We investigate the problem of inferring elastic moduli of nonlinearly elastic membranes from interior measurements of deformation and pressure. We begin by formulating a model of membrane deformation under a vertical force where the geometry of the membrane is star-like. The model makes no specification of the constitutive law by which stresses are calculated from applied strains. Under appropriate choice of the constitutive law and simplification of the geometry, we show that membranes of regular structure may be homogenized to an axisymmetric case. We then investigate numerical methods for the resolution of the axisymmetric model in terms of radial and vertical displacement. Examples are given for various boundary conditions and choices for elastic moduli. We present a method by which the moduli may be accurately recovered by algebraic calculation from knowledge of the displacements on the boundary and interior of the membrane together with measurement of the radial stress at one of the boundaries.

In practice, two forms of the acoustic wave equation, the velocity-stress and pressure forms, are used to simulate seismic experiments. These equations in their discrete forms lead to two families of finite difference schemes, the staggered-grid and centered difference schemes. These two difference schemes are widely used to numerically generate seismograms. Although these two difference schemes are widely used, there has been no distinction whether one is better than the other. The goal of this research is to formulate a heuristic based on computational cost and storage to determine which scheme is better than the other.

The large base displacement demands imposed by near field earthquakes on base isolated buildings and the development and implementation of novel semiactive control devices and new algorithms to overcome this problem, is a key challenge in the design of smart isolation systems, which is the main goal of this study. In this dissertation a comprehensive class of smart base isolated buildings, new control algorithms based on H 2/LQG, Hinfinity and time-frequency methods are developed. The frequency content of the earthquakes is incorporated into the H2/LQG and H infinity controllers using newly developed weighting filters. The time-frequency content of the earthquakes is also estimated by new control algorithm developed based on time-frequency methods, for variable stiffness isolation systems. Novel semiactive variable friction, variable damping and variable stiffness control devices are developed and their behavior studied analytically and experimentally. The new control algorithms and semiactive devices developed in this study are inherently smooth and do not cause sharp increases in floor accelerations or interstory drifts, while achieving reductions in base displacements. The newly developed semiactive devices and control algorithms are implemented in linear and nonlinear multi degree of freedom two and three dimensional smart base isolated buildings, subjected to a suite of near field earthquakes, and shown to be effective in reducing the response. A new smart base isolated benchmark building is developed to demonstrate the feasibility of implementation of the newly developed semiactive devices and controllers in full scale three dimensional structures subjected to strong near field earthquakes.

The effects of both stiffness and damping nonlinearities on force-limited, random vibration test specifications are investigated. The response of the source-load vibratory system to a random, Gaussian excitation is analyzed using the modal- and residual-mass two degree-of-freedom system. The technique of statistical linearization is used in conjunction with the frequency shift method to derive force-limiting specifications for a nonlinear load mass modeled as a Duffing, Rayleigh damped, and linear plus quadratically damped oscillator, respectively. The normalized force-limiting specification for each nonlinear system is determined for a range of nonlinear stiffness and damping coefficients and compared with its linear counterpart over the same range of effective mass parameters. In general, deviations in the force-limiting spectrum arising from nonlinear stiffness effects will be apparent only at low frequencies on systems that are lightly damped, have large nonlinear stiffness parameters, and that experience moderately high input excitations. Deviations in the force-limiting spectrum arising from nonlinear damping effects will be apparent at lower frequencies on systems that are lightly damped, but having smaller nonlinear damping parameters and input excitations than their nonlinear stiffness counterparts. Case studies are presented to illustrate the methodology for deriving both linear and nonlinear force-limiting specifications for use in the test laboratory.

