and the spacing, the location and the length of cracks on the stress intensity factors at the crack tips and the maximum crack opening displacement in the composite are studied.

Holistic but customized resources for a course in numerical methods

Prototype web based resources have been developed for an undergraduate course in Numerical Methods. The web modules are holistic, that is they include pre‐requisite information, real‐life applications, presentations and notes, simulations, and self‐assessment. The student interest and learning are maximized by providing customization of content based on a students engineering major and computational system of choice.

Assembly Procedures of Trunnion-Hub-Girder for Bascule Bridges

Abstract This work is concerned with avoiding failures during the assembly of a trunnion–hub–girder (THG) for bascule bridges. In the current assembly procedure, AP#1, the trunnion is shrunk fit into the hub, followed by the shrink fitting of the trunnion–hub assembly into the girder. Two separate incidents during assembly prompted this study. The first incident involved the development of cracks in the hub during the assembly process using AP#1. The second incident involved the trunnion getting stuck in the hub before the trunnion could be fully inserted. A complete analytical, numerical, and experimental study was conducted to understand these failures, and the results were used to develop specifications and recommendations for assembly. The causes of failures include the development of high stresses at low temperatures during assembly, while noting that fracture toughness of THG materials decreases with temperature. Recommended specifications included following an alternative assembly procedure that nearly doubles allowable crack length, and that lowers cooling temperatures to avoid trunnion sticking in the hub.

Effect of extrinsic and intrinsic factors on an indentation test

The effect of intrinsic and extrinsic factors on the measured results, such as load-displacement curves and interfacial stresses, from indentation tests of composite materials is studied using both analytical and finite element models. The intrinsic factors include properties of the fiber-matrix interface and the material symmetry of the fiber (transversely isotropic or isotropic). The extrinsic factors include the radius of the hole through which the fiber is pushed in, and the size and shape of the indentor. Out of the above factors, only the radius of the hole is found to have a negligible effect on the results of the indentation test.

Comparison of interphase models for a crack in fiber reinforced composite

Abstract The influence of a nonhomogeneous interphase on fracture mechanics of a fiber reinforced composite is studied. The stress intensity factor at the crack tips, maximum interfacial shear and normal stresses, maximum cleavage stress in the matrix and load diffusion along the length of the fiber are studied as a function of the fiber width, the interphase thickness, and the relative stiffness properties of the fiber, the matrix and the interphase. The normal stresses at the interface, which represents the possibility of debonding of the interface, is lowest for interphase thicknesses of the order of one-tenth of the fiber-diameter, when the crack is in the stiffer material. These normal stresses are highest at such interphase thicknesses if the crack is in the less stiffer material. The results obtained by using the nonhomogeneous interphase model are also compared with five other interphase models used in the literature for the interphase, namely the perfect, the homogeneous, the distributed uncoupled shear and normal springs, and the distributed shear springs. It is found that the trends of the above parameters as a function of interphase thicknesses are different for the spring and continuum models, if the crack is in a stiffer material.

Integrating a Research Problem in a Course in Applied Elasticity

An example of integrating a single research problem over a broad range of topics in a graduate-level course in applied elasticity (advanced strength of materials) is given in this paper. The research problem was obtained from an investigation of failures during the assembly of fulcrums of bascule bridges. Topics exemplified by using this problem included interference fits, axisymmetric problems, transformation of strains and stresses, comparison of failure theories, and the effect of temperature-dependent thermoelastic properties.

Effects of Staged Cooling in Shrink-Fitting Compounded Cylinders

This paper studies the effect of staged cooling of compounded cylinders in avoiding cracking due to the presence of large interference stresses and low fracture toughness in the presence of cryogenic temperatures. This study is motivated by the assembly procedure of the fulcrum (a compounded trunnion-hub assembly) of bascule bridges, where the fulcrum is shrunk by immersion in liquid nitrogen so that it can then be fitted into the girder of the bridge. In a few cases, the fulcrum developed cracks during the immersion in liquid nitrogen. To study the effect of staged cooling to avoid such cracking, a finite difference model was developed of a long compounded cylinder with axisymmetric response with temperature-dependent properties. The study showed that the resistance to failure was increased by as much as 50 per cent when the compounded cylinder is cooled first in a refrigerated air chamber and followed by immersion in liquid nitrogen.

Use of adjoint methods in the probabilistic finite element approach to fracture mechanics

The adjoint method approach to probabilistic finite element methods (PFEM) is presented. When the number of objective functions is small compared to the number of random variables, the adjoint method is far superior to the direct method in evaluating the objective function derivatives with respect to the random variables. The PFEM is extended to probabilistic fracture mechanics (PFM) using an element which has the near crack-tip singular strain field embedded. Since only two objective functions (i.e., mode I and II stress intensity factors) are needed for PFM, the adjoint method is well suited.