This study focuses on implementing probabilistic nature of material properties (Kevlar® 49) to the existing deterministic finite element analysis (FEA) of fabric based engine containment system through Monte Carlo simulations (MCS) and implementation of probabilistic analysis in engineering designs through Reliability Based Design Optimization (RBDO). First, the emphasis is on experimental data analysis focusing on probabilistic distribution models which characterize the randomness associated with the experimental data. The material properties of Kevlar® 49 are modeled using experimental data analysis and implemented along with an existing spiral modeling scheme (SMS) and user defined constitutive model (UMAT) for fabric based engine containment simulations in LS-DYNA. MCS of the model are performed to observe the failure pattern and exit velocities of the models. Then the solutions are compared with NASA experimental tests and deterministic results. MCS with probabilistic material data give a good prospective on results rather than a single deterministic simulation results. The next part of research is to implement the probabilistic material properties in engineering designs. The main aim of structural design is to obtain optimal solutions. In any case, in a deterministic optimization problem even though the structures are cost effective, it becomes highly unreliable if the uncertainty that may be associated with the system (material properties, loading etc.) is not represented or considered in the solution process. Reliable and optimal solution can be obtained by performing reliability optimization along with the deterministic optimization, which is RBDO. In RBDO problem formulation, in addition to structural performance constraints, reliability constraints are also considered. This part of research starts with introduction to reliability analysis such as first order reliability analysis, second order reliability analysis followed by simulation technique that are performed to obtain probability of failure and reliability of structures. Next, decoupled RBDO procedure is proposed with a new reliability analysis formulation with sensitivity analysis, which is performed to remove the highly reliable constraints in the RBDO, thereby reducing the computational time and function evaluations. Followed by implementation of the reliability analysis concepts and RBDO in finite element 2D truss problems and a planar beam problem are presented and discussed.

Ultra-concealable multi-threat body armor used by law-enforcement is a multi-purpose armor that protects against attacks from knife, spikes, and small caliber rounds. The design of this type of armor involves fiber-resin composite materials that are flexible, light, are not unduly affected by environmental conditions, and perform as required. The National Institute of Justice (NIJ) characterizes this type of armor as low-level protection armor. NIJ also specifies the geometry of the knife and spike as well as the strike energy levels required for this level of protection. The biggest challenges are to design a thin, lightweight and ultra-concealable armor that can be worn under street clothes. In this study, several fundamental tasks involved in the design of such armor are addressed. First, the roles of design of experiments and regression analysis in experimental testing and finite element analysis are presented. Second, off-the-shelf materials available from international material manufacturers are characterized via laboratory experiments. Third, the calibration process required for a constitutive model is explained through the use of experimental data and computer software. Various material models in LS-DYNA for use in the finite element model are discussed. Numerical results are generated via finite element simulations and are compared against experimental data thus establishing the foundation for optimizing the design.

Concrete design has recently seen a shift in focus from prescriptive specifications to performance based specifications with increasing demands for sustainable products. Fiber reinforced composites (FRC) provides unique properties to a material that is very weak under tensile loads. The addition of fibers to a concrete mix provides additional ductility and reduces the propagation of cracks in the concrete structure. It is the fibers that bridge the crack and dissipate the incurred strain energy in the form of a fiber-pullout mechanism. The addition of fibers plays an important role in tunnel lining systems and in reducing shrinkage cracking in high performance concretes. The interest in most design situations is the load where cracking first takes place. Typically the post crack response will exhibit either a load bearing increase as deflection continues, or a load bearing decrease as deflection continues. These behaviors are referred to as strain hardening and strain softening respectively. A strain softening or hardening response is used to model the behavior of different types of fiber reinforced concrete and simulate the experimental flexural response. Closed form equations for moment-curvature response of rectangular beams under four and three point loading in conjunction with crack localization rules are utilized. As a result, the stress distribution that considers a shifting neutral axis can be simulated which provides a more accurate representation of the residual strength of the fiber cement composites. The use of typical residual strength parameters by standards organizations ASTM, JCI and RILEM are examined to be incorrect in their linear elastic assumption of FRC behavior. Finite element models were implemented to study the effects and simulate the load defection response of fiber reinforced shotcrete round discrete panels (RDP's) tested in accordance with ASTM C-1550. The back-calculated material properties from the flexural tests were used as a basis for the FEM material models. Further development of FEM beams were also used to provide additional comparisons in residual strengths of early age samples. A correlation between the RDP and flexural beam test was generated based a relationship between normalized toughness with respect to the newly generated crack surfaces. A set of design equations are proposed using a residual strength correction factor generated by the model and produce the design moment based on specified concrete slab geometry.