Lori Graham
Johns Hopkins University
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Featured researches published by Lori Graham.
Probabilistic Engineering Mechanics | 2001
Lori Graham; George Deodatis
Abstract The variability of the random response displacements and eigenvalues of structures with multiple uncertain material and geometric properties are studied in this paper using variability response functions. The material and geometric properties are assumed to be described by cross-correlated stochastic fields. Specifically, two types of problems are considered: the response displacement variability of plane stress/plane strain structures with stochastic elastic modulus, Poissons ratio, and thickness, and the eigenvalue variability of beam and plate structures with stochastic elastic modulus and mass density. The variance of the displacement/eigenvalue is expressed as the sum of integrals that involve the auto-spectral density functions characterizing the structural properties, the cross-spectral density functions between the structural properties, and the deterministic variability response functions. This formulation yields separate terms for the contributions to the response displacement/eigenvalue variability from the auto-correlation of each of the material/geometric properties, and from the cross-correlation between these properties. The variability response functions are used to compute engineering-wise very important spectral-distribution-free realizable upper bounds of the displacement/eigenvalue variability. Using this formulation, it is also possible to compute the displacement/eigenvalue variability for prescribed auto- and cross-spectral density functions.
Structural Safety | 1998
Lori Graham; George Deodatis
In this paper, the weighted integral method and the concept of variability response function are successfully extended to plate bending problems where the elastic modulus of the structure is considered to be a two-dimensional, homogeneous stochastic field, overcoming earlier computational problems associated with the large number of terms in the expression for the variability response function. The concept of the variability response function is used to compute spectral-distribution-free upper bounds of the response variability. Such bounds are of paramount importance for the majority of real-life problems where only first and second moments of the stochastic material properties can be estimated with reasonable accuracy. Under the assumption of a prespecified power spectral density function of the stochastic field describing the elastic modulus, it is also possible to compute the response variability (in terms of second moments of response quantities) and the reliability (in terms of the safety index) of the stochastic plate. The use of a variability response function based on the local averaging method reduces the computational effort associated with the weighted integral method, with only a small loss of accuracy in most cases. Numerical examples are provided to demonstrate all of the above capabilities. One of the conclusions is that the coefficient of variation of certain response quantities can become larger than the coefficient of variation of the elastic modulus (the input quantity).
Probabilistic Engineering Mechanics | 2001
Lori Graham; Sarah C. Baxter
Abstract When analyzing the behavior of composite materials under various loading conditions, the assumption is generally made that the behavior due to randomness in the material can be represented by a homogenized, or effective, set of material properties. This assumption may be valid when considering displacement, average strain, or even average stress of structures much larger than the inclusion size. The approach is less valid, however, when considering either behavior of structures of size at the scale of the inclusions or local stress of structures in general. In this paper, Monte Carlo simulation is used to assess the effects of microstructural randomness on the local stress response of composite materials. In order to achieve these stochastic simulations, the mean, variance and spectral density functions describing the randomly varying elastic properties are required as input. These are obtained here by using a technique known as moving-window generalized method of cells (moving-window GMC). This method characterizes a digitized composite material microstructure by developing fields of local effective material properties. Once these fields are generated, it is straightforward to obtain estimates of the associated probabilistic parameters required for simulation. Based on the simulated property fields, a series of local stress fields, associated with the random material sample under uniaxial tension, is calculated using finite element analysis. An estimation of the variability in the local stress response for the given random composite is obtained from consideration of these simulations.
International Journal of Solids and Structures | 2001
Sarah C. Baxter; M.I Hossain; Lori Graham
Particle reinforced metal matrix composites offer a number of advantages over continuously reinforced composites. They generally can be made using conventional metal-working processes and often fabricated to near net shape. Like continuously reinforced composites though, the potential exists to tailor these materials for higher specific stiffnesses, greater strength and improved fracture properties over their homogeneous counterparts. Their effective use requires an accurate characterization, which is made difficult by a three-dimensional (3D) random microstructure. A micromechanics based moving window technique, used to develop material property fields associated with the random 3D microstructure of a particulate reinforced composite, is described in this paper. The resulting sample material property fields are computationally tractable and have a direct link to the composite microstructure. The method can be used to generate material property fields for elastic or inelastic properties. Statistical and probabilistic descriptions of these property fields can subsequently be used to simulate the material and characterize the variability of the material response. The method is illustrated in this paper by generating fields for selected elastic moduli developed from a numerically simulated microstructure.
