Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. Thus the understanding of the effect of uncertainties in laminated structures on their static and dynamic responses is highly important for a reliable design of such structures. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. Thus a shear-deformable laminated beam element, including warping effects, is derived to study the deterministic and probabilistic response of laminated beams. This twenty-one degrees of freedom element can be used for solving both static and dynamic problems. In the first-order shear deformable model used here we have employed a more accurate method to obtain the transverse shear correction factor. The dynamic version of the principle of virtual work for laminated composites is expressed in its nondimensional form and the element tangent stiffness and mass matrices are obtained using analytical integration. The stability is studied by giving the structure a small disturbance about an equilibrium configuration, and observing if the resulting response remains small. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity-Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis using the dynamic criterion. / Ph. D.

Over recent decades, the public tendency toward using the structural composite lumber (SCL), a common composite of wood made of wood strands or veneers glued and compressed together, as structural members (especially the main load bearing members such as beams and columns) has risen considerably. In contrast to the fast-paced market growth of these products, development is slow. The experimental development is gradual and time-consuming and the computational development is even slower. The objective of this project is to introduce appropriate numerical models for limit state analysis of a certain type of SCL material called PSL. Parallel strand lumber (PSL), has mesostructures characterized by the presence of voids that renders the mesostructure highly heterogeneous. In addition to material phase aberrations such as grain angle variations and defects, void heterogeneities play an important role in determining the failure modes and strength of PSL. In this study, virtual void structures were defined to form part of the input to finite element analysis of PSL for the purpose of investigating the sensitivity of strength to the void structure. Assuming the wood phase to be homogeneous and orthotropic, the following 2D and 3D characteristics of voids were investigated: volume fraction, volume, alignment and moments of inertia of voids, as well as second moment properties, lineal path function and chord length functions of the two phase mesostructure. In addition, a method was developed to generate virtual voids in order to simulate PSL and investigate the possible effects of the void distribution on material strength. An experimental program along with a statistical survey was conducted to quantify the mentioned characteristics of the voids in two 133 mm * 133 mm * 610 mm 2.0 E Eastern Species PSL billets. As expected, most of the voids lie on the longitudinal direction of the specimen and have approximately an ellipsoidal shape. Based on this shape data, the characteristics of the ellipsoids which best t the voids were calculated. Using the statistical data of the fitted ellipsoids, a random field of virtual ellipsoid shaped voids to simulate the mesostructure of PSL was generated. In this study, the simulation of PSL material is based on two simplifying assumptions: 1) The wood phase is continuum, homogeneous and orthotropic. While in reality, the wood phase consists of glued wood strands that are heterogeneous due to their mechanical variability and only roughly orthotropic on a macro scale as a result of the varying fiber angle; 2) Voids are the mere source of uncertainty. The linear elastic analysis of carefully defined (in mesostructural aspect) PSL models can be the first step of mechanical study of the material. The effective modulus of elasticity of material in presence of voids and the distribution of conventional, principal and effective stresses considering the effect of volume fraction and shape of the voids are the target of this preliminary study. Linear elastic uniaxial analyses showed good mechanical consistency between the models including actual void shapes and the models including ellipsoidal void representations. Also, they showed that the stress mutliaxiality at the tip of the voids is negligible. The study of mechanics of PSL is incomplete unless the question of material anisotropy is taken into consideration. PSL is brittle in tension and ductile in compression. The material heterogeneity increases the complexity of the problem by affecting the stress distribution in the member. A detailed nonlinear approach has been proposed in order to investigate the mechanical behavior of PSL structural members under different uniaxial loading scenarios. This approach introduces proper constitutive models for the wood phase along with good void generation techniques. In other words, this approach suggests what models should be used for the continuum-assumed wood phase to simulate its brittle behavior in tension and ductile behavior in compression; and moreover, tests the applicability and accuracy of ellipsoidal void representation. The models are calibrated using the results of experiments on PSL material. Because of the brittle behavior, all wood products show significant mechanical dependency to the member's size under tensile loading. Once good constitutive model and mesostructural simulation is found for tensile loading, it is easy to make and analyze PSL models with different sizes and investigate the effect of size on mechanical behavior. The simulation results have been compared to the available results of a previously done experimental study.