Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Radiocarbon and stable isotopes in the shell organic matrix: a new approach for the use of mollusk shells in the study of human evolution

Mollusk shells are often found in archeological sites, given their great preservation potential and high value as a multipurpose resource. They are often the only available material to use for radiocarbon dating, due to a lack of well-preserved bones in many archeological sites, especially for the key period of the Middle to Upper Paleolithic transition. However, radiocarbon dating on mollusk shells is often regarded as less reliable compared to bones, wood, or charcoals due to the various factors influencing their radiocarbon content (e.g., Isotope fractionation, marine reservoir effect etc.). For the development of more accurate chronologies using shells, it is fundamental to continue improving the precision of the techniques applied, as has been done for other materials (wood and bones). Thus, improving the chemical pretreatment on mollusk shells might allow researchers to obtain more reliable radiocarbon determinations allowing for the construction of new radiocarbon chronologies in archeological sites where so far it has not been possible. Furthermore, mollusk shells can provide information on the climatic and environmental variables present during their growth. Using shells for paleoclimatic reconstruction adds more evidence helpful for the interpretation of scenarios of human migration, adaptation, and behavior. Standard methods for both radiocarbon and stable isotope studies use the carbonate fraction of the shell. However, being biogenic structures, mollusk shells also consist of a minor organic fraction. The shell organic matrix has an important role in the formation of the calcium carbonate structure and is still not fully understood. This thesis explores the potential of using the shell organic matrix for radiocarbon dating and paleoenvironmental studies. The results of the work performed for this thesis represent a starting point for future research to build on, and further develop the approach and methodology proposed here.