The objective of this study is to investigate the accuracy and computational efficiency of two commonly used formulations for performing the geometrically nonlinear thermal analysis of plane framed structures. The formulations considered are the followings: the Beam-Column formulation and the updated Lagrangian version of the finite element formulation that has been adopted in the commercially well-known software SAP2000. These two formulations are used to generate extensive numerical data for three plane frame configurations, which are then compared to evaluate the performance of the two formulations. The Beam-Column method is based on an Eulerian formulation that incorporates the effects of large joint displacements. In addition, local member force-deformation relationships are based on the Beam-Column approach that includes the axial strain, flexural bowing, and thermal strain. The other formulation, the SAP2000, is based on the updated Lagrangian finite element formulation. The results for nonlinear thermal responses were generated for three plane structures by these formulations. Then, the data were compared for accuracy of deflection responses and for computational efficiency of the Newton-Raphson iteration cycles required for the thermal analysis. The results of this study indicate that the Beam-Column method is quite efficient and powerful for the thermal analysis of plane frames since the method is based on the exact solution of the differential equations. In comparison to the SAP2000 software, the Beam-Column method requires fewer iteration cycles and fewer elements per natural member, even when the structures are subjected to significant curvature effects and to restrained support conditions. The accuracy of the SAP2000 generally depends on the number of steps and/or the number of elements per natural member (especially four or more elements per member may be needed when structure member encounters a significant curvature effect). Succinctly, the Beam-Column formulation requires considerably fewer elements per member, fewer iteration cycles, and less time for thermal analysis than the SAP2000 when the structures are subjected to significant bending effects.

The standard genetic code (SGC) is the cipher used by nearly all organisms to transcribe information stored in DNA and translate it into its amino acid counterparts. Since the early 1960s, researchers have observed that the SGC is structured so that similar codons encode amino acids with similar physiochemical properties. This structure has been hypothesized to buffer the SGC against transcription or translational error because single nucleotide mutations usually either are silent or impart minimal effect on the containing protein. We herein briefly review different theories for the origin of that structure. We also briefly review different computational experiments designed to quantify buffering capacity for the SGC. We report on computational Monte Carlo simulations that we performed using a computer program that we developed, AGCT. In the simulations, the SGC was ranked against other, hypothetical genetic codes (HGC) for its ability to minimize physiochemical distances between amino acids encoded by codons separated by single nucleotide mutations. We analyzed unappreciated structural aspects and neglected properties in the SGC. We found that error measure type affected SGC ranking. We also found that altering stop codon positions had no effect on SGC ranking, but including stop codons in error calculations improved SGC ranking. We analyzed 49 properties individually and identified conserved properties. Among these, we found that long-range non-bonded energy is more conserved than is polar requirement, which previously was considered to be the most conserved property in the SGC. We also analyzed properties in combinations. We hypothesized that the SGC is organized as a compromise among multiple properties. Finally, we used AGCT to test whether different theories on the origin of the SGC could explain more convincingly the buffering capacity in the SGC. We found that, without accounting for transition/transversion biases, the SGC ranking was modest enough under constraints imposed by the coevolution and four column theories that it could be explained due to constraints associated with either theory (or both theories); however, when transition/transversion biases were included, only the four column theory returned a SGC ranking modest enough that it could be explained due to constraints associated with that theory. / Thesis / Master of Science (MSc) / The standard genetic code (SGC) is the cipher used almost universally to transcribe information stored in DNA and translate it to amino acid counterparts. Since the mid 1960s, researchers have recognized that the SGC is organized so that similar three-nucleotide RNA codons encode amino acids with similar properties; researchers consequently hypothesized that the SGC is structured to minimize effects from transcription or translation errors. This hypothesis has been tested using computer simulation. I briefly review results from those studies, complement them by analyzing unappreciated structural aspects and neglected properties, and test two theories on the origin of the SGC.