Composites Science and Technology | 2001
Erik A. Phillips; Carl T. Herakovich; Lori Graham
Abstract Implementation of a meso-scale damage model into the commercial finite element code ABAQUS via user-defined FORTRAN subroutines is described, and the results of investigations on damage development in structural configurations with large stress gradients are presented for carbon-fiber/polymer-matrix composites. The implemented model, which involves damage in both the meso-scale layer and an interface between the layers, is applied in a study of damage growth in finite-width angle-ply coupons and a composite panel with a terminated stiffener. The definition and evolution of state-dependent variables for layer damage is accomplished by means of a user-defined subroutine and the damageable interface is accomplished by using a user-defined element. It is demonstrated that as the fiber orientation progresses from 10 to 45°, the mode of damage changes from interlaminar damage, (i.e. delamination) to intralaminar damage, consistent with experimental observations. Analysis of damage development in the composite panel subjected to uniform compression shows that interlaminar shear stresses produce delamination at the skin-stiffener interface before failure of the panel due to tensile fiber rupture,— again consistent with experimental observations.
Probabilistic Engineering Mechanics | 2003
Lori Graham; Kurtis R. Gurley; Forrest J. Masters
In this paper, a moving-window micromechanics technique, Monte Carlo simulation, and finite element analysis are used to assess the effects of microstructural randomness on the local stress response of composite materials. The randomly varying elastic properties are characterized in terms of a field of local effective elastic constitutive matrices using a moving-window technique based on a finite element model of a given digitized composite material microstructure. Once the fields are generated, estimates of the random properties are obtained for use as input to a simulation algorithm that was developed to retain spectral, correlation, and non-Gaussian probabilistic characteristics. Rapidly generated Monte Carlo simulations of the constitutive matrix fields are used in a finite element analysis to create a series of local stress fields associated with the random material sample under uniaxial tension. This series allows estimation of the statistical variability in the local stress response for the random composite. The identification of localized extreme stress deviations from those of the aggregate or effective properties approach highlight the importance of modeling the stochastic variability of the microstructure.
Measurement Science and Technology | 2003
Jennifer J. Hooper; Timothy J. Foecke; Lori Graham; Timothy P. Weihs
The discovery of the RMS Titanic has led to a number of scientific studies, one of which addresses the role that structural materials played in the sinking of the ship. Early studies focused on the quality of the hull steel as a contributing factor in the ships rapid sinking, but experimental results showed that the material was state-of-the-art for 1911. Instead, it was suggested that the quality of the wrought iron rivets may have been an important factor in the opening of the steel plates during flooding. Here the quality of RMS Titanic wrought iron is examined and compared with contemporary wrought iron obtained from additional late 19th-/early 20th-century buildings, bridges, and ships. Traditional metallurgical analysis as well as compositional analysis, mechanical testing, and computer modeling are used to understand the variation in the mechanical properties of wrought iron as a function of its microstructure.
Shock and Vibration | 1998
Lori Graham
The variability of the maximum response displacement of random frame structures under deterministic earthquake loading are examined in this paper using stochastic finite element techniques. The elastic modulus and the mass density are assumed to be described by cross-correlated stochastic fields. Specifically, a variability response function formulation is used for this problem, which allows for calculation of spectral-distribution-free upper bounds of the maximum displacement variance. Further, under the assumption of prespecified correlation functions describing the spatial variation of the material properties, variability response functions are used to calculate the corresponding maximum displacement variance. Two numerical examples are provided to demonstrate the methodology. Results show that randomness in the material properties can lead to significant uncertainty in the maximum response displacement.
Journal of Engineering Mechanics-asce | 2001
Lori Graham; E. F. Siragy
Archive | 1997
George Deodatis; Lori Graham