Browsing by Author "Nordgren, Ronald P."
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Item An investigation of laser-welded corrugated-core sandwich beams and plates stiffened with concrete(2000) McCullough, Shawn Rita; Nordgren, Ronald P.This thesis focuses on the behavior of a corrugated-core sandwich panel with a concrete top layer under normal loads applied to the concrete face. This sandwich panel is composed of two steel face plates separated by a corrugated sheet welded to them at its crests and troughs. A concrete layer is placed on the top face of the sandwich panel, utilizing shear connectors to ensure composite action. The objective of this study is to examine the structural behavior of these composite panels. This thesis intends to provide design capabilities for applications in which this type of sandwich panel is well suited, e.g., emergency bridge repair, building floors, or fire walls. The panels are analyzed using both elementary beam theory (for narrow panels) and the classical theory of orthotropic plates. In order to complete the theory, the bending stiffnesses in the various directions are determined by structural analysis. To verify the theory, extensive experimental testing has been performed on the sandwich panels. It is found that compression of the core accounts for a majority of the deflection in the relatively thick specimens tested here. Measured deflections are compared with those obtained theoretically, and after corrections are made for core compression, they are in fair agreement.Item Analysis of laser-welded sandwich plates(1993) Hussain, Khaled Said; Nordgren, Ronald P.A comprehensive study is made of two types of sandwich plates under normal loads applied to their faces. The plates are composed of two plate facings separated by, and laser-welded to, either corrugated sheets or standard I-beams. The objective of this study is to provide the capability to design these plates for technical applications which require high bending stiffnesses. The plates are analyzed according to classical plate theory. The four stiffnesses of the orthotropic plates are derived from the component properties of the plates. The finite element method is used to analyze the plates. The plate models are constructed using three-dimensional elements and the deflections, strains, and stresses are evaluated for different sections. Experimental loading tests were performed on the two sandwich plates. The deflections and strains recorded during loading compared satisfactorily with the results of both theoretical solutions.Item Probabilistic analysis of the plastic collapse of random media(1997) Ku, Pao-Ding Albert; Nordgren, Ronald P.Two new, efficient probabilistic methods are presented for evaluating the reliability of an elastic/perfectly plastic continuous medium exhibiting randomly varying yield strength. Both the Tresca and Mohr-Coulomb yield criteria are considered in the present study. The two probabilistic methods developed are based on the upper and lower bound theorems of plastic limit analysis. By extending these two theorems to probabilistic cases the upper bound and lower bound reliability indices of a safety problem can be calculated for the elastic/plastic medium. Both two and three-dimensional problems are studied. These include a two-dimensional (2-D) wedge loaded on one face and the bearing capacity of a strip footing under constant normal pressure. Both the classical Prandtl and Hill mechanisms are considered for this strip footing problem and the Hill mechanism is found to be more critical probabilistically. The three-dimensional (3-D) problem considered is the extension of the 2-D problem wedge problem. In the 3-D problem the failure length in the longitudinal direction and the resisting strength provided by two vertical end sections play important roles in the reliability calculations, and numerical results are given to illustrate these effects. The spatially varying yield strength is modeled as a Gaussian random field in two or three dimensions, depending on which type of problems is analyzed. Several existing methods to discretize the random fields are reviewed, and their advantages and disadvantages when applied to the plastic random media problems are addressed. It is shown that the limit state functions in the upper bound reliability method can be formulated as linear ones and for the lower bound reliability method the limit state function is formulated as a linear programming problem. The proposed methods provide efficient analytical tools for the probabilistic analysis and design for continuous load-carrying media whose failure is defined by their plastic limit state. The reliability methods presented in this study can be applied to several important classes of problems in geotechnical engineering and are potentially applicable to the plastic failure of plates and shells.Item Probabilistic analysis of the stability of imperfection sensitive arch and shell structures(1996) Hussain, Khaled Said; Nordgren, Ronald P.The stability of arch and shell structures with random imperfections subjected to random loading is investigated. Arches are analyzed under different types of transverse loads while axial and/or pressure loading are considered for cylindrical shells. A probabilistic analysis of the randomness in the geometric imperfections along with the uncertainty in both loading and material properties is presented. The study investigates the effect of spatial variability of the different random parameters in the problem