A new algorithm is presented for the solution of structural optimization problems in which the stress constraints are nonsmooth. The allowable stresses of structural members may be governed by one of three types of behavior: yielding, inelastic buckling, or elastic buckling. Consequently, the strength of members is defined by a piecewise function that depends on the cross-section and other design parameters. Some of these allowable stress functions are discontinuous, while some are continuous but nonsmooth. The allowable stress functions are sometimes defined by nonsmooth envelope functions, wherein the strength is determined by the controlling failure mechanism. Absolute values of stresses are compared to positive allowable stresses for simplicity, and the absolute value function is nonsmooth at zero. Optimization of structural members with such nonsmooth constraint functions is limited, because derivative-based algorithms assume that the objective and constraint functions are smooth. Typical approaches in current practice are to oversimplify the constraints, use slower, derivative free methods, apply ad-hoc solutions, or ignore the problem altogether. In the approach taken here, the causes of the nonsmooth constraints in a typical design code are systematically identified and replaced with nearly equivalent alternatives so that the problem can be solved using readily available and powerful derivative-based optimization methods. Theoretical models, finite element models, and experimental data are used as benchmarks to predict the behavior. These are used to fit an appropriate set of curves for use in design. The new optimization algorithm presented uses a combination of a continuation method, then a judicious choice of added "secondary constraints" to transform the original nonsmooth problem to an equivalent smooth one. First, a solution is obtained for a smooth approximation of the original problem. It is used as a starting value to successively solve more and more nonsmooth, but closer approximations until a reasonably close solution to the original problem is determined. This solution is used to constrain the variables governing each of the piecewise defined functions. The original problem is thus transformed to a smooth problem with the added secondary constraints, and is solved using a standard derivative-based optimization method.

Uncertainty is an inherent part of many physical systems. This is often ignored to simplify mathematical models thereby leading to a deterministic treatment of the system. Incorporation of the uncertainty into the model, particularly in the presence of strong correlation across scales is a difficult task for the conventional modeling techniques. This work studies a biorthogonal wavelet framework for the representation of random fields. It is shown that such a representation scheme leads to significantly decorrelated wavelet coefficients. The amount of decorrelation obtained is an improvement over that achieved with orthonormal wavelet basis functions. It is shown that a biorthogonal dual wavelets with sufficient number of vanishing moments and corresponding to a low primal order perform better than Daubechies wavelets at this task. These observations are used in pursuing the development of Wavelet based Galerkin and Petrov-Galerkin schemes for one-dimensional and two-dimensional stochastic mechanics problems.

The Method of Integral Relations is used to predict stress distributions in a granular half-space due to a normally applied two-dimensional surface load. The resulting stress profiles are compared with Boussinesq's solution for a two-dimensional elastic medium and with the results of experiments which were carried out in sand using an axi-symmetric geometry. The theory predicts that the behaviour of the solutions depends primarily on the shape of the surface loading profiles. A parabolic loading profile equivalent to that observed experimentally yields vertical normal stress profiles which have good qualitative agreement with the experimental results and with the Diffusion Equation solution of Harr et al. As the surface pressure distribution approaches a uniform one, the theory predicts the existence of double-peaked vertical normal stress profiles similar to those observed in experiments in rock masses under equivalent loading conditions.

Laminates composed of alternating layers of metal and fiber reinforced polymers (FRP's) exhibit a number of properties, which are preferable to either metals or FRP's alone, making them attractive materials for a number of industries, particularly aerospace. A number of questions persist, however, before these new composites can be widely accepted and utilized; one of which is their response to impact, which may occur over a wide range of velocities. Numerical methods, especially the FEA method, have been widely used to simulate the impact response because they can reduce the cost and save time comparing with the experiment. In this work, a continuum damage based model (CDM) is developed and implemented into FEA commercial software ABAQUS. Using a rate-dependent plasticity model for the constitutive behavior of Aluminum and the CDM for the behavior of fiberglass laminates, the dynamic penetration is simulated using ABAQUS. Force vs. displacement results compare well with those obtained from the experiments. In addition, the computed damage region is in close agreement with that seen in sectioned specimens of the tested material. Simulations are also performed for ballistic experiments conducted on 150mm x 150mm clamped panels of the same laminates. Ballistic experiments involve both the local penetration response as well as the global deformation behavior, particularly at velocities near the ballistic limit, where significant flexural deformation takes place. Results from the simulation agree well with the ballistic experiment results. Given the validity of the modeling approach, the high velocity impact response of the other metal/fiber systems can be examined minimizing the need for trial and error fabrication.

It will be readily agreed upon by almost any engineer associated with the structural steel fabricating industry, that one of the most convenient and economical types of structural components in use today is the plate girder. Almost every structure built, which has long spans or has heavy loads to be carried, whether it be a building or a bridge, will have one or several of these most practical members. Until recently, specifications gave sufficiently wide scope to the designer to make these girders applicable in almost any case.

"Soil Mechanics" is the name given to the scientific approach to the understanding of soil action. It may be defined as the science dealing with all phenomena which affect the action of soil in a capacity in any way associated with engineering. It is a pioneer science which has grown very rapidly in the last two decades. Although experimental soil mechanics has been going on ever since man first built structures or tunnelled in the ground, it is the scientific approach to the problem which is only recent.