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Fertilizer Savings through Soil Testing
No full textDeep Soil Testing Offers the Potential to Reduce Fertilizer Cost
The Digital Religion Yearbook 2023
Get PDFAnnual Research YearbookThis publication was envisioned by the Network for New Media, Religion, and Digital Studies to highlight important research and scholarship being produced in the increasingly diverse, interdisciplinary, and international field of Digital Religion Studies. The 2023 Yearbook highlights top research studies, scholars, and students doing work in this area.Network for New Media, Religion, and Digital Studie
Analysis of Linear and Nonlinear Timoshenko-Ehrenfest Beams and Linear First Order Shear Deformation Theory Plates With the Theory of Functional Connections
Get PDFBeams and plates are critical structural components in almost any structure or mechanical device. For this reason, it is crucial for engineers to analyze these structural members with both high accuracy and low computational cost. For most complex structural problems in both research and industry, these structural members are analyzed using numerical techniques. The most popular numerical technique is the Finite Element Method (FEM). However, the recent development of the functional interpolation technique known as the Theory of Functional Connections (TFC) has shown promising computational results when applied to solve both linear and nonlinear differential equations.
This thesis demonstrates the computational advantages of using TFC to analyze beams and plates. Several linear and nonlinear Timoshenko-Ehrenfest beam problems are solved using both TFC and FEM. Additionally, the TFC solution methodology was expanded to solve the eigenvalue/eigenvector problems that naturally arise in linear buckling and linear free vibration analyses. In addition, the TFC framework was expanded from 1D static beam bending to 2D static plate bending analysis.
The research in this thesis suggests TFC provides an exponentially more accurate solution for most beam bending problems at a lower computational cost when compared to the FEM. TFC can result in an L2 norm on the order of machine-error level precision when the higher-order derivatives of the true solution are continuous and smooth. TFC also has the added benefit of calculating continuous and smooth analytical derivatives of the beam/plate displacement variables, which yields stress and strain fields that are continuous and smooth everywhere within the domain of the structural member. This is contrary to FEM whose stress field is piece-wise continuous and most accurate at the discrete integration points. In terms of linear buckling and linear free vibration analyses, the TFC methodology was validated because it produced results inline with FEM results. Likewise, the TFC results for 2D First-Order Shear Deformation Theory (FSDT) plate bending were validated with published FEM results