on the buckling load and the associated displacements. The imperfection sensitivity is studied for several geometrical configurations of the arches and shells and for various values of the statistical parameters for the random shape imperfections. One- and two-dimensional random fields are introduced with different types of autocorrelation functions to characterize the structures and the imperfections. A sufficient number of terms is considered using two series expansion methods to express the field in terms of its spectral decomposition. The first employs the Karhunen-Loeve theorem where the autocorrelation coefficient function is expanded in terms of its eigenvalues and eigenfunctions, while the second method utilizes any complete set of orthogonal functions. These techniques are compared with both the midpoint and local averaging methods for random field discretization and prove to be more computationally efficient within a given level of accuracy. Both first- and second-order reliability methods (FORM/SORM) along with Monte Carlo simulation are used to evaluate different modes of instability based on the buckling load or the associated displacements. The probability density and the cumulative distribution functions of the buckling load are presented for various distributions of the imperfections. The sensitivity of the buckling load and the postbuckling displacements to different parameters is also presented. An extensive parametric study through many numerical examples is performed to establish a better understanding of the effects of the spatially variable imperfections on the buckling of arches and shells.Item Reliability analyses of the collapse and burst of elastic/plastic tubes(2001) Li, Guang; Nordgren, Ronald P.; Durrani, Ahmad J.The innovative methods proposed in this thesis provide effective and efficient solutions to the reliability problems of burst and collapse of tubes with random geometric imperfections under internal or external pressure. Steel tubes have broad applications in petroleum offshore engineering and must be designed to a safe but yet economical standard. The variation of imperfections from tube to tube necessitates a statistical characterization in which the burst and collapse pressures become random variables. In order to evaluate the burst and collapse pressure of a pipe with deterministic geometric imperfections, the finite element method is employed with a cylindrical shell element based on classical nonlinear shell theory. This element implements the return mapping algorithm for an elastic/plastic material and includes the effects of shell thinning and geometric imperfections. Incorporation of this finite element program into a reliability program developed for this study provides an effective numerical tool for the probabilistic analyses of the burst and collapse problems. For these analyses, the pipe thickness is modeled as an axially homogeneous and circumferentially inhomogeneous Gaussian random field based on measured data from two groups of pipes. Using the developed shell finite element program, Monte Carlo simulation (MCS) can be applied to the burst/collapse reliability problems. However, the enormous computational effort makes MCS infeasible except as a check for selected cases. Unfortunately, the system reliability method does not apply to the present problems because there are an infinite number of design points due to the special structure of the imperfections. Thus, a new approximate method is developed for the burst problem based on the correlations between the minimum thickness and burst pressure. The probability distribution of minimum thickness is obtained through an innovative homogenization procedure. Similarly, the collapse reliability problem is solved through introduction of a homogenized collapse function whose minimum correlates with the collapse pressure. The proposed reliability methods are applied to selected cases and verified by MCS. The effect of length on reliability in burst and collapse is investigated. Compared to MCS, the efficiency of the new methods makes them especially applicable to engineering problems, such as pipeline design and manufacturing quality control.Item Stability of elastic/plastic columns and circular rings with random geometric imperfections(1998) Kondubhatla, Subba Rao Venka; Nordgren, Ronald P.The stability of elastic/plastic columns and circular rings with random geometric imperfections is investigated. Columns are analyzed for axial loading and rings for uniform external pressure. A procedure is developed to evaluate the reliability of imperfect elastic/plastic columns and rings against instability. The geometric imperfections are modeled as Gaussian random field in one dimension with given mean, variance, and covariance functions. The random field is discretized by the method of orthogonal series expansion using a Fourier series. The weak form of the boundary value problems for column and ring is formulated using Galerkin's method. A mixed finite element is used in which the primary degrees of freedom are transverse deflection and bending moment. For illustration purposes the material behavior is taken as elastic/perfectly plastic. The computationally efficient first- and second-order reliability methods are used to evaluate the failure probabilities and Monte Carlo simulation is used as a check. The variation of the probability of failure of columns and rings over a range of applied loads is presented for different amounts of random geometric imperfections.