A numerical procedure for analysis of general laminated plates under transverse load is developed utilizing the Mindlin plate theory, the finite volume discretization, and a segregated solution algorithm. The force and moment balance equations with the laminate constitutive relations are written in the form of a generic transport equation. In order to obtain discrete counterparts of the governing equations, the plate is subdivided into N control volumes by a Cartesian numerical mesh. As a result, five sets of N linear equations with N unknowns are obtained and solved using the conjugate gradient method with preconditioning.

ABSTRACT Key Words: Adhesively Bonded Carbon/Titanium JointsUnder In-plane and Bending Loads Mahmood M. Shokrieh 1* , Larry B. Lessard 2 , and Adnan Golubovic 2 (1) Department of Mechanical Engineering, Iran University of Science andTechnology, Tehran, Iran(2) Department of Mechanical Engineering, McGill University, Montreal, Canada Received 5 February 2006; accepted 27 May 2007 T he goal of this research is to optimize the design of single-lap joints made byjoining composite material to metals. The single-lap joint under both out-of-planeload and tensile load was examined. It is observed that designing a joint for onekind of load is not always satisfactory because for other load cases, different stresseswould govern the design. Local stress peaks were investigated in order to find waysto decrease these peaks. An approach for optimizing the joint was chosen so thestress peaks at each end could be minimized (peel, axial and shear stress). By taper-ing the titanium adherend inside and outside, the stress distribution in the adhesivecan be significantly changed at the tapered end and all three important stresses thatgoverned the design (peel, axial and shear stress) are decreased for a joint under ten-sion and out-of-plane load. For dissimilar adherends, the numerically largest stressesalways occur in the adhesive at the edge of the overlap adjacent to the adherend withthe lower value of flexural stiffness and the relative difference in these peaks is a func-tion of the relative flexural stiffness of two adherends. Using an outer bead of adhe-sive decreases the stress peak at composite edge. Thus, two methods are used toreduce adhesive stresses: tapering and addition of adhesive beads. Having complet-ed a finite element stress analysis, the results are used to predict the strength of agiven joint. A strain energy based on failure criteria was evaluated, which addressedthe problem of stress singularities in the finite element method. Three point bendingtests were performed using different bonding configurations to verify the strength ofthe adhesive joint and to evaluate the failure criterion. Optimization of the parametersof the joint geometry was achieved from the results of this study.

The evolution of the crystallization front from a planar to a dendritic one as a function of the GL/(Rc0) parameter was investigated during the crystallization of Al-Cu alloys by the vertical Bridgman method. Six series of alloys with different initial composi- tions of Cu were solidified at different growth rates. A mathematical model for the heat transfer during vertical Bridgmen crystal growth was developed. The model was solved using the finite element method. The temperature gradient in the melt at the beginning of crystal growth was calculated using the obtained model. Discrete stages of the crystalliza- tion front were identified in the experiments, as the ratio GL/(Rc0) decreased.