MCE - Department of Mechanical and Civil Engineering

The evolution of designs in nature has been the inspiration for this thesis, which seeks to develop a framework for efficient automatic engineering design synthesis based on evolutionary methods. The design synthesis process is equated to an evolutionary process. Because of this, the same formalization for evolution, the evolution algorithm, is used as a design synthesis formalism. Implementation of the evolution algorithm on a computer allows evolution of non-biological systems, and, hence, automatic engineering design synthesis. The early and canonical versions of such evolutionary computation are bare bones evolution tools that neglect several key aspects of evolutionary systems. Some universal aspects of good designs are identified, three of which are dealt with in this thesis. These are variable complexity, modularity, and speciation. Framed in an evolutionary context, each of these characteristics are requisites for being able to evolve in correspondence with a dynamic environment. Those that are most evolvable will survive. After all, if a species cannot evolve quickly enough with changes in the environment, it will perish. In a design context, this indicates that the characteristics are vital for efficiency and shorter design cycles. An integrated framework is developed to address all three aspects individually or in any combination thereof, which has not been done heretofore. Because of the poor theoretical foundations of evolutionary computation, the effectiveness of the developed approach is determined through computer experimentation on several test and design problems. Results are promising as all three aspects were successfully achieved in comparison to canonical evolutionary computation.

Each stage of the engineering design process, and particularly the preliminary phase, includes imprecision, stochastic uncertainty, and possibilistic uncertainty. A technique is presented by which the various levels of imprecision (where imprecision is: uncertainty in choosing among alternatives) in the description of design elements may be represented and manipulated. The calculus of Fuzzy Sets provides the foundation of the approach. An analogous method to representing and manipulating imprecision using probability calculus is presented and compared with the fuzzy calculus technique. Extended Hybrid Numbers are then introduced to combine the effects of imprecision with stochastic and possibilistic uncertainty. Using the results, a preliminary set of metrics is proposed by which a designer can make decisions among alternative configurations in preliminary design.In general, the hypothesis underlying the techniques described above is that making more information available than conventional approaches will enhance the decision-making capability of the designer in preliminary design. A number of elemental concepts toward this hypothesis have been formulated during the evolution of this work: • Imprecision is a hallmark of preliminary engineering design. To carry out decisions based on the information available to the designer and on basic engineering principles, the imprecise descriptions of possible solution technologies must be formalized and quantified in some way. The application of the fuzzy calculus along with a fundamental interpretation provides a new and straight-forward means by which imprecision can be represented and manipulated. • Besides imprecision, other uncertainties, categorized as stochastic and possibilistic, are prevalent in design, even in the early stages of the design process. Providing a method by which these uncertainties can be represented in the context of the imprecision is an important and necessary step when considering the evaluation of a design's performance. Extended Hybrid Numbers have been introduced in this work in order to couple the stochastic and possibilistic components of uncertainty with imprecision such that no information is lost in the process. • Because of the size, coupling, and complexity of the functional requirement space in any realistic design, it is difficult to make decisions with regard to the performance of a design, even with an Extended Hybrid Number representation. Defining and utilizing metrics (or figures of merit) in the evaluation of how well a design meets the functional requirements reduces the complexity of this process. Such metrics also have merit when we begin to think of languages of design and adding the necessary pragmatics of will a generated or proposed design satisfy the performance requirements with respect to the ever-present and unavoidable uncertainties?. These concepts form the central focus of this work. The mathematical methods presented here were developed to support and formalize these ideas.

The liquefaction phenomenon in soil has been studied in great detail during the past 20 years. The need to understand this phenomenon has been emphasized by the extent of the damages resulting from soil liquefaction during earthquakes. Although an overall explanation exists for this phenomenon through the concept of effective stress, the basic mechanism of loss of strength of the soil skeleton has not been thoroughly examined and remains unclear.The present study proposes a numerical model for simulations of the behavior of saturated granular media. The model was developed with two main objectives:1. To represent the mechanical response of an assemblage of discrete particles having the shape of discs.2. To model and represent the interaction of interstitial pore fluid present with the idealized granular media.The representation of the solid skeleton is based on Cundall and Strack's distinct element model, in which discrete particles are modelled as discs in two dimensions, each obeying Newton's laws. Interparticle contacts consisting of springs and frictional element dashpots are included. Assuming a Newtonian incompressible fluid with constant viscosity and density, and quasi-steady flow, the fluid phase is described by Stokes' equations. The solution to Stokes' equations is obtained through the boundary integral element formulation. Several validation test cases are presented along with four simple shear tests on dry and saturated granular assemblages. For these last four tests, the numerical results indicate that the model is able to represent qualitatively the behavior of real soil, while at the same time clarifying the processes occurring at the microscale that influence soil response.

