Andrew Shaw

Extension of the Touratier Kinematic Model to Large Strains, Displacements, and Rotations

A concept for the modeling of a laminated and curvilinear shell that is deformed in a geometrically nonlinear elastic manner is reported in this technical note. The shell is assumed to be sufficiently thin and all the laminate materials sufficiently stiff to facilitate a degenerated approximation. The model equations are derived to be valid for problems involving large strains and rotations and to take into account transverse shear deformations. This is accomplished by combining an unrestricted displacement form of the strain tensor with the Touratier kinematic model and then expressing the resulting equations in terms absolute nodal coordinates instead of displacement vector components. It is anticipated that the theory documented here can be used to develop a specialized degenerate finite-element type.

Stochastic micromechanical and macromechanical reliability analyses of composite plates

A reliability analysis of a composite plate or shel l will typically involve complex coupling between a reliability method and a finite element c ode. The work presented here is a contribution to the development of such a modeling tool. A mathematically idealized benchmark is derived to test the reliability method in isolation prior to coupling with a deterministic finite element method. It consists of a simply supported, rectangular plate subjected to either a uniform or line load and clos ed form solutions exist for the stress tensor components. Two case studies are carried out: a macromechanical analysis of an isotropic short fiber, composite plate; a micromechanical ana lysis of an orthotropic, unidirectional, fiber reinforced composite plate. The former is use d to examine techniques for addressing correlated variables and the later to assess the re lative advantages and disadvantages of a micromechanics modeling approach.