We consider steady state unsaturated flow in bounded randomly heterogeneous soils under influence of random forcing terms. Our purpose is to predict pressure heads and fluxes and evaluate uncertainties associated with these predictions, without resorting to Monte Carlo simulation, upscaling or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. Following Tartakovsky et al. [1999], by assuming that the Gardner model is valid and treating the corresponding exponent a as a random constant, the steady-state unsaturated flow equations can be linearized by means of the Kirchhoff transformation. This allows us develop exact integro-differential equations for the conditional first and second moments of transformed pressure head and flux. The conditional first moments are unbiased predictions of the transformed pressure head and flux, and the conditional second moments provide the variance and covariance associated with these predictions. The moment equations are exact, but they cannot be solved without closure approximations. We developed their recursive closure approximations through expansion in powers of σᵧ and σᵦ, the standard deviations of Y = lnK(s), and β = ln α, respectively, where K(s), is saturated hydraulic conductivity. Finally, we solve these recursive conditional moment equations to second-order in σᵧ and σᵦ, as well as second-order in standard deviations of forcing terms by finite element methods. Computational examples for unsaturated flow in a vertical plane, subject to deterministic forcing terms including a point source, show an excellent agreement between our nonlocal solutions and the Monte Carlo solution of the original stochastic equations using finite elements on the same grid, even for strongly heterogeneous soils.

Not available / text

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

The purpose of this dissertation is to establish a unified theory of porohyperelasticity with transport and growth and to demonstrate the capability of this theory using a finite element model developed in MATLAB. The theory of volumetric growth is combined with the theory of mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new method that models growth of biological soft tissues. The conservation equations and constitutive equations are developed for both solid-only growth and solid-fluid growth. An axisymmetric finite element framework is introduced for the new theory of growing MPHETS (GMPHETS). To demonstrate the difference of the GMPHETS model from a traditional hyperelastic (HE) growth model, several finite element test problems with example growth laws are considered, including time-dependent, concentration-dependent, and stress-dependent growth. In particular, this work demonstrates that the solid-only growth of an MPHETS model of a stylized artery results in a more uniform hoop stress than in a HE model under solid-only growth for the same amount of growth time using the same growth law. This may have implications in the context of developing residual stresses in soft tissues under intraluminal pressure. To my knowledge, this is the first description of an MPHETS model with growth. The developed computational framework can be used together with novel in-vitro and in-vivo experimental approaches to identify the governing growth laws for various soft tissues.

The results of a study to model a circular mine shaft constructed in a time-dependent medium are presented. The construction sequence is considered as well as the time-dependent properties of the media around the shaft. The loads acting on the shaft liner are due to excavation of the shaft material and to the loads relieved from the media onto the liner. The results show the importance of considering the time-dependent behavior of media. The analysis was carried out using the Finite Element Method. Axisymmetric triangular and quadrilateral elements were used to model the medium, and axisymmetric shell elements were used to model the liner. The construction sequence was modeled by analyzing the system under small load increments where each load increment represents a construction step. The time behavior was modeled by using the initial strain method, which assigns a different strain value for each element in the medium. The strains are transferred to stresses and then to forces, and an incremental process is started to cover the time range desired. The results for a 400-foot shaft are shown, and changes in liner stresses were monitored as time passes. Different rock materials were modeled by using different constants in the creep law. Some materials showed significant changes in the results, and others did not. The liner horizontal displacement, and horizontal and vertical stresses increased when material constants for rock salt and anhydrite were used. Stresses in the elements adjacent to the liner decreased as time passed by, and some even went into a tensile stress site. A comparison between two solutions, one representing a multi-step construction sequence and another representing an instantaneous construction of the lined shaft, showed that liner stresses are much higher when the construction sequence is not modeled. This is due to the fact that when the excavation is modeled the forces representing the construction sequence are applied to the medium. In the other case, the forces are directly applied to the liner.

A computer algorithm is developed for clipping and capping N-sided polyhedra with arbitrary planes. The algorithm is then expanded to include the processing of general two and three dimensional geometric finite element model data. Data processing is included for the transformation of original model results to match the clipped and capped graphical display model. The algorithms are implemented in a FORTRAN program that may be directly substituted into the MOVIE.BYU/ARIZONA graphics system. The new SECTION program maintains all the functions of the original version while incorporating several major new features. These new features include the expansion of the geometric library to two and three dimensional elements and two new general forms for polygons and polyhedra. Another significant change in the processing is the implementation of the reentrant clipping and capping routines. This feature permits a previously clipped model to be clipped again and again by new and different clipping planes. The above features as well as enhanced input data schemes including a preliminary interface to NASTRAN are offered as a skeleton for future modifications. The major routines in the program have taken advantage of dynamic memory allocation via FORTRAN subroutine argument calls. Through this latter feature new capability can be concatenated to the end of the current processing in a prototype manner for rapid implementation and exploration.

Many applications require deployable structures to meet operational objectives such as satellites that unfurl antenna arrays. Typically, most deployment efforts involve the use of explosive and non-explosive actuators (EAs and NEAs respectively) that have implementation drawbacks such as the expense associated with special handling and the bulk encountered with mounting the devices. To mitigate EA and NEA drawbacks, the integration of shape memory alloys (SMA) as a deployment actuator was investigated. SMA specimens were heated and pulled to failure developing an environmental and structural operating envelope for application as deployment mechanisms. A Finite Element Model (FEM) was also created to model the response behavior induced during specimen testing so that modeled performance could be used in lieu of testing when integrating SMA actuators into deployment systems. Experimental results verified that SMAs can be implemented as deployment actuators. Recorded data showed that SMA fracture is possible over a wide range of temperatures and strains, filling a material performance gap not found in the literature. The obtained information allows design engineers to appropriately size SMAs given design requirements achieving the desired deployment effects. The Finite Element Model was partially successful, capable of emulating strained ambient material behavior up to approximately 6.1%. The limited response is due to lack of experimentally derived large stress and strain available for model emulation.

No description available.