The nonlinear seismic response of concrete gravity dams is investigated experimentally through the use of small-scale models. Of primary interest is crack formation, crack opening and closing, and sliding along crack planes. Also of concern is the stability of the structure after cracking. Three small-scale models (length scale = 115) of a single monolith of Pine Flat Dam are tested to determine the extent of such behavior and its effect on structural stability. The models are constructed of one polymer-based and two plaster-based materials developed for these experiments. The plaster-based materials fulfill the strength, stiffness, and density requirements established by the laws of similitude, while the polymer-based material fulfills only the stiffness and density requirements and is used only in the lower part of the dam where cracking is not expected. The excitation is a modified version of the N00E component of the 1940 Imperial Valley earthquake, applied to each model's base in the stream direction through a vibration table with high-frequency capability. Tests are performed with and without water in the reservoir. The response of each earthquake test is presented in the form of acceleration and displacement time histories, Fourier spectra, and frames taken from high-speed films of the model's response. The -results of the experiments indicate that the neck region of a concrete gravity dam is most susceptible to cracking, although crack profiles can differ as a result of variations in excitation, material properties, and construction techniques. These results also indicate alternate design techniques which could improve the seismic stability of a cracked gravity dam.

The dynamic mechanism of slope failure is studied both experimentally and analytically to establish the spatial and temporal process of failure initiation and propagation during collapse of a natural or man-made slope.Model slopes, constructed of a brittle cemented sand material, are tested to collapse in a geotechnical centrifuge and the dynamics of failure recorded by motion picture film and mechanical detectors within the slope specimen. Shear failure is observed to initiate at the toe and propagate rapidly to the crest in the presence of crest tension cracking.A finite difference approach is taken to numerically solve the plane strain slope stability problem under gravity, based on unstable material behavior. Using a Lagrangian differencing scheme in space and explicit integration in time with dynamic relaxation, the numerical method finds the equilibrium state of the slope as the large-time limit of a dynamic problem with artificial parameters. The solution predicts localized shear failure zones which initiate at the slope toe and propagate to the slope crest in the manner and geometry observed in the centrifuge tests. In so doing, the finite difference algorithm also demonstrates an apparent ability to predict shear failure mechanisms in solid continua in general.

A nonlinear finite element procedure for arch dams is described in which the gradual opening and closing of vertical contraction joints and predetermined horizontal cracking planes are considered. A special joint element approximately represents the deformations due to plane sections not remaining plane at each open joint and allows a single shell element discretization in the thickness direction to be used for the dam. Compressive and sliding nonlinearities are not included. Finite element treatments are also used for the water, assumed incompressible, and for the foundation rock, assumed massless, with all degrees of freedom (dof) off the dam condensed out. For efficiency in the computations, the condensed water and foundation matrices are localized in a way which maintains good accuracy. The response of Pacoima Dam to the 1971 San Fernando ground motion recorded on a ridge over one abutment and scaled by two-thirds is computed first for water at the intermediate level that existed during the 1971 earthquake and then for full reservoir. In the first analysis, the dam exhibits pronounced opening and separation of the contraction joints, allowing violation of the no-slip assumption. The presence of a full reservoir greatly increases the dam response, enough to bring some of the assumptions of the analysis into question. Reducing the ground motion scale to 0.44 with full reservoir drops the response back to a reasonable level, but the contraction joint separations remain.

Theoretical investigations of the dynamic behavior of some important fluid-structure systems are conducted to seek a better understanding of: 1) the hydrodynamic pressures generated in the fluid as a result of both the rigid body and the vibrational motions of the structure, and 2) the effects of the fluid on the dynamic properties of the structure as well as on its response to earthquake ground motions.Explicit formulas are presented for the hydrodynamic pressures generated in fluid domains having boundaries which can be approximated by simple geometries. Such domains may be reservoirs behind dams, or around intake towers, water around bridge piers or liquids stored in circular cylindrical tanks. The formulas are used to calculate the hydrodynamic pressures analytically and the results are exhibited in a form showing the pressure dependence on the various parameters of the problem.The fluid-structure interaction problems of long straight walls, having uniform rectangular sections, and long straight gravity dams, having uniform triangular sections, are investigated. The natural frequencies of vibration and the associated mode shapes are found in the former case, through a fully analytical approach for both the structure and the fluid domains, and in the latter, by discretizing the dam into finite elements and treating the reservoir as a continuum by boundary solution techniques. A method is presented for computing the earthquake response of both structures, based on superposition of their free vibrational modes.The problems of limited length dam or wall-reservoir systems are investigated. The natural frequencies of the structure and the corresponding mode shapes are found by the Rayleigh-Ritz method. This method is also used to obtain the frequency domain response of the structure to all three components of the ground motion. The validity of the two dimensional approximation, often made in the analysis of gravity dams, and the effect of the length to height ratio on the dynamic properties and response of the structure are studied.Time domain responses to arbitrary earthquake ground notions are evaluated by superposing the frequency domain responses, to individual Fourier components of the excitation, through the Fourier Integral. For efficiency of computation, a fast Fourier analysis is used for both the forward transform of the ground excitation and the inverse transform of the Fourier Integral.